text:
\section{Introduction}

In the big data era, a large quantity of multimedia data from Internet as well as social media spring up, where they are often collected without the label information~\cite{DBLP:journals/tkde/WangYL20,DBLP:conf/mm/Huang0P021,DBLP:conf/mm/ZhangLW0DZ21}. Clustering techniques have attracted more and more attention in the unsupervised data mining and machine learning community. Many classical clustering methods have been proposed to automatically explore the correlations between different data objects, such as $k$-means as well as its variants, spectral clustering, and subspace clustering. Despite impressive performance, they are merely suitable to single view scenario. In practical applications, data are often represented with diverse features from multiple sources or feature extractors. For instance, a webpage is represented by multiview features based on text, image and video. News can be reported by different languages. Multiple views or feature subsets comprehensively describe different aspects of the data, and it is generally infeasible to just consider single view rather than multiple views. Therefore, multiview clustering is developed to well integrate multiple views or subspace structures to improve the clustering performance.

Considerable efforts have been recently made in the development of multiview clustering to investigate the diverse and complementary information among multiple views~\cite{DBLP:conf/ijcai/NieLL17,DBLP:conf/mm/ZhangLW0DZ21,DBLP:conf/mm/ZhangWLZZLZZ21}, in which the existing literatures can be divided into three main categories, i.e., the co-training based models, graph based algorithms and subspace clustering based methods. The co-training based models aim at maximizing the mutual agreement between different views via alternately training~\cite{DBLP:conf/nips/KumarRD11,DBLP:conf/icml/KumarD11}. For instance, in~\cite{DBLP:conf/nips/KumarRD11}, Kumar et al. co-regularized the clustering hypotheses such that different representations could agree with each other. The work in~\cite{DBLP:conf/icml/KumarD11} proposed to seek for the clusters agreeing across multiple views. Ye at al. studied the underlying clustering by maximizing the sum of weighted affinities between different clusterings of multiple views~\cite{DBLP:conf/icpr/YeLYZ16}. The graph based algorithms attempt to combine multiple views for recovering the relationships between views~\cite{DBLP:conf/aaai/NieCL17,ZhangOne-step20}. One of the earliest literatures made bipartite graph construction to link features from different views~\cite{de2005spectral}. In~\cite{DBLP:conf/aaai/NieCL17}, Nie et al. proposed to simultaneously learn the clustering/semi-supervised classification as well as local structure. The work in~\cite{DBLP:journals/tkde/WangYL20} coupled the similarity-induced graph associated with multiple views, unified graph and indicator into a unified framework. Supposing that views are generated from the latent subspace, the subspace clustering based methods are developed to learn subspace representations based on the self-expressive property. In~\cite{luo2018consistent}, Luo et al. simultaneously explored consistency and specificity in multiple subspace representations. The work in~\cite{ZhangOne-step20} proposed a one-step kernel subspace clustering model, in which the shared affinity representation was learned from multiple views. Chen et al. jointly studied the low-rank representation tensor as well as affinity matrix while keeping the local structures~\cite{DBLP:journals/pr/ChenXZ20}. Nevertheless, most of existing works suffer from high computational cost (typically quadratic or even cubic complexity for inevitable $n\times n$ affinity graph construction), which seriously restricts their efficiency when dealing with large-scale multiview data.

\begin{figure*}[!t]
	\begin{center}
		\includegraphics[width=1.0\linewidth]{figures/AIMVCflows.pdf}
		\caption{Illustration of the proposed AIMC method. The adaptively-weighted latent integral space depicting the common cluster assignment is modeled via view generation models with input view observations carrying diverse adaptive confidences.}
		\label{fig:Flowchart}
	\end{center}
\end{figure*}

In view of this, some large-scale oriented multiview clustering algorithms have been proposed, which can be mainly divided into two categories, i.e., matrix factorization style algorithms~\cite{DBLP:conf/ijcai/CaiNH13a,DBLP:journals/pr/NieSL20,DBLP:journals/tip/YangZNWYW21,DBLP:conf/iccv/0003LYL0LS21} and anchor graph based methods~\cite{DBLP:conf/aaai/LiNHH15,DBLP:conf/aaai/KangZZSHX20}. The matrix factorization style algorithms are able to reduce computational burden without the construction of affinity graph. For instance, Wang et al. attempted to explore the cluster structure with a constrained factor matrix~\cite{DBLP:conf/ijcai/WangNHM11}. The work in~\cite{DBLP:conf/aaai/HanSNL17} treated the intermediate factor matrix as a diagonal matrix in 3-factor factorization, improving the efficiency of matrix multiplication in optimization. In~\cite{DBLP:conf/ijcai/CaiNH13a}, Cai et al. efficiently combined heterogeneous factor matrices of large-scale data. Nie et al. ~\cite{DBLP:journals/pr/NieSL20} proposed to conduct the clustering task simultaneously on row and column of the original data. In~\cite{DBLP:conf/iccv/0003LYL0LS21}, Liu et al. unified matrix factorization with partition learning without the non-negativity constraint. However, the efficiency of this kind of algorithms would significantly decrease when facing with large data feature dimension, owing to their direct factorization of the original data observation. The anchor graph based methods often deploy correlations between anchor representation and original data to construct the anchor graph. For instances, the work in~\cite{DBLP:conf/aaai/LiNHH15} achieved the fusion graph construction for multiple anchor graphs via a local manifold fusion strategy. Kang at al. developed an anchor graph-based subspace clustering framework~\cite{DBLP:conf/aaai/KangZZSHX20}, in which view-specific graph was explored with pre-defined anchor representations. The work in~\cite{DBLP:conf/mm/SunZWZTLZW21} attempted to explore anchor graph construction based on the underlying data distribution. Similarly, Wang et al. studied the shared anchor graph with the guidance of consensus anchor representation in multiview data~\cite{DBLP:journals/tip/WangLZZZGZ22}. Despite significant success, the view-insufficiency issue is neglected among them, with the assumption that each individual view is sufficient to recover the cluster partition. Besides, they fail to simultaneously discover the latent integral space from multiple insufficient views as well as the common cluster structure shared by multiview data.

To address the aforementioned problems, in this paper, a novel \underline{A}daptively-weighted \underline{I}ntegral Space for Fast \underline{M}ultiview \underline{C}lustering (AIMC) method is developed. Instead of performing direct factorization of the original data observation as the existing matrix factorization based literatures, a latent integral space revealing the cluster structure is focused by considering different adaptive contributions from multiple views in our framework, which is the enhanced formulation associated with the general fast multiview $k$-means and flexibly avoids the curse of dimensionality. To be specific, for each view, we design a view generation model to map the latent integral space into the corresponding view observation while adpatively considering their diverse contributions. Reversely, with input view observations, we can restore the latent integral space by mapping back from given view observations with the corresponding self-conducted confidence. Additionally, a centroid representation with orthogonality constraint and cluster assignment are directly constructed to approximate the latent integral space, which not only focuses on the space itself but also seamlessly associates it with the underlying data partition. For clarity, the flowchart of the proposed AIMC method is illustrated in \figurename~\ref{fig:Flowchart}. A four-step alternate minimizing strategy is designed with empirical convergence, in which each variable can be updated efficiently to receive the closed-form solution. Consequently, the reconstruction error and distortion error of data partition are merged in our model to further improve the effectiveness and efficiency of clustering.

The main contributions of our work are summarized as follows:
\begin{itemize}
	\item Considering the view-insufficiency issue, we study an adaptively weighted integral space for fast multiview clustering, which is coupled with the underlying cluster partition.
	\item We develop an alternate minimizing strategy to solve the optimization problem, by which the proposed method is proved to have linear time complexity	\textit{w.r.t.} the number of samples.
	\item Extensive experiments are conducted on multiple challenging datasets, including several big datasets, to demonstrate the superiority of the proposed method compared with the state-of-the-art methods.
\end{itemize}

The rest of this paper is organized as follows. In Section~\ref{sec:preliminaries}, the main notations and basic preliminaries of matrix factorization are provided. The proposed Adaptively-weighted Integral Space for Fast Multiview Clustering method is described in Section~\ref{sec:proposed method} in which the optimization algorithm and time computational analysis as well as space complexity analysis are provided. In Section~\ref{sec:experiments}, the experimental results are reported, where nine real-world datasets are used and nine state-of-the-art methods are compared. Finally, the paper is concluded in Section~\ref{sec:conclusion}.

\section{Preliminaries}
\label{sec:preliminaries}
\subsection{Notations}

Throughout this paper, matrices are represented as uppercase letters. The $i$-th row of matrix $A$ is denoted as $A_{i,:}$, with its $j$-th entry being $A_{ij}$. $\|A\|_F^2$ represents the square of Frobenius norm of matrix $A$, and $\|A_{i,:}\|_1$ denotes the $l_1$ norm of the row vector $A_{i,:}$. The trace of $A$ can be written as $Tr(A)$. We denote the $v$-th view observation of $A$ as $A^{(v)}$. In particular, $I_d$ stands for the $d$ dimensional identity matrix.

\subsection{Matrix Factorization}

Non-negative matrix factorization (NMF) and its variants are often employed in clustering owing to the success in feature extraction. In this part, we will make brief introduction of NMF and one-sided orthogonal NMF~\cite{Ding2006OrthogonalNM}. Given the data matrix $X\in\mathbb{R}^{d\times n}$ drawn from $k$ partitions, the regularization term about matrix factorization can be generally defined as
\begin{equation}
	\begin{aligned}
		\label{mf1}
		\mathop{\min}\mathcal{L}\left(X,WH\right) ,~~~\text{s.t.~~~}W\in\mathcal{C}_1,H\in\mathcal{C}_2,
	\end{aligned}
\end{equation}
where $\mathcal{L}\left(\cdot\right)$ stands for the loss function. $W$ and $H$ are the factor matrices constrained respectively by $\mathcal{C}_1$ and $\mathcal{C}_2$.

NMF aims to decompose a non-negative input matrix into two non-negative representation products, i.e., the base matrix and coefficient representation, whose decomposition can be formulated as
\begin{equation}
	\begin{aligned}
		\label{nmf1}
		\mathop{\min}\limits_{W,H}\|X_+-WH\|_F^2,~~~\text{s.t.~~~}W\geq0,H\geq0,
	\end{aligned}
\end{equation}
where $W\in\mathbb{R}^{d\times k}$ is denoted as the base matrix, and $H\in\mathbb{R}^{k\times n}$ represents the coefficient representation. It can be known that $H$ is a low-rank coefficient matrix, on which the final cluster partition can be acquired by performing classical clustering algorithm (e.g. $k$-means).

The concept of one-sided orthogonal NMF was first proposed by Ding et al, in which the orthogonality constraint was applied to a factor matrix~\cite{Ding2006OrthogonalNM}. The objective formulation can be written as
\begin{equation}
	\begin{aligned}
		\label{onmf1}
		\mathop{\min}\limits_{W,H}\|X_+-WH\|_F^2,~~~\text{s.t.~~~}WW^T=I_d,H\geq0,
	\end{aligned}
\end{equation}
where the base matrix $W$ becomes an orthogonal matrix. Meanwhile, the formulation above is inherently associated with $k$-means algorithm while keeping the orthogonality constraint.

\section{The Proposed Method}
\label{sec:proposed method}

In this section, we will first describe the proposed Adaptively-weighted Integral Space for Fast Multiview Clustering (AIMC) model, followed by the detailed optimization procedure. In the meantime, an analysis about the computational time and memory usage is conducted to demonstrate the time and space efficiency of AIMC.

\subsection{Formulation}

Since each distinct view representation only consists of partial information about multiple data samples, and the data collection may be noisy, in this paper, we develop a fast multiview clustering framework based on the adaptively-weighted integral space, which depicts the data structure in essence and reveals the common cluster partition shared by different views. As shown in~\cite{DBLP:journals/pami/XuTX15}, the view specific observation can be generated by mapping from one latent integral space via certain view generation model. Given a multiview dataset $\left\{X^{(v)}\in\mathbb{R}^{d_v\times n}\right\}_{v=1}^{m}$ with its $v$-th view dimensionality, sample size and view number being respectively $d_v$, $n$ and $m$, the corresponding objective function can be formulated as follow
\begin{equation}
	\begin{aligned}
		\label{obj1}
		&\mathop{\min}\limits_{G^{(v)},F,Y}\sum_{v=1}^{m}\|X^{(v)}-G^{(v)}FY\|_F^2,\\
		&\text{s.t.~~~}{G^{(v)}}^TG^{(v)}=I_d,F^TF=I_k,Y\in Ind,
	\end{aligned}
\end{equation}
where $G^{(v)}\in\mathbb{R}^{d_v\times d}$ represents the $v$-th view generation model. $F\in\mathbb{R}^{d\times k}$ denotes the centroid representation with its column being the cluster centroid of different partitions, and $Y\in\mathbb{R}^{k\times n}$ is the cluster assignment matrix with $Y_{ij}=1$ if the $j$-th instance is assigned to the $i$-th cluster and 0 otherwise. Accordingly, the centroid representation and cluster assignment matrix are constructed to approximate the latent integral space, directly ensuring the reliability of view generation model from raw data observation to the underlying data structure. The orthogonality constraint imposed on $G^{(v)}$ aims to avoid pushing the integral space arbitrarily, while the one about $F$ attempts to attain mutual independence between different cluster centroid representation.

Despite of this, the model in Eq.~\eqref{obj1} treats each view observation equally to discover the integral space, paying no attention to different contributions of multiple views and may resulting in the sub-optimal performance. Therefore, in this paper, an adaptively weighting strategy is designed~\cite{DBLP:conf/ijcai/NieLL17}, and the overall objective function can be rewritten as,
\begin{equation}
	\begin{aligned}
		\label{obj2}
		&\mathop{\min}\limits_{G^{(v)},F,Y}\sum_{v=1}^{m}\alpha_v\|X^{(v)}-G^{(v)}FY\|_F^2,\\
		&\text{s.t.~~~}{G^{(v)}}^TG^{(v)}=I_d,F^TF=I_k,Y\in Ind,
	\end{aligned}
\end{equation}
where $\alpha_v$ is defined as
\begin{equation}
	\begin{aligned}
		\label{alphaobj}
		\alpha_v\overset{\underset{\mathrm{def}}{}}{=}\frac{1}{2\|X^{(v)}-G^{(v)}FY\|_F}.
	\end{aligned}
\end{equation}

Note that according to Eq.~\eqref{alphaobj}, $\alpha_v$ is dependent on $G^{(v)}$, $F$ and $Y$. Particularly, if view $v$ is good, $\|X^{(v)}-G^{(v)}FY\|_F$ should be small, and thus the weight $\alpha_v$ of view $v$ would be large according to Eq.~\eqref{alphaobj}. Otherwise, small weights would be assigned to poor views, which demonstrates the significance of the self-weighted learning strategy. Further, it is easy to observe that Eq.~\eqref{obj2} is equivalent to the following formulation
\begin{equation}
	\begin{aligned}
		\label{extendobj}
		&\mathop{\min}\limits_{G^{(v)},F,Y}\sum_{v=1}^{m}\|X^{(v)}-G^{(v)}FY\|_F,\\
		&\text{s.t.~~~}{G^{(v)}}^TG^{(v)}=I_d,F^TF=I_k,Y\in Ind.
	\end{aligned}
\end{equation}

To some extent, the formulation is a multiview least-absolute residual model, which can induce robustness via mitigating the impact of outliers with the present first power residual and achieving dimension reduction by flexible and lower dimension of view generation model during the learning procedure.

\subsection{Optimization}

Due to the non-smoothness and unsupervised learning, it is difficult to handle the problem in Eq.~\eqref{extendobj}. Hence, the following observation is put forward to make it tractable.
\begin{mythm}
	\label{def:objthm}
	The model in Eq.~\eqref{extendobj} is equivalent to the following formulation
	\begin{equation}
		\begin{aligned}
			\label{overallobj}
			&\mathop{\min}\limits_{G^{(v)},F,Y,\alpha_v}\sum_{v=1}^{m}\alpha_v\|X^{(v)}-G^{(v)}FY\|_F^2,\\
			&\text{s.t.~~~}{G^{(v)}}^TG^{(v)}=I_d,F^TF=I_k,Y\in Ind,\alpha\in\Delta_v.
		\end{aligned}
	\end{equation}
\end{mythm}

Then, an alternate minimizing algorithm is designed to solve the optimization problem in Eq.~\eqref{overallobj} by optimizing each variable while fixing the others.

\textbf{$G^{(v)}$-subproblem:} By fixing other variables, the optimization problem for updating $G^{(v)}$ can be formulated as
\begin{equation}
	\begin{aligned}
		\label{g1}
		\mathop{\min}\limits_{G^{(v)}}\sum_{v=1}^{m}\alpha_v\|X^{(v)}-G^{(v)}FY\|_F^2,~~~\text{s.t.~~~}{G^{(v)}}^TG^{(v)}=I_d.
	\end{aligned}
\end{equation}

Since each $G^{(v)}$ is independent from each other in terms of different views, we can further transform the optimization problem in Eq.~\eqref{g1} into the following model,
\begin{equation}
	\begin{aligned}
		\label{g2}
		\mathop{\max}\limits_{G^{(v)}}Tr({G^{(v)}}^TH^{(v)}),~~~\text{s.t.~~~}{G^{(v)}}^TG^{(v)}=I_d,
	\end{aligned}
\end{equation}
where $H^{(v)}=X^{(v)}Y^TF^T$. The optimal solution of $G^{(v)}$ can be efficiently solved by singular value decomposition (SVD) technique based on $H^{(v)}$, and specifically $G^{(v)}$ can be obtained by calculating $U_HV_H^T$, where $H^{(v)}=U_{H}\Sigma_HV_H^T$~\cite{DBLP:conf/ijcai/WangLZTLHXY19}.

\begin{algorithm}[!t]
	\caption{Adaptively-weighted Integral Space for Fast Multiview Clustering}
	\label{Alg:AIalg}
	{\bfseries Input:} Multiview dataset $\left\{X^{(v)}\in\mathbb{R}^{d_v\times n}\right\}_{v=1}^{m}$, dimension $d$ and cluster number $k$.
	\begin{algorithmic}[1]
		\STATE Initialize $G^{(v)}$, $F$, $Y$. Initialize $\alpha_v$ with $\frac{1}{m}$.
		\WHILE {not converged}
		\STATE Update $G^{(v)}, \forall v$ by solving the problem in Eq.~\eqref{g2}.
		\STATE Update $F$ by solving the problem in Eq.~\eqref{f2}.
		\STATE Update $Y$ via the optimal row obtained by Eq.~\eqref{y3}.
		\STATE Update $\alpha_v$ by solving the problem in Eq.~\eqref{alphaobj}.
		\ENDWHILE
	\end{algorithmic}
	{\bfseries Output:} The final consensus cluster assignment matrix $Y$.
\end{algorithm}

\textbf{$F$-subproblem:} By fixing the other variables, the objective function \textit{w.r.t.} $F$ can be transformed into the following formulation
\begin{equation}
	\begin{aligned}
		\label{f1}
		\mathop{\min}\limits_{F}\sum_{v=1}^{m}\alpha_v\|X^{(v)}-G^{(v)}FY\|_F^2,~~~\text{s.t.~~~}F^TF=I_k.
	\end{aligned}
\end{equation}

Similar to $G^{(v)}$, it is equivalent to solving $F$ by the following problem
\begin{equation}
	\begin{aligned}
		\label{f2}
		\mathop{\max}\limits_{F}Tr(F^TJ),~~~\text{s.t.~~~}F^TF=I_k,
	\end{aligned}
\end{equation}
where $J=\sum_{v=1}^{m}\alpha_v{G^{(v)}}^TX^{(v)}Y^T$. Therefore, the closed-form solution of $F$ is equal to $U_JV_J^T$, where $J=U_J\Sigma_JV_J^T$.

\textbf{$Y$-subproblem:} By fixing other variables, $Y$ can be updated by solving the following problem
\begin{equation}
	\begin{aligned}
		\label{y1}
		&\mathop{\min}\limits_{Y}\sum_{v=1}^{m}\alpha_v\|X^{(v)}-G^{(v)}FY\|_F^2,\\
		&\text{s.t.~~~}Y_{ij}\in\left\{0,1\right\},\sum_{i=1}^{k}Y_{ij}=1,\forall j=1,2,\cdots,n.
	\end{aligned}
\end{equation}

However, it is difficult to directly solve $Y$ as a whole, since there is one and only one non-zero entry (i.e., 1) in each column of the cluster assignment matrix. Inspired by~\cite{DBLP:conf/sdm/DingH05}, we can solve the optimization problem in Eq.~\eqref{y1} independently for each object. Therefore, for each object, we can have
\begin{equation}
	\begin{aligned}
		\label{y2}
		&\mathop{\min}\limits_{Y_{:,j}}\sum_{v=1}^{m}\alpha_v\|X_{:,j}^{(v)}-G^{(v)}FY_{:,j}\|^2,\\
		&\text{s.t.~~~}Y_{:,j}\in\left\{0,1\right\}^k,\|Y_{:,j}\|_1=1.
	\end{aligned}
\end{equation}

We can settle the above optimization problem by finding one optimal row $i^{\ast}$ in $Y_{:,j}$ such that $Y_{i^{\ast},j}=1$ and 0 for other entries in the $j$-th column. Then, the optimal row can be searched by
\begin{equation}
	\begin{aligned}
		\label{y3}
		i^{\ast}=\mathop{\arg\min}_{i}\sum_{v=1}^{m}\alpha_v\|X_{:,j}^{(v)}-G^{(v)}F_{:,i}\|^2.
	\end{aligned}
\end{equation}

As a matter of fact, the optimal solution of cluster assignment can be obtained by minimizing the distance between the data sample and the cluster centroid.

\textbf{$\alpha_v$-subproblem:} By fixing the other variables except $\alpha_v$, the optimization problem is equivalent to dealing with the model in Eq.~\eqref{alphaobj}, which is solved by the computed $G^{(v)}$, $F$ and $Y$ in each iteration.

According to the convex property and optimal solution of each sub-problem, the objective function in Eq.~\eqref{overallobj} will decrease monotonically in each iteration until convergence. For clarity, the procedure of solving the proposed AIMC model is summarized in Algorithm~\ref{Alg:AIalg}.

\begin{table}[!t
	\caption{Statistics of the nine real-world datasets.}
	\label{TableDataset}
	\centering
	\begin{tabular}{@{}c@{}ccc@{}c@{}}
		\hline     Datasets    & \#Object  & \#View           & \#Class  & View dimension     \\
		\hline HandWritten            & 2000             & 6             & 10       & 216, 76, 64, 6, 240, 47    \\
		Notting-Hill            & 4660               &  3             & 5         & 6750, 3304, 2000        \\
		SUNRGBD            & 10335               &  2             & 45         & 4096, 4096        \\
		AwA            & 30475               &  6             & 50         &  2688, 2000, 252, 2000, 2000, 2000        \\
		VGGFace2-50          & 34027            & 4              & 50       & 944, 576, 512, 640        \\
		YTF-10            & 38654               & 4             & 10         & 944, 576, 512, 640         \\
		YTF-20                & 63896           & 4   &20    & 944, 576, 512, 640   \\
		YTF-50         & 126054              & 4                 & 50         & 944, 576, 512, 640        \\
		YTF-100         & 195537              & 4                 & 100         & 944, 576, 512, 640         \\
		\hline
	\end{tabular}
\end{table}

\textbf{Remark.} In particular, the view generation model in the proposed AIMC method is exploited to discover the underlying latent integral space, which reflects the data structure as well as cluster partition in essence, and avoids the curse of dimensionality to some degree. To validate the effectiveness of AIMC, we additionally employ a naive orthogonal and non-negative matrix factorization method for multiview clustering (NONMF), whose formulation can be rewritten as
\begin{equation}
	\begin{aligned}
		\label{naiveobj}
		&\mathop{\min}\limits_{F^{(v)},Y}\sum_{v=1}^{m}\|X^{(v)}-F^{(v)}Y\|_F^2,\\
		&\text{s.t.~~~}{F^{(v)}}^TF^{(v)}=I_k,Y\in Ind,
	\end{aligned}
\end{equation}
where $F^{(v)}$ is the view-specific cluster centroid matrix with orthogonality constraint, and $Y$ denotes the shared cluster assignment representation. Due to the direct factorization of original data matrix, the effectiveness and efficiency of NONMF would decrease significantly when the data feature dimension is large. Besides, NONMF can not seek for the underlying data space, failing to take the latent semantics among views into account. More details can be found in Section~\ref{sec:experiments}.

\subsection{Complexity Analysis}

\textbf{Computational complexity.} The computational burden of AIMC is composed of four parts, i.e., the cost of optimization about each variable. The first part is to update $G^{(v)}$, whose cost is $O\left(d_vd^2\right)$ and $O\left(d_vdk^2\right)$ respectively for SVD and matrix multiplication. The second part is about the $F$ subproblem, which requires $O\left(dk^2\right)$ for performing SVD on $J$ and $O\left(dk^3\right)$ for matrix multiplication similar to $G^{(v)}$. The third part is to compute the final consensus cluster assignment matrix $Y$, and $O\left(mnk\right)$ is needed. The last part is to solve the weight $\alpha_v$, and it only costs $O(1)$. Therefore, the overall computational complexity to solve the proposed AIMC method is $O\left((hd^2+hdk^2+dk^2+dk^3+mnk)t\right)$, in which $h=\sum_{v=1}^{m}d_v$ is the summation of feature dimensions, and $t$ stands for the number of iterations of these four parts. Consequently, due to the property of large scale datasets (i.e., $n\gg d, k, m$), the computational complexity of AIMC is nearly linear to the number of samples $O\left(n\right)$.

\textbf{Space complexity.} The major space usages of the proposed AIMC method are matrices $G^{(v)}\in\mathbb{R}^{d_v\times d}$, $F\in\mathbb{R}^{d\times k}$, and $Y\in\mathbb{R}^{k\times n}$. Consequently, the major space complexity of AIMC is $O\big(nk+(h+k)d\big)$, which is nearly linear to the number of samples $O\left(n\right)$ as well.

\section{Experiments}
\label{sec:experiments}

\begin{table}[!t]
	\caption{Complexity analysis on compared methods and AIMC. ``Max Reported'' represents the largest dataset size reported in the original reference.}
	\label{TableMemory}
	\centering
	\renewcommand{\arraystretch}{1.2}
	\begin{tabular}{@{}cc@{}cc@{}}
		\hline     Method    & Space Complexity  & Time Complexity          & Max Reported     \\
		\hline AMGL            & $O\left(mn^2+nk\right)$           & $O\left(n^3\right)$               & 12643       \\
		SwMC            & $O\left(n^2+nk\right)$            & $O\left(kn^2\right)$             & 2000    \\
		GMC            & $O\left((m+1)n^2+nk\right)$               &  $O\left((m+k)n^2\right)$             & 11025         \\
		PMSC         & $O\left(2mn^2+(m+1)nk\right)$            & $O\left(n^3\right)$              & 2386            \\
		\hline
		LMVSC            & $O\left(mk(n+h)\right)$               & $O\left(n\right)$             & 30,000                \\
		SMVSC               & $O\left(mn+(h+m)k\right)$           & $O\left(n\right)$   &101,499       \\
		FPMVS         & $O\left(nk+(h+k)k\right)$              & $O\left(n\right)$                 & 101,499              \\
		OPMC         & $O\left(nk+(h+k)k\right)$              & $O\left(n\right)$                 & 101,499              \\
		NONMF           & $O\left(nk+hd\right)$                                      & $O\left(n\right)$            & $\llap{|}$ \\
		AIMC         & $O\left(nk+(h+k)d\right)$              & $O\left(n\right)$                 & 195,537                 \\
		\hline
	\end{tabular}
\end{table}

In this section, to verify the effectiveness of the proposed AIMC method, extensive experiments are conducted on nine real-world datasets, including several large-scale multiview image datasets, to compare the proposed AIMC method with four state-of-the-art multiview clustering methods and five large-scale oriented algorithms in terms of clustering performance and running time. In the meantime, parameter analysis and empirical convergence analysis are also conducted for a comprehensive study. All of the experiments are implemented in Matlab 2021a on a standard Window PC with an Intel 2.4-GHz CPU and 64-GB RAM (64-bit).

\begin{table*}[!t
	\centering
	\caption{Comparison results in terms of ACC on nine real-world datasets. N/A implies the out-of-memory error.}
	\label{table:ComparisonResultsI}
	\begin{tabular}{m{0.75cm}<{\centering}m{1.45cm}<{\centering}m{1.45cm}<{\centering}m{1.45cm}<{\centering}m{1.45cm}<{\centering}m{1.65cm}<{\centering}m{1.45cm}<{\centering}m{1.45cm}<{\centering}m{1.45cm}<{\centering}m{1.45cm}}
		\toprule
		\multirow{1}{*}{Methods} &\multicolumn{1}{c}{HandWritten} &\multicolumn{1}{c}{Notting-Hill} &\multicolumn{1}{c}{SUNRGBD} &\multicolumn{1}{c}{AwA} &\multicolumn{1}{c}{VGGFace2-50} &\multicolumn{1}{c}{YTF-10} &\multicolumn{1}{c}{YTF-20} &\multicolumn{1}{c}{YTF-50} &\multicolumn{1}{c}{YTF-100} \\
		\hline
		\multirow{1}*{AMGL}
		&0.8082$_{\pm0.0566}$	&0.3609$_{\pm0.0178}$	&0.2143$_{\pm0.0119}$	&N/A	&N/A	&N/A	&N/A   &N/A	   &N/A \\
		\multirow{1}*{SwMC}
		&0.8740$_{\pm0.0000}$	&0.3388$_{\pm0.0000}$	&0.1181$_{\pm0.0000}$	&N/A	&N/A	&N/A	&N/A   &N/A	   &N/A \\
		\multirow{1}*{GMC}
		&0.8820$_{\pm0.0891}$	&0.3124$_{\pm0.0000}$	&0.1277$_{\pm0.0000}$	&N/A	&N/A	&N/A	&N/A   &N/A	   &N/A \\
		\multirow{1}*{PMSC}
		&0.6318$_{\pm0.0440}$	&0.7782$_{\pm0.0617}$	&N/A	&N/A	&N/A	&N/A	&N/A   &N/A	   &N/A \\
		\multirow{1}*{LMVSC}
		&\underline{0.9225$_{\pm0.0000}$} &\textbf{0.9133$_{\pm0.0000}$} &0.1810$_{\pm0.0000}$ &0.0760$_{\pm0.0000}$ &0.1113$_{\pm0.0000}$ &0.7566$_{\pm0.0000}$ &0.7092$_{\pm0.0000}$ &0.6825$_{\pm0.0000}$ &0.6006$_{\pm0.0000}$ \\
		\multirow{1}*{SMVSC}
		&0.8205$_{\pm0.0000}$ &0.8081$_{\pm0.0000}$ &0.2223$_{\pm0.0000}$ &0.0908$_{\pm0.0000}$ &0.1127$_{\pm0.0000}$ &0.7389$_{\pm0.0000}$ &\underline{0.7125$_{\pm0.0000}$} &0.6681$_{\pm0.0000}$ &0.5907$_{\pm0.0000}$ \\
		\multirow{1}*{FPMVS}
		&0.8230$_{\pm0.0000}$ &0.7131$_{\pm0.0000}$ &\underline{0.2388$_{\pm0.0000}$} &0.0912$_{\pm0.0000}$ &0.1098$_{\pm0.0000}$ &0.7325$_{\pm0.0000}$ &0.6948$_{\pm0.0000}$ &0.6851$_{\pm0.0000}$ &0.5293$_{\pm0.0000}$\\
		\multirow{1}*{OPMC}
		&0.8915$_{\pm0.0000}$ &0.7431$_{\pm0.0000}$ &0.1930$_{\pm0.0000}$ &0.0925$_{\pm0.0000}$ &\underline{0.1160$_{\pm0.0000}$} &0.7532$_{\pm0.0000}$ &0.6782$_{\pm0.0000}$ &\underline{0.7165$_{\pm0.0000}$} &0.6443$_{\pm0.0000}$\\
		\multirow{1}*{NONMF}
		&0.8400$_{\pm0.0000}$ &0.8027$_{\pm0.0000}$ &0.2324$_{\pm0.0000}$ &\underline{0.0965$_{\pm0.0000}$} &0.1054$_{\pm0.0000}$ &\underline{0.7726$_{\pm0.0000}$} &0.6509$_{\pm0.0000}$ &0.7135$_{\pm0.0000}$ &\underline{0.6610$_{\pm0.0000}$}\\
		\multirow{1}*{AIMC}
		&\textbf{0.9345$_{\pm0.0000}$} &\underline{0.9064$_{\pm0.0000}$} &\textbf{0.2536$_{\pm0.0000}$} &\textbf{0.1008$_{\pm0.0000}$} &\textbf{0.1186$_{\pm0.0000}$} &\textbf{0.8881$_{\pm0.0000}$} &\textbf{0.7640$_{\pm0.0000}$} &\textbf{0.7602$_{\pm0.0000}$} &\textbf{0.6789$_{\pm0.0000}$}\\
		\bottomrule
	\end{tabular}
\end{table*}

\begin{table*}[!t
	\centering
	\caption{Comparison results in terms of NMI on nine real-world datasets. N/A implies the out-of-memory error.}
	\label{table:ComparisonResultsII}
	\begin{tabular}{m{0.75cm}<{\centering}m{1.45cm}<{\centering}m{1.45cm}<{\centering}m{1.45cm}<{\centering}m{1.45cm}<{\centering}m{1.65cm}<{\centering}m{1.45cm}<{\centering}m{1.45cm}<{\centering}m{1.45cm}<{\centering}m{1.45cm}}
		\toprule
		\multirow{1}{*}{Methods} &\multicolumn{1}{c}{HandWritten} &\multicolumn{1}{c}{Notting-Hill} &\multicolumn{1}{c}{SUNRGBD} &\multicolumn{1}{c}{AwA} &\multicolumn{1}{c}{VGGFace2-50} &\multicolumn{1}{c}{YTF-10} &\multicolumn{1}{c}{YTF-20} &\multicolumn{1}{c}{YTF-50} &\multicolumn{1}{c}{YTF-100} \\
		\hline
		\multirow{1}*{AMGL}
		&0.8463$_{\pm0.0294}$	&0.0780$_{\pm0.0208}$	&0.1686$_{\pm0.0109}$    &N/A	&N/A	&N/A	&N/A   &N/A	   &N/A \\
		\multirow{1}*{SwMC}
		&\underline{0.8886$_{\pm0.0000}$}	&0.0877$_{\pm0.0000}$	&0.0287$_{\pm0.0000}$	&N/A	&N/A	&N/A	&N/A   &N/A	   &N/A \\
		\multirow{1}*{GMC}
		&\textbf{0.9041$_{\pm0.0000}$}	&0.0923$_{\pm0.0000}$	&0.0728$_{\pm0.0000}$	&N/A	&N/A	&N/A	&N/A   &N/A	   &N/A \\
		\multirow{1}*{PMSC}
		&0.6567$_{\pm0.0391}$	&0.6563$_{\pm0.0430}$	&N/A	&N/A	&N/A	&N/A   &N/A	   &N/A    &N/A \\
		\multirow{1}*{LMVSC}
		&0.8576$_{\pm0.0000}$ &\underline{0.7966$_{\pm0.0000}$} &0.2283$_{\pm0.0000}$	&0.0879$_{\pm0.0000}$ &0.1332$_{\pm0.0000}$ &0.7670$_{\pm0.0000}$ &0.7751$_{\pm0.0000}$ &0.8098$_{\pm0.0000}$ &0.7804$_{\pm0.0000}$ \\
		\multirow{1}*{SMVSC}
		&0.7886$_{\pm0.0000}$ &0.7371$_{\pm0.0000}$ &0.2280$_{\pm0.0000}$	&0.1089$_{\pm0.0000}$ &\underline{0.1366$_{\pm0.0000}$} &0.7980$_{\pm0.0000}$ &0.7913$_{\pm0.0000}$ &0.8258$_{\pm0.0000}$ &0.7991$_{\pm0.0000}$ \\
		\multirow{1}*{FPMVS}
		&0.7923$_{\pm0.0000}$ &0.6772$_{\pm0.0000}$ &0.2413$_{\pm0.0000}$	&0.1088$_{\pm0.0000}$ &0.1365$_{\pm0.0000}$ &0.7740$_{\pm0.0000}$ &0.7790$_{\pm0.0000}$ &0.8364$_{\pm0.0000}$ &0.7532$_{\pm0.0000}$\\
		\multirow{1}*{OPMC}
		&0.8131$_{\pm0.0000}$ &0.7638$_{\pm0.0000}$ &\textbf{0.2523$_{\pm0.0000}$}	&\underline{0.1195$_{\pm0.0000}$} &0.1344$_{\pm0.0000}$ &0.8014$_{\pm0.0000}$ &0.7726$_{\pm0.0000}$ &0.8278$_{\pm0.0000}$ &0.8079$_{\pm0.0000}$\\
		\multirow{1}*{NONMF}
		&0.7981$_{\pm0.0000}$ &0.7126$_{\pm0.0000}$ &0.2359$_{\pm0.0000}$	&0.1173$_{\pm0.0000}$ &0.1324$_{\pm0.0000}$ &\underline{0.8144$_{\pm0.0000}$} &\underline{0.7952$_{\pm0.0000}$} &\underline{0.8479$_{\pm0.0000}$} &\underline{0.8280$_{\pm0.0000}$}\\
		\multirow{1}*{AIMC}
		&0.8823$_{\pm0.0000}$ &\textbf{0.8226$_{\pm0.0000}$} &\underline{0.2501$_{\pm0.0000}$}	&\textbf{0.1200$_{\pm0.0000}$} &\textbf{0.1489$_{\pm0.0000}$} &\textbf{0.8704$_{\pm0.0000}$} &\textbf{0.8334$_{\pm0.0000}$} &\textbf{0.8643$_{\pm0.0000}$} &\textbf{0.8431$_{\pm0.0000}$}\\
		\bottomrule
	\end{tabular}
\end{table*}

\begin{table*}[!t
	\centering
	\caption{Comparison results in terms of Purity on nine real-world datasets. N/A implies the out-of-memory error.}
	\label{table:ComparisonResultsIII}
	\begin{tabular}{m{0.75cm}<{\centering}m{1.45cm}<{\centering}m{1.45cm}<{\centering}m{1.45cm}<{\centering}m{1.45cm}<{\centering}m{1.65cm}<{\centering}m{1.45cm}<{\centering}m{1.45cm}<{\centering}m{1.45cm}<{\centering}m{1.45cm}}
		\toprule
		\multirow{1}{*}{Methods} &\multicolumn{1}{c}{HandWritten} &\multicolumn{1}{c}{Notting-Hill} &\multicolumn{1}{c}{SUNRGBD} &\multicolumn{1}{c}{AwA} &\multicolumn{1}{c}{VGGFace2-50} &\multicolumn{1}{c}{YTF-10} &\multicolumn{1}{c}{YTF-20} &\multicolumn{1}{c}{YTF-50} &\multicolumn{1}{c}{YTF-100} \\
		\hline
		\multirow{1}*{AMGL}
		&0.8281$_{\pm0.0475}$	&0.3677$_{\pm0.0161}$	&0.2631$_{\pm0.0087}$    &N/A	&N/A	&N/A	&N/A   &N/A	   &N/A \\
		\multirow{1}*{SwMC}
		&0.8795$_{\pm0.0000}$	&0.3710$_{\pm0.0000}$	&0.1311$_{\pm0.0000}$    &N/A	&N/A	&N/A	&N/A   &N/A	   &N/A \\
		\multirow{1}*{GMC}
		&0.8820$_{\pm0.0000}$	&0.3380$_{\pm0.0000}$	&0.1415$_{\pm0.0000}$    &N/A	&N/A	&N/A	&N/A   &N/A	   &N/A \\
		\multirow{1}*{PMSC}
		&0.8311$_{\pm0.0363}$	&0.7948$_{\pm0.0488}$    &N/A	&N/A	&N/A	&N/A   &N/A	   &N/A  &N/A \\
		\multirow{1}*{LMVSC}
		&0.9225$_{\pm0.0000}$ &\textbf{0.9133$_{\pm0.0000}$} &0.1856$_{\pm0.0000}$	&0.0868$_{\pm0.0000}$ &\textbf{0.1401$_{\pm0.0000}$} &\underline{0.8125$_{\pm0.0000}$} &0.7614$_{\pm0.0000}$ &\underline{0.7688$_{\pm0.0000}$} &0.6827$_{\pm0.0000}$ \\
		\multirow{1}*{SMVSC}
		&0.8205$_{\pm0.0000}$ &0.8324$_{\pm0.0000}$ &0.3292$_{\pm0.0000}$	&0.0966$_{\pm0.0000}$ &0.1157$_{\pm0.0000}$ &0.7726$_{\pm0.0000}$ &0.7700$_{\pm0.0000}$ &0.6926$_{\pm0.0000}$ &0.6104$_{\pm0.0000}$ \\
		\multirow{1}*{FPMVS}
		&0.8230$_{\pm0.0000}$ &0.7850$_{\pm0.0000}$ &0.3399$_{\pm0.0000}$	&0.0963$_{\pm0.0000}$ &0.1142$_{\pm0.0000}$ &0.7621$_{\pm0.0000}$ &0.7259$_{\pm0.0000}$ &0.7140$_{\pm0.0000}$ &0.5446$_{\pm0.0000}$\\
		\multirow{1}*{OPMC}
		&0.8915$_{\pm0.0000}$ &0.8285$_{\pm0.0000}$ &\textbf{0.3974$_{\pm0.0000}$}	&\textbf{0.1140$_{\pm0.0000}$} &0.1241$_{\pm0.0000}$ &0.8061$_{\pm0.0000}$ &0.7250$_{\pm0.0000}$ &0.7686$_{\pm0.0000}$ &0.6983$_{\pm0.0000}$\\
		\multirow{1}*{NONMF}
		&0.8400$_{\pm0.0000}$ &0.8027$_{\pm0.0000}$ &0.3327$_{\pm0.0000}$	&0.1025$_{\pm0.0000}$ &\underline{0.1324$_{\pm0.0000}$} &0.8057$_{\pm0.0000}$ &0.7381$_{\pm0.0000}$ &0.7531$_{\pm0.0000}$ &\underline{0.6995$_{\pm0.0000}$}\\
		\multirow{1}*{AIMC}
		&\textbf{0.9345$_{\pm0.0000}$} &\underline{0.9064$_{\pm0.0000}$} &\underline{0.3519$_{\pm0.0000}$}	&\underline{0.1097$_{\pm0.0000}$} &0.1271$_{\pm0.0000}$ &\textbf{0.8881$_{\pm0.0000}$} &\textbf{0.8110$_{\pm0.0000}$} &\textbf{0.7879$_{\pm0.0000}$} &\textbf{0.7267$_{\pm0.0000}$}\\
		\bottomrule
	\end{tabular}
\end{table*}

\begin{table*}[!t
	\centering
	\caption{Comparison results in terms of Fscore on nine real-world datasets. N/A implies the out-of-memory error.}
	\label{table:ComparisonResultsIV}
	\begin{tabular}{m{0.75cm}<{\centering}m{1.45cm}<{\centering}m{1.45cm}<{\centering}m{1.45cm}<{\centering}m{1.45cm}<{\centering}m{1.65cm}<{\centering}m{1.45cm}<{\centering}m{1.45cm}<{\centering}m{1.45cm}<{\centering}m{1.45cm}}
		\toprule
		\multirow{1}{*}{Methods} &\multicolumn{1}{c}{HandWritten} &\multicolumn{1}{c}{Notting-Hill} &\multicolumn{1}{c}{SUNRGBD} &\multicolumn{1}{c}{AwA} &\multicolumn{1}{c}{VGGFace2-50} &\multicolumn{1}{c}{YTF-10} &\multicolumn{1}{c}{YTF-20} &\multicolumn{1}{c}{YTF-50} &\multicolumn{1}{c}{YTF-100} \\
		\hline
		\multirow{1}*{AMGL}
		&0.7681$_{\pm0.0853}$	&0.3654$_{\pm0.0040}$	&0.1422$_{\pm0.0046}$    &N/A	&N/A	&N/A	&N/A   &N/A	   &N/A \\
		\multirow{1}*{SwMC}
		&0.8624$_{\pm0.0000}$	&0.3690$_{\pm0.0000}$	&0.1204$_{\pm0.0000}$    &N/A	&N/A	&N/A	&N/A   &N/A	   &N/A \\
		\multirow{1}*{GMC}
		&\underline{0.8653$_{\pm0.0000}$}	&0.3694$_{\pm0.0000}$	&0.1215$_{\pm0.0000}$    &N/A	&N/A	&N/A	&N/A   &N/A	   &N/A \\
		\multirow{1}*{PMSC}
		&0.5539$_{\pm0.0476}$	&0.6568$_{\pm0.0565}$    &N/A	&N/A	&N/A	&N/A   &N/A	   &N/A   &N/A \\
		\multirow{1}*{LMVSC}
		&0.8499$_{\pm0.0000}$ &\underline{0.8347$_{\pm0.0000}$} &0.1154$_{\pm0.0000}$	&0.0377$_{\pm0.0000}$ &0.0524$_{\pm0.0000}$ &0.7001$_{\pm0.0000}$ &0.6268$_{\pm0.0000}$ &0.5794$_{\pm0.0000}$ &0.5171$_{\pm0.0000}$ \\
		\multirow{1}*{SMVSC}
		&0.7525$_{\pm0.0000}$ &0.7870$_{\pm0.0000}$ &0.1487$_{\pm0.0000}$	&\textbf{0.0641$_{\pm0.0000}$} &\underline{0.0604$_{\pm0.0000}$} &0.6982$_{\pm0.0000}$ &0.6518$_{\pm0.0000}$ &0.6157$_{\pm0.0000}$ &0.5036$_{\pm0.0000}$ \\
		\multirow{1}*{FPMVS}
		&0.7556$_{\pm0.0000}$ &0.6928$_{\pm0.0000}$ &\underline{0.1604$_{\pm0.0000}$}	&\underline{0.0640$_{\pm0.0000}$} &0.0597$_{\pm0.0000}$ &0.6959$_{\pm0.0000}$ &0.6261$_{\pm0.0000}$ &0.6381$_{\pm0.0000}$ &0.3541$_{\pm0.0000}$\\
		\multirow{1}*{OPMC}
		&0.8033$_{\pm0.0000}$ &0.7395$_{\pm0.0000}$ &0.1339$_{\pm0.0000}$	&0.0469$_{\pm0.0000}$ &0.0550$_{\pm0.0000}$ &0.7225$_{\pm0.0000}$ &0.6206$_{\pm0.0000}$ &0.6376$_{\pm0.0000}$ &\underline{0.5651$_{\pm0.0000}$}\\
		\multirow{1}*{NONMF}
		&0.7757$_{\pm0.0000}$ &0.7802$_{\pm0.0000}$ &0.1506$_{\pm0.0000}$	&0.0634$_{\pm0.0000}$ &0.0580$_{\pm0.0000}$ &\underline{0.7461$_{\pm0.0000}$} &\underline{0.6590$_{\pm0.0000}$} &\underline{0.6573$_{\pm0.0000}$} &0.5463$_{\pm0.0000}$\\
		\multirow{1}*{AIMC}
		&\textbf{0.8790$_{\pm0.0000}$} &\textbf{0.8565$_{\pm0.0000}$} &\textbf{0.1709$_{\pm0.0000}$}	&\underline{0.0640$_{\pm0.0000}$} &\textbf{0.0606$_{\pm0.0000}$} &\textbf{0.8288$_{\pm0.0000}$} &\textbf{0.7372$_{\pm0.0000}$} &\textbf{0.7004$_{\pm0.0000}$} &\textbf{0.6161$_{\pm0.0000}$}\\
		\bottomrule
	\end{tabular}
\end{table*}

\begin{table*}[!t]
	\caption{Comparison results on nine real-world datasets in terms of running time in seconds. N/A implies the out-of-memory error.}
	\label{table:runtime}
	\centering
	\renewcommand{\arraystretch}{1.3}
	\begin{tabular}{ccccccccccc}
		\hline   Datasets~ &~AMGL~ &~SwMC~ &~GMC~ &~PMSC~ & ~LMVSC~ & ~SMVSC~ & ~FPMVS~ & ~OPMC~ & ~NONMF~ & ~AIMC~ \\
		\hline HandWritten  &40.65~ &144.71~&21.75~&2133.26~&\underline{2.20}~&14.58~&21.49~&\textbf{0.97}~&6.13~&2.60~ \\
		Notting-Hill  &592.33~ &3276.04~ &27.72~ &3287.20~ &\textbf{2.35}~ &375.08~ &729.19~ &\underline{20.21}~ &34.45~ &21.57~ \\
		SUNRGBD  &4504.63~ &1522.83~ &483.24~ &N/A~ &\textbf{8.94}~ &551.70~ &1070.34~ &145.45~ &122.22~ &\underline{51.42}~ \\
		AwA  &N/A~ &N/A~ &N/A~ &N/A~ &\textbf{55.14}~ &2265.28~ &4025.50~ &897.73~ &301.95~ &\underline{166.15}~ \\
		VGGFace2-50~	  &N/A~ &N/A~ &N/A~ &N/A~ &\textbf{21.98}~ &820.42~ &1279.40~ &256.09~ &131.42~ &\underline{76.16}~ \\
		YTF-10~	 &N/A~ &N/A~ &N/A~ &N/A~ &\textbf{6.78}~ &903.47~ &1378.40~ &\underline{47.85}~ &60.55~ &49.91~  \\
		YTF-20~  &N/A~ &N/A~ &N/A~ &N/A~ &\textbf{15.34}~ &1906.92~ &2717.5~ &\underline{60.33}~ &153.77~ &76.84~ \\
		YTF-50~  &N/A~ &N/A~ &N/A~ &N/A~ &\textbf{119.02}~ &3981.79~ &7030.41~ &245.94~ &284.69~ &\underline{180.49}~ \\
		YTF-100~ &N/A~ &N/A~ &N/A~ &N/A~ &\underline{345.61}~ &16331.04~ &19978.28~ &576.28~ &404.28~ &\textbf{336.32}~ \\
		\hline
		Rank~   &8.0~      &8.7~      &5.3~     &10.0~     &\textbf{1.2}~     &5.2~      &6.3~     &2.9~     &3.7~     &\underline{2.3}~ \\
		\hline
	\end{tabular}
\end{table*}

\subsection{Datasets and Compared Methods}

Nine widely used datasets are adopted in the evaluation, whose statistics are summarized in Table~\ref{TableDataset}. \textbf{HandWritten} consists of ten-class handwritten digits, and each digit has 200 samples~\cite{DBLP:journals/kybernetika/BreukelenDTH98}. In our experiments, six features are selected, which are 216-D profile correlation, 76-D Fourier coefficient, 64-D Karhunen-Love coefficient, 6-D morphological feature, 240-D pixel average and 47-D Zernike moment. \textbf{Notting-Hill} contains 4660 facial images where the faces of five main casts are selected~\cite{zhang2009character}. In our experiments, three features are selected, including 6750-D Gabor feature, 3304-D LBP feature and 2000-D intensity feature. \textbf{SUNRGBD} consists of 10335 indoor scene images of 45 object categories collected from Princeton University~\cite{DBLP:conf/cvpr/SongLX15}. In our experiments, two features are selected, whose dimensions are both 4096. \textbf{AwA} is an animal dataset consisting of 30475 images belonging to 50 animal categories~\cite{DBLP:journals/pami/LampertNH14}. In our experiments, six features are extracted, which are 2688-D color histogram, 2000-D local self-similarity, 252-D PHOG feature, 2000-D SIFT feature, 2000-D color SIFT feature and 2000-D SURF feature. \textbf{VGGFace2-50}\footnotemark[1] is a face image dataset containing 34027 images in 50 classes. In our experiments, four features are selected, which are 944-D LBP feature, 576-D HOG feature, 512-D GIST feature and 640-D Gabor feature. \textbf{YTF-10} (YouTube Faces), \textbf{YTF-20}, \textbf{YTF-50} and \textbf{YTF-100} are different subsets of face videos obtained from YouTube\footnotemark[2], whose data size are respectively 38654, 63896, 126054 and 195537. In our experiments, features of four views are extracted in all these four datasets, including 944-D LBP feature, 576-D HOG feature, 512-D GIST feature and 640-D Gabor feature.
\footnotetext[1]{\url{https://www.robots.ox.ac.uk/~vgg/data/vgg_face2/.}}
\footnotetext[2]{\url{https://www.cs.tau.ac.il/~wolf/ytfaces/.}}

The proposed AIMC method is compared with the following state-of-the-art baselines. \textbf{Parameter-free Auto-weighted Multiple Graph Learning (AMGL)}~\cite{DBLP:conf/ijcai/NieLL16} proposes to learn the optimal weights for each graph. \textbf{Self-weighted Multiview Clustering with Multiple Graphs (SwMC)}~\cite{DBLP:conf/ijcai/NieLL17} attempts to study a Laplacian rank constrained graph. \textbf{Graph-based Multiview Clustering (GMC)}~\cite{DBLP:journals/tkde/WangYL20} learns similarity-induced graphs from multiple views and unified fusion graph in a mutual manner. \textbf{Partition Level Multiview Subspace Clustering (PMSC)}~\cite{DBLP:journals/nn/KangZPZZPCX20} develops a unified multiview subspace clustering model. \textbf{Large-scale Multiview Subspace Clustering in Linear Time (LMVSC)}~\cite{DBLP:conf/aaai/KangZZSHX20} proposes a multiview subspace clustering framework for large-scale data in which a smaller graph for each view is studied. \textbf{Scalable Multiview Subspace Clustering with Unified Anchors (SMVSC)}~\cite{DBLP:conf/mm/SunZWZTLZW21} attempts to construct graph representation based on actual latent data distribution. \textbf{Fast Parameter-Free Multiview Subspace Clustering With Consensus Anchor Guidance (FPMVS)}~\cite{DBLP:journals/tip/WangLZZZGZ22} studies the subspace representation with consensus anchor guidance. \textbf{One-pass Multiview Clustering for Large-scale Data (OPMC)} considers matrix factorization together with partition generation~\cite{DBLP:conf/iccv/0003LYL0LS21}. \textbf{Naive Orthogonal and Non-negative Matrix Factorization for multiview clustering (NONMF)} makes direct factorization of original data matrix, which is included for ablation study to confirm the superiority of AIMC.

For comparison, we summarize the major space and time complexity of the compared methods in Table~\ref{TableMemory}.

\subsection{Experimental Setup}

For all methods, including the proposed AIMC method and nine compared methods, experiments are conducted twenty times for each of them and the average performance as well as the standard deviation (std. dev.) are reported. In the meantime, $k$-means algorithm is needed to achieve the final clustering performance for most of the methods, and thus in each experiment, it is run ten times to eliminate the random initialization. For our method, the dimension of the view generation model $d$ is tuned from $\left[k:5:300\right]$ for the benchmark datasets, where $d\geq k$ should be satisfied so as to better describe the cluster space. For the compared methods, the best parameters are tuned as suggested by the corresponding papers.

Comprehensively, the clustering performance is evaluated by four widely used metrics, i.e., accuracy (ACC), normalized mutual information (NMI), purity and Fscore. For all the above evaluation metrics, higher values indicate better clustering performance. More detailed descriptions of the four measures can be referred to~\cite{DBLP:journals/tnn/WangCHLY21}. Since each evaluation metric penalizes or favours certain property in clusterings, a more comprehensive evaluation can be received by reporting clustering performance via the four diverse metrics.

\subsection{Comparison Results}
\subsubsection{Clustering Performance}

The clustering performance obtained by different multiview clustering methods on the nine real-world datasets are reported in terms of ACC, NMI, Purity and Fscore in Table~\ref{table:ComparisonResultsI},~\ref{table:ComparisonResultsII},~\ref{table:ComparisonResultsIII} and ~\ref{table:ComparisonResultsIV}, where the mean as well as the standard deviation (std. dev.) are reported over 20 runs. In these tables, the best performance for distinct datasets in terms of each measure is highlighted in boldface, while the second best one in underline. Note that N/A implies that the algorithm suffers out-of-memory error on the corresponding dataset on our device, and thus no result is reported. According to the four tables, the following observations can be obtained.
\begin{enumerate}
	\item In general, the proposed AIMC method achieves the best clustering performance on most of the benchmark datasets, and always obtains better results than other multiview clustering methods for large-scale datasets. For instance, on the VGGFace2-50 dataset, AIMC significantly outperforms the other five large-scale oriented algorithms by achieving improvements of 1.57$\%$, 1.23$\%$, 1.24$\%$, 1.45$\%$ and 1.65$\%$ in terms of NMI. On the YTF-10 dataset, the performance improvements over the other algorithms in terms of NMI are respectively 10.34$\%$, 7.24$\%$, 9.64$\%$, 6.90$\%$ and 5.60$\%$.
	\item It could be concluded that the anchor based methods (LMVSC, SMVSC, FPMVS) or matrix factorization based methods (OPMC, NONMF, AIMC) are more suitable for large-scale datasets while comparing with the traditional multiview subspace clustering methods (AMGL, SwMC, GMC, PMSC).
	\item Despite good results achieved by NONMF, the performance of the proposed AIMC method is obviously superior with meaningful discovery of the latent integral space constructed by data cluster structure.
\end{enumerate}

Consequently, empirical comparison results validate the superiority of the proposed AIMC model.

\subsubsection{Running Time}

For further study, the comparison of running time in seconds consumed by all compared algorithms on the nine real-world datasets is reported in Table~\ref{table:runtime}. From the table, it can be observed that a relatively good trade-off between the clustering performance and computational burden is achieved by the proposed AIMC method, which averagely ranks the second best on computational time. Despite less computational time cost by LMVSC, its clustering performance is worse than AIMC on the whole. This is mainly due to that LMVSC merely focuses on the construction of multiple view-specific graph representations, neglecting the cross-view complementary information and underlying correlations from the latent integral space. Note that on the largest benchmark dataset (i.e., YTF-100), the proposed AIMC method needs the least computational cost, indicating the strong potential for facing with bigger data. As a result, large-scale multiview data clustering problems can be tackled by the proposed AIMC method with efficient computation.

\begin{figure}[!t]
	\centerline{
		\subfigure[HandWritten]{
			\includegraphics[width=0.5\linewidth]{figures/Handwalld.pdf}
		}
		\subfigure[SUNRGBD]{
			\includegraphics[width=0.5\linewidth]{figures/SUNalld.pdf}
		}
	}
	\centerline{
		\subfigure[VGGFace2-50]{
			\includegraphics[width=0.5\linewidth]{figures/VGGFalld.pdf}
		}
		\subfigure[YTF-20]{
			\includegraphics[width=0.5\linewidth]{figures/YTF20alld.pdf}
		}
	}
	\caption{Parameter analysis: Performance in terms of ACC and NMI with different dimension of the view generation model $d$ on the four datasets.}
	\label{Figure:paraAnalysis}
\end{figure}

\begin{figure}[!t]
	\centerline{
		\subfigure[HandWritten]{
			\includegraphics[width=0.5\linewidth]{figures/Handwconvergence.pdf}
		}
		\subfigure[SUNRGBD]{
			\includegraphics[width=0.5\linewidth]{figures/SUNconvergence.pdf}
	}}
	\centerline{
		\subfigure[VGGFace2-50]{
			\includegraphics[width=0.5\linewidth]{figures/VGGFconvergence.pdf}
		}
		\subfigure[YTF-20]{
			\includegraphics[width=0.5\linewidth]{figures/YTF20convergence.pdf}
		}
	}
	\caption{Convergence analysis: The objective value as a function of the iteration step on the four datasets.}
	\label{Figure:ConverAnalysis}
\end{figure}

\subsection{Parameter Analysis}

In this subsection, parameter analysis about the dimension of the view generation model $d$ is conducted on multiple datasets. Due to the page limit, the influences of different parameter values in terms of ACC and NMI on the four randomly selected benchmark datasets, i.e., HandWritten, SUNRGBD, VGGFace2-50 and YTF-20, are illustrated in \figurename~\ref{Figure:paraAnalysis}, in which the selection of $d$ is searched from $\left[k:5:300\right]$ according to different properties of multiple datasets. From the figure, it can be observed that the performance of AIMC is relatively stable over the corresponding ranges of parameter value on different datasets. Meanwhile, we can easily acquire the best clustering performance on different datasets according to the subfigures.

\subsection{Convergence Analysis}

Since the objective formulation in Eq.~\eqref{overallobj} solved by the alternate minimizing algorithm is non-increasing with iterations, the method can be guaranteed to converge finally. In this subsection, empirical convergence analysis is conducted on the HandWritten, SUNRGBD, VGGFace2-50 and YTF-20 datasets to verify the convergence property of the proposed AIMC method. The objective values on the four benchmark datasets are illustrated in \figurename~\ref{Figure:ConverAnalysis}. From the figure, we can observe that the corresponding objective value decreases monotonically to a minimum within the first 10 iterations, showing that the proposed model is able to converge within just a few iterations.

\section{Conclusion}
\label{sec:conclusion}
In this paper, we develop a novel model termed Adaptively-weighted Integral Space for Fast Multiview Clustering (AIMC) with nearly linear complexity. Within the framework, a view-specific generation model is designed to map the latent integral space into the corresponding view observation with diverse adaptive contributions. Reversely, with input view observations, the latent integral space can be restored by mapping back from given view observations with corresponding self-conducted confidences. In addition, the orthogonal centroid representation and cluster assignment are seamlessly constructed to approximate the latent integral space. By merging the reconstruction error and distortion error of data partition, AIMC is able to simultaneously discover the latent integral space as well as cluster partition. An alternate minimizing algorithm is developed to solve the optimization problem, which is proved to have linear time complexity \textit{w.r.t.} the sample size. Compared with the state-of-the-art multiview clustering methods and large-scale oriented methods, extensive experimental results on several large-scale datasets have validated the superiority of the proposed method.

\ifCLASSOPTIONcaptionsoff
  \newpage
\fi

\appendices

\bibliographystyle{IEEEtran}

redpajama_set_name: RedPajamaArXiv


text:
Q: How to pick/calculate component values for a tuned amplifier centered on 13.56Mhz? Background
As a fun / learning project I wanted to build a circuit which can tell me if a given RFID reader on a wall is 125Khz or 13.56Mhz ( by lighting LEDs).
My approach is to build two filters which lead to diode detectors - one filter + detector for 125khz, and one for 13.56Mhz.
I was hoping to use a length of wire or an unmeasured coil of wire as the input (pickup).
Problem
I can't figure out how to calculate values for the tuned circuit - I havent found any online calculator or sensible derivation (I don't understand the math/electronics enough to do it from first principles, I know Ohms law + basic AC theory + putting numbers into formulas).
Complication: I cant give an exact value of the 'drive' (input impedance?) of the input coil, nor can I work out the impedance of the diode envelope detector on the amps output. Can we just guess these?
The whole circuit so far, including the 125Khz section

Why cant HF be as easy as 125Khz? Cheap op-amps work at 125Khz.
The tuned amplifier schematic so far

A: You could design two seperate  tuned      loop antennas one by one .If you dont load the tuned circuit too much by say using a high input impedance preamp like say a MPF102 JFET .This means that the Q will be high in both cases and the standard formulae for resonant frequency of a tuned circuit will work fine .I have not done any 125KHz or 13.56 MHz work but I think that any open field coil would work as a receiving antenna .A bundle of ferrite rods from dead transistor AM radios would work at 125KHz .The proposed use of N bundled rods rather than just one will reduce the number of turns needed in rough proportion .Litz wire is actually still beneficial at 125 KHz because you will need lots of turns .If you dont want to do litz then consider space winding or wave winding or bank winding or any other technique to reduce proximity effect and parasitic capacitance .Coils with low parasitic capacitance tend to have higher Q which for your application means better sensitivity and batter selectivity .The 13.58 MHz is better on solid wire because     normal litz thinks that it is solid above about 3 MHz due to its significant capacitance .You could use a ferrite rod or an air cored multi turn loop with good results .If you get the Antennas right with high Q then you have enough selectivity to differentiate these far apart signals .

A: Last time I made a 13.56Mhz receiver I used a single square loop of wire and a resonatign capacitor in parallel with the loop antenna.
The antenna was a square loop having edges of about 8 inches each.  An 8 inch square loop will form an inductor of about 737nH.  You can find a coil inductance calculator here...
https://www.eeweb.com/toolbox/rectangle-loop-inductance
The resonatign capacitor needs to be chosen such that it resonates with the antenna inductance at 13.56MHz.
The resonant frequency of an LC circuit is...
w = 1/sqrt(L * C)
so...
C = 1/(w^2 * L) = 1/ ((2 * pi * 13.56MHz)^2 * 737nH) = 187pF
It is likely that parasitic capacitances and inductances will be important in the circuit so you may want to make the capacitor a little less than 187pF and then add a variable capacitor to tune the circuit.  Or alternately make the capacitor a little smaller and add a variable inductor.

redpajama_set_name: RedPajamaStackExchange


Rhum J.M. Vintage 1999 was tasted at Meeting No. 59 on June 28, 2017. Out of 5, we rated it very highly at 3.83. Rhum J.M. Vintage 1999 ranks 2nd overall in Rum. Costing $240, this spirit is expensive, but worth it.
Light and delicate nose. Rich, layered toasty rum, but missing the overly sweet notes of your molasses based rum. Perfectly warming. Nuanced. Yum.
Coffee cake #rhum - booyakashaka. Raisin ferry princesses prancing on Miami Beach.
Sweet nose and the sweet hot body of a freshly baked spice cake after a fall harvest. A drunken spice cake. I need eggnog.
Smells like a Claxton fruitcake. Candy flavored but not overly sweet.
great fun nose of Nilla Wafers, more nutmeg and vanilla. Not as much dried fruit as I was expecting. Really great taste with more of the same but you do start to pick up some black licorice and a tiny hint of cereal or maybe caramel. After tasting I'm convinced that this has to be a used whisky barrel my 3 guesses are Bourbon, Madeira or an unseated Scotch barrel. Fun drink for sure.


text:
Buies Creek 10, Winston-Salem 4 (F/7)
W: Gabriel Valdez (1-2)
L: Danny Dopico (0-3)
S: None
WINSTON-SALEM, N.C. (May 23, 2018) – Luis Basabe and Joel Booker both homered in Wednesday's twin bill finale, but Winston-Salem fell to Buies Creek 10-4 in game two at BB&T Ballpark to split the twin bill with the Astros.
The Dash (24-22) played as the away team in Wednesday's second contest due to a rainout that occurred at Jim Perry Stadium last Thursday. Winston-Salem went down in order to start the game, and Buies Creek (26-20) responded by plating five runs against Dash starter Danny Dopico (0-3) in the bottom of the first.
Osvaldo Duarte led off with a triple on Dopico's first pitch of the game and scored on Ronnie Dawson's RBI double. Then, Abraham Toro crushed a home run to right field to put the Astros up 3-0. Dopico then proceeded to load the bases via a hit-by-pitch, a single and a walk, and Alfredo Angarita followed by driving in two more runs with an RBI single that made it a 5-0 contest.
Blake Hickman replaced Dopico in the bottom of the second and retired the first batter he faced on a flyout. However, J.J. Matijevic followed with a line-drive home run to the right-field corner to extend Buies Creek's lead to 6-0.
In the bottom of the third, the Astros added three more runs to blow the game open. After Angarita and Duarte singled, Dawson hit a long three-run home run to right center to make it 9-0 Buies Creek.
However, in the top of the fourth inning, Basabe followed with a homer of his own, as he drove a solo shot onto the bridge beyond the right-field fence. The home run was the first hit of the game for the Dash against Buies Creek starter Gabriel Valdez (1-2), and it cut the deficit to eight.
After Yelmison Peralta entered the game in the bottom of the fourth and tossed a scoreless frame, the Dash plated another run in the top of the fifth. Mitch Roman led off the inning with a single to right field and advanced to third on Basabe's one-out single. Then, with Micker Adolfo batting, Valdez threw a wild pitch that allowed Roman to score.
In the bottom of the fifth inning, though, Buies Creek got the run right back, as Matijevic hit his second home run of the game onto the Nature's Select Knoll in left field to make it 10-2 Astros.
Matt Foster entered the game in the bottom of the sixth and tossed a perfect 1-2-3 inning, striking out two Astros in the process. Then, in the top of the seventh, the Dash proceeded to close the gap. Roman led off the inning with a triple to center field, and Booker followed with a home run to left field, his fourth of the season.
Winston-Salem proceeded to load the bases on singles by Basabe and Adolfo and a walk from Gavin Sheets, but the Dash rally came up short, as Yeyson Yrizarri fouled out to end the game.
Winston-Salem's series with Buies Creek will conclude at BB&T Ballpark on Thursday night at 7 p.m. Dash right-hander Dylan Cease (5-2, 3.12 ERA), the White Sox fifth-best prospect per MLB Pipeline, will get the start against Astros starter Brett Adcock (3-1, 2.00 ERA).
Thursday's game will be the first of seven Dash telecasts this season with NBC Sports Chicago. The contest will air live on the station, and it will be streamed on NBCSportsChicago.com/WatchLive. It will also be made available via the NBC Sports app on tablets and smartphones.
Meanwhile, the series finale will be broadcasted on WSJS Sports (600 AM & 101.5 FM), wsjssports.com, MiLB.tv and the TuneIn Radio App. Pregame radio coverage begins at 6:45 p.m.
Related TopicsAstrosBlake HickmanBuies CreekHPJoel BookerLuis basabeNTOsvaldo DurarteRonnie DawsonWS Dash
More in WS Dash
WARTHOGS CRUSH FOUR HOMERS IN 12-3 WIN OVER SALEM ON WEDNESDAY
Winston-Salem 12, Salem 3 W: Konnor Pilkington (4-9) L: Daniel Gonzalez (5-10) S: None...
DASH FALL IN WALK-OFF LOSS AT LYNCHBURG ON WEDNESDAY
Lynchburg 4, Winston-Salem 3 W: Yapson Gomez (2-6) L: Jacob Lindgren (1-1) S: None...
VARNELL, BIG FIFTH INNING PUSH RAYADOS PAST P-NATS ON SUNDAY
Winston-Salem 4, Potomac 1 W: Taylor Varnell (1-1) L: Jackson Tetreault (2-2) S: Will...
DASH HOLD ON FOR 8-7 WIN THURSDAY AT MYRTLE
MYRTLE BEACH, S.C. (Aug. 8, 2019) – Andrew Perez, Jacob Lindgren and Will Kincanon...
Sheets, Remillard Homer in Dash 12-4 loss to Astros
Lambert Registers Quality Start in Dash 4-0 Loss to P-Nats

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: Linux : Setting which php bin to use in CLI Hi i'm trying to use php command in linux. However I have two installations of php, one I got from the sudo-apt-get and one from a stack, Lappstack. Don't ask how I got there, but nevertheless i'm trying to execute php in CLI .
$ php file.php

it both works whichever php it points to but I want to use the php that I use in the stack.
when I try to execute :
$ which php

It returns :
/usr/bin/php

But I have to use the php I have in my lappstack which is in :
/home/userName/lappstack/php/bin

How do I change the php bin that my CLI php points to?

A: You can either have /home/userName/lappstack/php/bin first in your $PATH or use alias:

alias php='/home/userName/lappstack/php/bin/php'

A: You can replace the php in /usr/bin by yours like this:
sudo rm /usr/bin/php
sudo ln -s /home/userName/lappstack/php/bin/php /usr/bin/php

Hope this helps


text:
Central Maine Power Supports Pilot Program for Digital Inclusion and Intelligent Infrastructure
U.S. Sen. Angus King applauds selection of Maine Communities
AUGUSTA, Maine May 1, 2018 Central Maine Power Company, a subsidiary of AVANGRID Inc. (NYSE:AGR), is hailing the selection of Maine communities for a national pilot program to evaluate innovative ways to integrate ultra-high-speed internet with other utility infrastructure to promote digital inclusion, sustainable resource management and economic development. Among the five community partners the Post Road Foundation has selected for the nationwide pilot program are the City of Sanford; the Old Town Orono Fiber Corporation; and a collaboration of community groups in the Downeast region, including Eastern Maine Electric Cooperative and Downeast Broadband. Funding for the Post Road Foundation program, and related research at Harvard University, has been provided by The Rockefeller Foundation.
CMP's history of working with stakeholders to expand broadband service includes installation of fiber-optic cable under Penobscot Bay as part of a project to upgrade service to Islesboro. The energy company remains open to future collaboration with other rural communities that need better broadband access.
"Central Maine Power congratulates the Maine communities who have been selected by the Post Road Foundation to enhance the infrastructure necessary to advance Maine's rural economy, said CMP President and CEO Doug Herling. "We applaud the Post Road Foundation for its investment and look forward to working collaboratively on this important initiative."
Senator Angus King applauded the selection of the communities in Maine, saying, in part, "These public-private partnerships will build upon efforts to close the digital divide in regions in Maine that are struggling with slow connectivity and advance innovative approaches to deploy smart fiber networks " two important steps that will strengthen Maine's economy and infrastructure."
The Post Road Foundation's non-profit, research platform bridges the gap between communities and investors by exploring ways to reduce barriers to the development, financing, and deployment of sustainable, intelligent infrastructure, particularly in places lacking 21st century communications.
For inquiries, please contact Waide Warner at waide.warner@postroadfoundation.org or Seth Hoedl at shoedl@postroadfoundation.org.
About AVANGRID: AVANGRID, Inc. (NYSE: AGR) is a leading, sustainable energy company with $32 billion in assets and operations in 27 states. AVANGRID has two primary lines of business: Avangrid Networks and Avangrid Renewables. Avangrid Networks owns eight electric and natural gas utilities, serving 3.2 million customers in New York and New England. Avangrid Renewables owns and operates 7.1 gigawatts of electricity capacity, primarily through wind power, with a presence in 22 states across the United States. AVANGRID employs approximately 6,600 people. AVANGRID supports the U.N.'s Sustainability Development Goals, received a Climate Development Project climate score of A-, the top score received in the utilities sector, and has been recognized for two consecutive years by Ethical Boardroom as the North American utility with the "best corporate governance practices." For more information, visit www.avangrid.com.
About CMP: Central Maine Power Company (CMP) is a subsidiary of AVANGRID, Inc. As Maine's largest electricity transmission and distribution utility, CMP serves approximately 624,000 homes and businesses, representing about 80% of Maine's customer base. J.D. Power and Associates has ranked the company #1 in customer satisfaction seven times. For more information, visit www.cmpco.com.
Gail Rice
gail.rice@avangrid.com
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We are authorised to act on behalf of numerous flag administrations to verify that your vessels comply with MARPOL. Our involvement ranges from initial plan approval and on-board surveys to annual and renewal surveys to ensure compliance is maintained. We are also able to issue type approval certification for marine pollution prevention equipment and sewage treatment plants.
We closely monitor activities at IMO and IACS to enable us to better advise you and keep you up to date with forthcoming changes to the regulations and what they will mean to you. We also offer training courses to help you better understand the requirements.
The new regulations relate to STS transfers, and we have produced a plan and checklist to help operators to comply with MARPOL regulations governing the transfer of oil at sea, while meeting best-practice standards for safety and environmental protection. Ship-to-ship (STS) oil-cargo transfers at sea are a common feature of the tanker trades, and preventing spills and helping to ensure safety has long been an industry priority.
Clarification on NOx certification for dual fuel and gas-fuelled engines. IMO produced Guidance on the Application of Regulation 13 of MARPOL Annex VI Tier III Requirements to Dual Fuel and Gas-fuelled Engines, published as circular MEPC.1_Circ.854. See Class News No.10/2016 for further guidance.
IMO Resolution MEPC.248(67) introduced requirements for oil tankers for stability instruments which can verify intact and damage stability requirements. See Class News No.17/2015 for further guidance.
IMO Resolution MEPC.251(66) introduced Tier III requirements for NOx control to diesel engines. See Class News No.20/2015 for further guidance.
IMO Resolution MEPC.258(67) introduced changes to the IAPP Record of Construction format. See Class News No.09/2016 for further guidance.
IMO Resolution MEPC.266(68) introduced requirements for sludge piping to Regulation 12 of MARPOL Annex I. See Class News No.29/2016 for further guidance.
IMO Resolution MEPC.271(69) introduces requirements to record when engines change over from Tier II operation to Tier III operation on applicable ships entering Tier III ECAs.
IMO Resolution MEPC.274(69) and its corrigendum introduce changes to the format of the ISPP certificate relating to the introduction of the Baltic Sea Special Area.
IMO Resolution MEPC.275(69) postpones the introduction of the Baltic Sea Special Area requirements until 2019 for new passengers ships and 2021 for existing passenger ships. See Class News No.27/2015 and 06/17 for further guidance.
IMO Resolution MEPC.278(70) introduces new requirements for ships of ≥5000gt to collect and report ship fuel oil consumption data from calendar year 2019. See Class News No. 33/2017 for further guidance. See also information on EU MRV regulation here.
IMO Resolution MEPC.277(70) introduces requirements related to "E-waste", cargo residues, including the cargo hold washing water that are declared as "Harmful to Marine Environment" (HME)" and changes to the format of garbage record book. See Class News 05/2018 for further guidance.
Ships when operating outside the existing ECA for SOx emissions (Baltic, North Sea, North America & US Caribbean) any fuel oil used on board shall not exceed 0.50% sulphur content, under Regulation 14.1.3 of MARPOL Annex VI. For further information see our Sulphur 2020 webpage and Class News 08/2018: The 2020 IMO global sulphur limit.
IMO Resolution MEPC.305(73) modifies Regulation 14.1 so that ships when operating outside the existing ECA for SOx emissions (Baltic, North Sea, North America & US Caribbean) any fuel oil used or carried on board shall not exceed 0.50% sulphur content. For further information see our Sulphur 2020 webpage and Class News 02/2019: Preparation for 1 January 2020 - low sulphur fuel requirement.


For the county, we have a total of 3 records from 3 sites. First recorded in 1886.
VC61. Spurn, 9.7.1994 (BRS). NEW COUNTY RECORD.
VC64. Bellflask, 9.7.1999 (B&SM). NEW VICE-COUNTY RECORD.
2012 (CHF): We only have three records of this scarce species, the two above and an old unpublished (and probably unconfirmed) record from Birstwith in 1886. Several other scarce species which feed on traveller's joy occur at a low density in the county and this moth may be resident in very low numbers. The VC65 record mentioned in Beaumont 2002 is in fact in VC64 (as above).


One issue that has puzzled me is what role, if any, does theory play in modern chemistry, other than having a number of people writing papers. Of course some people are carrying out computations, but does any of their work influence other chemists in any way? Are they busy talking to themselves? The reason why this has struck me is that the latest "Chemistry World" has an article "Do hydrogen bonds have covalent character?" Immediately below is the explanation, "Scientists wrangle over disagreement between charge transfer measurements." My immediate reaction was, what exactly is meant by "covalent character" and "charge transfer"? I know what I think a covalent bond is, which is a bond formed by two electrons from two atoms pairing to form a wave function component with half the periodic time of the waves on the original free atom. I also accept the dative covalent bond, such as that in the BH3NH3 molecule, where two electrons come from the same atom, and where the resultant bond has a strength and length as if the two electrons originated from separate atoms. That is clearly not what is meant for the hydrogen bond, but the saviour is that word "character". What does that imply?
What puzzles me here is that on reading the article, there are no charge transfer measurements. What we have, instead, are various calculations based on models, and the argument is whether the model involves transfer of electrons. However, as far as I can make out, there is no observational evidence at all. In the BH3NH3 molecule, obviously the two electrons for the bond start from the nitrogen atom, but the resultant dipole moment does not indicate a whole electron is transferred, although we could say it is, and then sent back to form the bond. However, in that molecule we have a dipole moment of over 6 Debye units. What is the change of dipole moment in forming the hydrogen bond? If we want to argue for charge transfer, we should at least know that.
From my point of view, the hydrogen bond is essentially very weak, and is at least an order of magnitude less strong than similar covalent bonds. This would suggest that if there were charge transfer, it is relatively minor. Why would such a small effect not be simply due to polarization? With the molecule BH3NH3 it is generally accepted that the lone pair on the ammonia enters the orbital structure of the boron system, with both being tetrahedral in structure, more or less. The dipole moment is about 6 Debye units, which does not correspond to one electron fully transferring to the boron system. There is clear charge transfer and the bond is effectively covalent.
Now, if we then look at ammonia, do we expect the lone pair on the nitrogen to transfer itself to the hydrogen atom of another ammonia molecule to form this hydrogen bond? If it corresponded to the boron example, then we would expect a change of at least several Debye units but as far as I know, there is no such change of dipole moment that is not explicable in terms of it being a condensed system. The article states there are experimental data to support charge transfer, but what is it?
Back to my original problem with computational chemistry: what role, if any, does theory play in modern chemistry? In this article we see a statement such as the NBO method falls foul of "basis set superposition error". What exactly does that mean, and how many chemists appreciate exactly what it means? We have a disagreement where one is accused of focusing on energies, while they focus on charge density shifts. At least energies are measurable. What bothers me is that such arguments on whether different people use the same terminology differently is a bit like arguing about how many angels can dance on the head of a pin. What we need from theory is a reasonably clear statement of what it means, and a clear statement of what assumptions are made, and what part validation plays in the computations.


Nestled in the scenic Valley of 1000 Hills, The 1000 Hills Brewery forms part of the acclaimed 1000 Hills Chef School, where Advanced Students learn the art of craft beer brewing. The Brewery creatively crafts its brews with food and flavour in mind, experimenting with different styles and flavour combinations.
The Brewery is open to the public on the weekends, along with the school's on-site Deli which offers a delicious artisanal menu. Visitors can book free tours of the brewery between Friday to Sunday, where the secret of the brewing process is revealed. Complimentary tastings are included in the tour, and also available at The Deli if you're finding it hard to decide which brew is the one for you. Currently, there are five standard flavours on offer - The Cheerleader, The Graduate, The Dean, The Quarterback and The FES, all of which are available at The Deli and selected stockists.
If you're feeling rebellious, order The Rebel, a mystery brew exclusive to The Deli. This limited edition flavour is ever-changing - it can be anything from a blonde ale to a pilsner or milk stout - well worth a try.
Such a stunning place! Incredible experience to watch these youngsters (guess 18 - 24-year-olds) prepare gourmet meals and desserts. The tea and craft beer tasting was also an experience! Brilliant value for money with all ingredients hand made by the trainee chefs at Chef School. Will definitely be back! Superb!
The food was delicious but I have to commend the brewery on supplying one of the best IPA's I've had the pleasure of tasting. They have a great variety to choose from which you can have as a taster before selecting the one that you like. I am an avid craftbeer connoisseur and there's not many IPAs that have such a delicious well rounded mouthfeel!
We were greeted in the parking by a young chef fondly referred to as 'back leg' and courteously seated. Our order arrived and we tucked in. The craft beer called The Graduate is one of a number of beers brewed at the school and is a fantastic IPA (India Pale Ale ). 5 star is too few of a rating. 10 out of 10. We are definitely coming back.


was wondering if anyone experiences itchyness?? especially right after i put the taz all over my face, it gets itchy around my jawline.
im on my 8th week, and still breaking out horrible!
im on my 8th week, and still breaking out :( horrible!


This superbly equipped caravan is situated in one of the best spots on Devon Cliffs. Wth a panoramic seaview and a large veranda.
This superbly equipped caravan is situated on one of the best spots on Devon Cliffs; with a panoramic seaview and a large veranda you can see the beauty of the Devon Cliffs scenery.
It is a homely, well equipped caravan with outdoor furniture, 2 showers and toilets (1 en-suite). There is a TV and DVD player in the lounge, with freeview, and a TV in all bedrooms. All rooms have electric heaters.
Quilts and pillows are provided, but you will need to bring your own linen, or it can be hired on site.
There is plenty of parking space outside the caravan.
A deposit of £100 will secure your booking, which is non-refundable.
The balance of your holiday will be due 6 weeks prior to your holiday.
This is a superbly located holiday home.
Budleigh Salterton, Powderham Castle, Exmouth beach and town centre, World of Country Life.


TV and radio presenter Fearne Cotton wore a Olivia Rubin Spring 2010 dress to the Brit Awards Shortlist Party at the O2 Arena in London earlier this week.
She teamed the dress with a pair of tights from House Of Holland's Pretty Polly range with "Wanna Party" written up the back.
We're used to seeing Fearne in quirky pieces and although I'm not normally a fan of comedy accessories, these tights seemed event (and person) appropriate.
I love this shade of blue on Fearne, and really like how the black waistband cinches her in.
Fearne is a fan of this designer and we have seen her in Olivia Rubin before.
Red lips and curls completed her look.


I needed to write a PowerShell utility to create Exchange mailboxes for new users in Active Directory. The utility needed to create the mailboxes, use different databases, retention policies, and take users from several Organisational Units along with users in child OUs. This utility is available to download from the Microsoft TechNet Gallery, PowerShell Gallery and GitHub….


text:
WebMD says not in talks over a potential acquisition
Healthcare portal WebMD Health Corp said on Thursday it was not negotiating a sale of all or part of its business, a day after the Financial Times reported about talks over a potential deal.
WebMD's shares were down 6.8 percent at $49.53 in late morning trading after the company's statement, reversing from a near five-year high of $58.25 hit early in the session.
The company was said to be in talks with Walgreens Boots Alliance Inc and UnitedHealth Group Inc for the sale, the Financial Times reported, citing people familiar with the matter. (http://on.ft.com/1n0J0tM)
Early last year, the company collaborated with Walgreens on making available a wellness-coaching program on the Walgreens website, aimed at improving health and wellness.
The digital company might also choose to not push for a sale, after reviewing its options, the sources told the newspaper.
Shares of the company, which has a market value of about $2 billion, had gained 22 percent in 2015.
(Reporting by Sneha Teresa Johny and Rosmi Shaji in Bengaluru; Editing by Sunil Nair and Sriraj Kalluvila)
Women's blood pressure rises earlier in life than men's: Study
Press, public has varying opinions on 'Megxit': Report
US airports to screen passengers from China for new illness


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Copyright © 2019, Exto, Inc.


text:
    TwelveCraft make road.
    Written by Daniel Keep.

    Copyright 2013.
    Released under the MIT license.
  ]]

--[[
    Usage: make-road [-gravity] [-floor] [LENGTH]

    Note: LENGTH can also be a negative number indicating that the road should
    be the default length *minus* a given distance.  Useful for resuming an
    aborted run.
  ]]

local args = {...}
local VERSION = 0.6

local DEFAULT_LENGTH = 31
local CHECK_FLOOR = false

local EDGE_SLOT = 1
local PAVE_SLOT = 2
local FLOOR_SLOT = 15
local FUEL_SLOT = 16
local SEARCH_SLOT_FIRST = 3
local SEARCH_SLOT_LAST = 15

local GRAVITY_WAIT = 0
local YIELD_WAIT = 0.01
local DEFAULT_GRAVITY_WAIT = 0.4

local FORWARD = 0
local RIGHT = 1
local BACK = 2
local LEFT = 3

local t = turtle
local heading = 0

local length = DEFAULT_LENGTH

for i,arg in ipairs(args) do
    if arg == "-gravity" then
        GRAVITY_WAIT = DEFAULT_GRAVITY_WAIT
    elseif arg == "-floor" then
        CHECK_FLOOR = true
    elseif tonumber(arg) ~= nil then
        local n = tonumber(arg)
        if n < 0 then
            length = length + n
        else
            length = tonumber(arg)
        end
    else
        print("Usage: make-road [-gravity] [-floor] [LENGTH]")
        return
    end
end

print("make-road v", VERSION)

do
    local abort = false

    local fuelNeeded = 2 + length*5
    if CHECK_FLOOR then
        fuelNeeded = fuelNeeded + length*5*2
    end
    t.select(FUEL_SLOT)
    while t.getFuelLevel() < fuelNeeded do
        if not t.refuel(1) then
            print(string.format("Need fuel level of %d; currently have %d.",
                fuelNeeded, t.getFuelLevel()))
            abort = true
        end
    end

    local edgeNeeded = 2*length
    local edgeGot = t.getItemCount(EDGE_SLOT)
    t.select(EDGE_SLOT)
    for i=SEARCH_SLOT_FIRST, SEARCH_SLOT_LAST do
        if t.compareTo(i) then
            edgeGot = edgeGot + t.getItemCount(i)
        end
    end
    if edgeGot < edgeNeeded then
        print(string.format("Need %d edge blocks, have %d.",
            edgeNeeded, edgeGot))
        abort = true
    end

    local paveNeeded = 3*length
    local paveGot = t.getItemCount(PAVE_SLOT)
    t.select(PAVE_SLOT)
    for i=SEARCH_SLOT_FIRST, SEARCH_SLOT_LAST do
        if t.compareTo(i) then
            paveGot = paveGot + t.getItemCount(i)
        end
    end
    if paveGot < paveNeeded then
        print(string.format("Need %d paving blocks, have %d.",
            paveNeeded, paveGot))
        abort = true
    end

    if CHECK_FLOOR then
        local floorNeeded = 5*length
        local floorGot = t.getItemCount(FLOOR_SLOT)
        t.select(FLOOR_SLOT)
        for i=SEARCH_SLOT_FIRST, SEARCH_SLOT_LAST do
            if t.compareTo(i) then
                floorGot = floorGot + t.getItemCount(i)
            end
        end
        if floorGot < floorNeeded then
            print(string.format("WARNING: may need up to %d flooring blocks, "
                .. "have %d.", floorNeeded, floorGot))
            if floorGot == 0 then
                abort = true
            end
        end
    end

    if abort then return end
end

local function ccw()
    t.turnLeft()
    heading = (heading - 1) % 4
end

local function cw()
    t.turnRight()
    heading = (heading + 1) % 4
end

local function face(h)
    h = h % 4
    local diff = h - heading
    local dir = cw
    if (diff < 0 and diff >= -2) or diff == 3 then
        dir = ccw
    end
    while heading ~= h do dir() end
end

local function faceLeft()
    face(LEFT)
end

local function faceRight()
    face(RIGHT)
end

local function faceForward()
    face(FORWARD)
end

local function ensure(fn, ...)
    while not fn(...) do
        os.sleep(YIELD_WAIT)
    end
end

local function forward(dontClearDown)
    local noDown = dontClearDown or false
    while t.detect() do
        t.dig()
        os.sleep(GRAVITY_WAIT)
    end
    ensure(t.forward)
    while t.detectUp() do
        t.digUp()
        os.sleep(GRAVITY_WAIT)
    end
    if t.detectDown() and not dontClearDown then
        t.digDown()
    end
end

local function placeFromSlot(testSlot, dir)
    local slot = testSlot
    t.select(testSlot)
    for i=SEARCH_SLOT_FIRST, SEARCH_SLOT_LAST do
        if t.compareTo(i) then
            slot = i
            break
        end
    end
    t.select(slot)
    if t.compareDown() then
        -- Nothing to do
        return
    end
    if dir ~= nil then
        face(dir)
    end
    ensure(t.placeDown)
end

local function floor()
    if not CHECK_FLOOR then return end
    t.down()
    if not t.detectDown() then
        placeFromSlot(FLOOR_SLOT)
    end
    t.up()
end

local function edge(h)
    floor()
    placeFromSlot(EDGE_SLOT, h)
end

local function pave()
    floor()
    placeFromSlot(PAVE_SLOT)
end

local function times(n, fn, ...)
    for i=1,n do fn(...) end
end

faceLeft()
times(2, forward)

local dir = RIGHT

for i=1,length do
    os.sleep(YIELD_WAIT)
    t.digDown()
    edge(-dir)
    face(dir)
    times(3, function()
        forward()
        pave()
    end)
    forward()
    edge(dir)
    faceForward()
    forward(true)
    dir = -dir
end

face(dir)
times(2, forward, true)
faceForward()

redpajama_set_name: RedPajamaGithub


text:
The Unoriginal Life of Edward Zero
Edward Zero is the "Agency's" former best secret operative whose life in 2038 is at the hands of a child operative from the agency in which he was once the shining star. As he speaks to the child, he begins to explain his story about how one of the world's best agents fell from grace. From chapter to chapter, we see many of Zero's missions, ranging from returning a stolen bioweapon in the Gaza Strip to eliminating a former agent who is now the leader of a nonviolent community in Brazil. Along the way, we meet the people in Zero's life: Zizek, his trainer and mentor, Mina, his childhood love, Cooke, the new leader of the agency who is highly suspicious of Zero, and Ginsberg Nova, a masked man who is known as the leader of global terrorism who claims to know and remember Zero.
Zero Volume 1: "An Emergency"
What ensues in Zero Vol. 1: "An Emergency," is a relatively standard story of a rogue agent of the CIA or some fictional secret operative agency that is supposed to represent the CIA. For the most part, each checkpoint in Zero's escape from the agency is fairly predictable; Zero begins to break away from his stoic, machine-like, humanity-void countenance and protocol when he experiences emotional trauma. The first break happens when his love Mina is killed. The second break happens when he has to kill another rogue agent. Then, the major break happens when he simultaneously begins to ask questions about his parents, whom he cannot remember, and also realize that his agency is responsible for some bio-hazard material that has transformed people into lumpy, blob-like beings that look a little too much like a hybrid cross between Samantha Eggar in David Cronenberg's The Brood and the pustule-laden Baron Harkonnen in David Lynch's Dune.
I reference these two films because the blob creatures are only a minor example of a sad and disappointing trend in the Zero series: watered down motifs, plot devices, and characters taken directly from films. As a graphic novel, Zero is not entirely a failure. As I read it, I was moderately interested and was at least motivated enough to complete the volume. And from a visual perspective, there is some stunning artwork in the series, with each chapter illustrated by a different artist in order to add visual segmentation of the different phases of Edward Zero. However, upon completing the reading, I had an overwhelmingly unsettling feeling that what I had just read was a graphic novel reconstitution of pieces of films. After spending some time talking to Generoso about the volume, three films came up in our discussion: the Bourne trilogy, The Conversation, and Three Days of the Condor.
Zero takes plot devices and themes from these films and fails to do what they all do so brilliantly: create suspense and an overall feeling of cynicism toward the agency one is part of while creating a sympathetic central figure that the audience hopes will succeed. Like the Bourne series, the narrative of Zero has a semi-paternal relationship between Zizek (the trainer) and Zero, the agent/trainee. In addition, Zero begins to go rogue as he begins to question about his past which has been wiped from his memory, which is the identical to the motivations of Jason Bourne when he goes rogue. Like Joe Turner in Three Days of the Condor, Zero falls from the top of the agency when he gains prohibited knowledge of a secret operation. And, like Harry Caul in The Conversation, what leads to Zero's end is what he was himself.
Okay, so sure, as long as the story was engaging, I should not take too many points away from the graphic novel. But what makes Zero an unsatisfying read is that not only did it mimic narrative branches from some excellent films about espionage and secret operations but it also failed to combine these duplicated devices in a way that created suspense or allowed me to connect with Edward Zero as a character. Despite the small moments of human emotion that we see in Edward Zero, there is little to motivate the reader to sympathize with him and to desire to see him accomplish and triumph, which I feel is essential in any narrative where anyone leaves an affiliated organization and former friends and colleagues become enemies.
By the time I completed the first volume of Zero, I felt that I wished I had seen a film instead. There are intricacies in the espionage genre that just were not captured in Zero, despite the fact that it used material from some impeccable sources. Consequently, the failure of Zero as a graphic novel is even more upsetting because the story is both unoriginal, with identifiable pieces from other older material, and dull, failing to capture the paranoia, the suspense, and the constant desire to see the protagonist triumph over corruption and evil that make a betrayal, rebellion, or fall from grace story thought-provoking and alluring. Zero combines multiple motifs and themes used in the espionage genre, and yet, is unable to execute any one of them completely and successfully.
Zero is written by Ales Kot and is available via Image Comics.
Tags Ales Kot, Zero
Bovine Ska and Rocksteady 9/24/14: The Passing of Tito Simon
How to Make Lily's Version of Cantonese Tomato and Egg


On December 8, SDSN-Amazonia along with several partner organizations is organizing the Amazon Solutions Day at COP20 to advance the sustainable development agenda in the region. Event details are available here.
UNESCO has launched an online public consultation on their 2016 Global Monitoring Report (GMR) on "'Education, sustainability and the post-2015 development agenda" until January 28, 2015. Submit your comments here.
On November 20, 2014, SDSN and Center for International Relations and Sustainable Development (CIRSD) co-organized an conference on "Climate Change and the Green Economy" in Belgrade, Serbia. Read the event summary here.
On November 17, 2014, SDSN co-sponsored an event at Columbia University entitled Road to 2015: A Pivotal Year for Sustainable Development with keynote speakers on the four major development priorities of 2015: the Sustainable Development Goals (SDGs), Data Revolution, Financing, and COP21. Watch the presentations here.
On November 11, the Columbia Center on Sustainable Investment (CCSI), with SDSN and several partner organizations, held an expert roundtable to examine the lessons learned from efforts to improve the governance of natural resource investments, particularly in extractives and land. Read more here.
Laval University has also launched a new online course (in French) on sustainable development. Details are available here.
The Science and Technology Alliance for Global Sustainability (the Alliance) has recently announced the appointment of the Future Earth Engagement Committee with 15 members. Read more here.
Subscribe to receive monthly updates from SDSN.