You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Given labeled data represented by a binary matrix, we consider the task to derive a Boolean matrix factorization which identifies commonalities and specifications among the classes. While existing works focus on rank-one factorizations which are either specific or common to the classes, we derive class-specific alterations from common factorizations as well. Therewith, we broaden the applicability of our new method to datasets whose class-dependencies have a more complex structure. On the basis of synthetic and real-world datasets, we show on the one hand that our method is able to filter structure which corresponds to our model assumption, and on the other hand that our model assumption is justified in real-world application. Our method is parameter-free.

Cited Abstract(s):
[1]: Although tagging has become increasingly popular in online image and video sharing systems, tags are known to be noisy, ambiguous, incomplete and subjective. These factors can seriously affect the precision of a social tag-based web retrieval system. Therefore improving the precision performance of these social tag-based web retrieval systems has become an increasingly important research topic. To this end, we propose a shared subspace learning framework to leverage a secondary source to improve retrieval performance from a primary dataset. This is achieved by learning a shared subspace between the two sources under a joint Nonnegative Matrix Factorization in which the level of subspace sharing can be explicitly controlled. We derive an efficient algorithm for learning the factorization, analyze its complexity, and provide proof of convergence. We validate the framework on image and video retrieval tasks in which tags from the LabelMe dataset are used to improve image retrieval performance from a Flickr dataset and video retrieval performance from a YouTube dataset. This has implications for how to exploit and transfer knowledge from readily available auxiliary tagging resources to improve another social web retrieval system. Our shared subspace learning framework is applicable to a range of problems where one needs to exploit the strengths existing among multiple and heterogeneous datasets.

[2]: Nonnegative matrix factorization based methods provide one of the simplest and most effective approaches to text mining. However, their applicability is mainly limited to analyzing a single data source. In this chapter, we propose a novel joint matrix factorization framework which can jointly analyze multiple data sources by exploiting their shared and individual structures. The proposed framework is flexible to handle any arbitrary sharing configurations encountered in real world data. We derive an efficient algorithm for learning the factorization and show that its convergence is theoretically guaranteed. We demonstrate the utility and effectiveness of the proposed framework in two real-world applications—improving social media retrieval using auxiliary sources and cross-social media retrieval. Representing each social media source using their textual tags, for both applications, we show that retrieval performance exceeds the existing state-of-the-art techniques. The proposed solution provides a generic framework and can be applicable to a wider context in data mining wherever one needs to exploit mutual and individual knowledge present across multiple data sources.

[3]: Joint modeling of related data sources has the potential to improve various data mining tasks such as transfer learning, multitask clustering, information retrieval etc. However, diversity among various data sources might outweigh the advantages of the joint modeling, and thus may result in performance degradations. To this end, we propose a regularized shared subspace learning framework, which can exploit the mutual strengths of related data sources while being immune to the effects of the variabilities of each source. This is achieved by further imposing a mutual orthogonality constraint on the constituent subspaces which segregates the common patterns from the source specific patterns, and thus, avoids performance degradations. Our approach is rooted in nonnegative matrix factorization and extends it further to enable joint analysis of related data sources. Experiments performed using three real world data sets for both retrieval and clustering applications demonstrate the benefits of regularization and validate the effectiveness of the model. Our proposed solution provides a formal framework appropriate for jointly analyzing related data sources and therefore, it is applicable to a wider context in data mining.
For social media retrieval, introduce Joint Subspace Matrix Factorization (JSMF) [1] . Focusing on the two-class setting, they assume that data points (rows of the data matrix) emerge not only from discriminative but also from common subspaces. JSMF infers for a given nonnegative data matrix and ranks @math and @math a factorization as displayed in Fig. . Multiplicative updates minimize the weighted sum of class-wise computed RSS. In Regularized JSNMF (RJSNMF), a regularization term is used to prevent that shared feature vectors swap into discriminative subspaces and vice versa [3] . The arising optimization problem is solved by the method of Lagrange multipliers. Furthermore, a provisional method to determine the rank automatically is evaluated. However, this involves multiple runs of the algorithm with increasing rank of shared and discriminative subspaces, until the approximation error barely decreases. A pioneering extension to the multi-class case is provided in [2] .