You are presented with multiple paper abstracts, alongside the associated literature review and chapter titles. Given the provided information, you are going to do a literature review. Please generate a coherent literature review that synthesizes the content, draws connections between different works, highlights major findings, and identifies any gaps in the existing research.

Literature Review Title: A survey on heterogeneous transfer learning 
Chapter Title:  SHFR 
1. Abstract of Cited Paper (BIB001):  One of the most important issues in machine learning is whether one can improve the performance of a supervised learning algorithm by including unlabeled data. Methods that use both labeled and unlabeled data are generally referred to as semi-supervised learning. Although a number of such methods are proposed, at the current stage, we still don't have a complete understanding of their effectiveness. This paper investigates a closely related problem, which leads to a novel approach to semi-supervised learning. Specifically we consider learning predictive structures on hypothesis spaces (that is, what kind of classifiers have good predictive power) from multiple learning tasks. We present a general framework in which the structural learning problem can be formulated and analyzed theoretically, and relate it to learning with unlabeled data. Under this framework, algorithms for structural learning will be proposed, and computational issues will be investigated. Experiments will be given to demonstrate the effectiveness of the proposed algorithms in the semi-supervised learning setting. 
2. Abstract of Cited Paper (BIB002):  When large multivariate datasets are analyzed, it is often desirable to reduce their dimensionality. Principal component analysis is one technique for doing this. It replaces the p original variables by a smaller number, q, of derived variables, the principal components, which are linear combinations of the original variables. Often, it is possible to retain most of the variability in the original variables with q very much smaller than p. Despite its apparent simplicity, principal component analysis has a number of subtleties, and it has many uses and extensions. A number of choices associated with the technique are briefly discussed, namely, covariance or correlation, how many components, and different normalization constraints, as well as confusion with factor analysis. Various uses and extensions are outlined. ::: ::: ::: Keywords: ::: ::: dimension reduction; ::: factor analysis; ::: multivariate analysis; ::: variance maximization 
3. Abstract of Cited Paper (BIB003):  Suppose x is an unknown vector in Ropfm (a digital image or signal); we plan to measure n general linear functionals of x and then reconstruct. If x is known to be compressible by transform coding with a known transform, and we reconstruct via the nonlinear procedure defined here, the number of measurements n can be dramatically smaller than the size m. Thus, certain natural classes of images with m pixels need only n=O(m1/4log5/2(m)) nonadaptive nonpixel samples for faithful recovery, as opposed to the usual m pixel samples. More specifically, suppose x has a sparse representation in some orthonormal basis (e.g., wavelet, Fourier) or tight frame (e.g., curvelet, Gabor)-so the coefficients belong to an lscrp ball for 0<ples1. The N most important coefficients in that expansion allow reconstruction with lscr2 error O(N1/2-1p/). It is possible to design n=O(Nlog(m)) nonadaptive measurements allowing reconstruction with accuracy comparable to that attainable with direct knowledge of the N most important coefficients. Moreover, a good approximation to those N important coefficients is extracted from the n measurements by solving a linear program-Basis Pursuit in signal processing. The nonadaptive measurements have the character of "random" linear combinations of basis/frame elements. Our results use the notions of optimal recovery, of n-widths, and information-based complexity. We estimate the Gel'fand n-widths of lscrp balls in high-dimensional Euclidean space in the case 0<ples1, and give a criterion identifying near- optimal subspaces for Gel'fand n-widths. We show that "most" subspaces are near-optimal, and show that convex optimization (Basis Pursuit) is a near-optimal way to extract information derived from these near-optimal subspaces 
4. Abstract of Cited Paper (BIB004):  We propose a manifold alignment based approach for heterogeneous domain adaptation. A key aspect of this approach is to construct mappings to link different feature spaces in order to transfer knowledge across domains. The new approach can reuse labeled data from multiple source domains in a target domain even in the case when the input domains do not share any common features or instances. As a pre-processing step, our approach can also be combined with existing domain adaptation approaches to learn a common feature space for all input domains. This paper extends existing manifold alignment approaches by making use of labels rather than correspondences to align the manifolds. This extension significantly broadens the application scope of manifold alignment, since the correspondence relationship required by existing alignment approaches is hard to obtain in many applications. 
5. Abstract of Cited Paper (BIB005):  In real-world applications, “what you saw” during training is often not “what you get” during deployment: the distribution and even the type and dimensionality of features can change from one dataset to the next. In this paper, we address the problem of visual domain adaptation for transferring object models from one dataset or visual domain to another. We introduce ARC-t, a flexible model for supervised learning of non-linear transformations between domains. Our method is based on a novel theoretical result demonstrating that such transformations can be learned in kernel space. Unlike existing work, our model is not restricted to symmetric transformations, nor to features of the same type and dimensionality, making it applicable to a significantly wider set of adaptation scenarios than previous methods. Furthermore, the method can be applied to categories that were not available during training. We demonstrate the ability of our method to adapt object recognition models under a variety of situations, such as differing imaging conditions, feature types and codebooks. 
6. Abstract of Cited Paper (BIB006):  We propose a new learning method for heterogeneous domain adaptation (HDA), in which the data from the source domain and the target domain are represented by heterogeneous features with different dimensions. Using two different projection matrices, we first transform the data from two domains into a common subspace in order to measure the similarity between the data from two domains. We then propose two new feature mapping functions to augment the transformed data with their original features and zeros. The existing learning methods (e.g., SVM and SVR) can be readily incorporated with our newly proposed augmented feature representations to effectively utilize the data from both domains for HDA. Using the hinge loss function in SVM as an example, we introduce the detailed objective function in our method called Heterogeneous Feature Augmentation (HFA) for a linear case and also describe its kernelization in order to efficiently cope with the data with very high dimensions. Moreover, we also develop an alternating optimization algorithm to effectively solve the nontrivial optimization problem in our HFA method. Comprehensive experiments on two benchmark datasets clearly demonstrate that HFA outperforms the existing HDA methods. 
7. Abstract of Cited Paper (BIB007):  In this paper, we present an efficient multi-class heterogeneous domain adaptation method, where data from source and target domains are represented by heterogeneous features of different dimensions. Specifically, we propose to reconstruct a sparse feature transformation matrix to map the weight vector of classifiers learned from the source domain to the target domain. We cast this learning task as a compressed sensing problem, where each binary classifier induced from multiple classes can be deemed as a measurement sensor. Based on the compressive sensing theory, the estimation error of the transformation matrix decreases with the increasing number of classifiers. Therefore, to guarantee reconstruction performance, we construct sufficiently many binary classifiers based on the error correcting output coding. Extensive experiments are conducted on both a toy dataset and three real-world datasets to verify the superiority of our proposed method over existing state-of-the-art HDA methods in terms of prediction accuracy.

Literature Review:
Zhou et al. BIB008 proposed a method for HDA tasks when more than two classes are present. The proposed method is called Sparse Heterogeneous Feature Representation (SHFR) and it aims to solve the HDA problem through a sparse feature transformation matrix G. This is an asymmetric transformation to map the weight vectors learned from the binary classifiers of the source domain (as multi-class problems are commonly decomposed into multiple binary classifiers) to those of the target. The transformation G, is learned using multi-task learning from BIB002 and the goal is to minimize the distance between the weight vectors as to reduce the difference between the domains after transformation. In other words, both the source and target have assigned weight vectors to their classifiers and a transformation metric is constructed which minimizes the difference between the transformed source and target vectors. Learning this feature mapping is based on two assumptions: (1) the feature mapping G is highly sparse and (2) the transformation is class-invariant meaning all classes share the same mapping. This sparse, classinvariant transformation helps reduce bias of weak binary classifiers and improve overall performance. The learning task is conducted as a compressed sensing BIB004 problem (CS). Through CS theory, it can be shown that the estimation error of the transformation matrix decreases with an increased number of classifiers. The issue becomes how to create enough binary classifiers for optimal performance without making redundant, extra classifiers. The method proposes using the Error Correcting Output Codes BIB001 (ECOC) scheme to generate the binary classifiers. This method increases the robustness and accuracy of SHFR as it uses a voting scheme for prediction. This is particularly useful as not all the learned binary target classifiers will have high predictive capabilities due to limited labeled training data. As long as there are more correct classifiers than incorrect, then the prediction will be accurate. Linear SVM's are used during the learning process and are trained using the target and transformed source. In the study, experiments were performed for text document classification, two being cross-lingual and one being cross-view. The proposed method was compared with DAMA BIB005 , ARC-t BIB006 , HFA BIB007 , standard SVM trained using only target data using one-vs-one and one-vs-all strategy for multi-class classification, and SHFR using one-vs-one as to test the ECOC scheme. Principal Component Analysis BIB003 (PCA) was used to reduce the number of dimensions as the baseline methods cannot handle such high-dimensional features. The proposed method SHFR with ECOC performed best for all tests and demonstrated to be an effective method for multi-class HDA.