This paper addresses the multi-view subspace clustering problem and proposes the self-paced enhanced low-rank tensor kernelized multi-view subspace clustering (SETKMC) method, which is based on two motivations: (1) singular values of the representations and multiple instances should be treated differently. The reasons are that larger singular values of the representations usually quantify the major information and should be less penalized; samples with different degrees of noise may have various reliability for clustering. (2) many existing methods may cause the degraded performance when multi-view features reside in different nonlinear subspaces. This is because they usually assumed that multiple features lie within the union of several linear subspaces. SETKMC integrates the nonconvex tensor norm, self-paced learning, and kernel trick into a unified model for multi-view subspace clustering. The nonconvex tensor norm imposes different weights on different singular values. The self-paced learning gradually involves instances from more reliable to less reliable ones while the kernel trick aims to handle the multi-view data in nonlinear subspaces. One iterative algorithm is proposed based on the alternating direction method of multipliers. Extensive results on seven real-world datasets show the effectiveness of the proposed SETKMC compared to fifteen state-of-the-art multi-view clustering methods.

Zero-shot learning (ZSL) aims to identify unseen classes with zero samples during training. Broadly speaking, present ZSL methods usually adopt class-level semantic labels and compare them with instance-level semantic predictions to infer unseen classes. However, we find that such existing models mostly produce imbalanced semantic predictions, i.e. these models could perform precisely for some semantics, but may not for others. To address the drawback, we aim to introduce an imbalanced learning framework into ZSL. However, we find that imbalanced ZSL has two unique challenges: (1) Its imbalanced predictions are highly correlated with the value of semantic labels rather than the number of samples as typically considered in the traditional imbalanced learning; (2) Different semantics follow quite different error distributions between classes. To mitigate these issues, we first formalize ZSL as an imbalanced regression problem which offers empirical evidences to interpret how semantic labels lead to imbalanced semantic predictions. We then propose a re-weighted loss termed Re-balanced Mean-Squared Error (ReMSE), which tracks the mean and variance of error distributions, thus ensuring rebalanced learning across classes. As a major contribution, we conduct a series of analyses showing that ReMSE is theoretically well established. Extensive experiments demonstrate that the proposed method effectively alleviates the imbalance in semantic prediction and outperforms many state-of-the-art ZSL methods.

Multiview clustering (MVC), which can dexterously uncover the underlying intrinsic clustering structures of the data, has been particularly attractive in recent years. However, previous methods are designed for either complete or incomplete multiview only, without a unified framework that handles both tasks simultaneously. To address this issue, we propose a unified framework to efficiently tackle both tasks in approximately linear complexity, which integrates tensor learning to explore the inter-view low-rankness and dynamic anchor learning to explore the intra-view low-rankness for scalable clustering (TDASC). Specifically, TDASC efficiently learns smaller view-specific graphs by anchor learning, which not only explores the diversity embedded in multiview data, but also yields approximately linear complexity. Meanwhile, unlike most current approaches that only focus on pair-wise relationships, the proposed TDASC incorporates multiple graphs into an inter-view low-rank tensor, which elegantly models the high-order correlations across views and further guides the anchor learning. Extensive experiments on both complete and incomplete multiview datasets clearly demonstrate the effectiveness and efficiency of TDASC compared with several state-of-the-art techniques.

Covariate shift assumption based domain adaptation approaches usually utilize only one common transformation to align marginal distributions and make conditional distributions preserved. However, one common transformation may cause loss of useful information, such as variances and neighborhood relationship in both source and target domain. To address this problem, we propose a novel method called homologous component analysis (HCA) where we try to find two totally different but homologous transformations to align distributions with side information and make conditional distributions preserved. As it is hard to find a closed form solution to the corresponding optimization problem, we solve them by means of the alternating direction minimizing method (ADMM) in the context of Stiefel manifolds. We also provide a generalization error bound for domain adaptation in semi-supervised case and two transformations can help to decrease this upper bound more than only one common transformation does. Extensive experiments on synthetic and real data show the effectiveness of the proposed method by comparing its classification accuracy with the state-of-the-art methods and numerical evidence on chordal distance and Frobenius distance shows that resulting optimal transformations are different.

Domain adaptation has proven to be successful in dealing with the case where training and test samples are drawn from two kinds of distributions, respectively. Recently, the second-order statistics alignment has gained significant attention in the field of domain adaptation due to its superior simplicity and effectiveness. However, researchers have encountered major difficulties with optimization, as it is difficult to find an explicit expression for the gradient. Moreover, the used transformation employed here does not perform dimensionality reduction. Accordingly, in this article, we prove that there exits some scaled LogDet metric that is more effective for the second-order statistics alignment than the Frobenius norm, and hence, we consider it for second-order statistics alignment. First, we introduce the two homologous transformations, which can help to reduce dimensionality and excavate transferable knowledge from the relevant domain. Second, we provide an explicit gradient expression, which is an important ingredient for optimization. We further extend the LogDet model from single-source domain setting to multisource domain setting by applying the weighted Karcher mean to the LogDet metric. Experiments on both synthetic and realistic domain adaptation tasks demonstrate that the proposed approaches are effective when compared with state-of-the-art ones.