Existing domain adaptation methods aim to reduce the distributional difference between the source and target domains and respect their specific discriminative information, by establishing the Maximum Mean Discrepancy (MMD) and the discriminative distances. However, they usually accumulate to consider those statistics and deal with their relationships by estimating parameters blindly. This paper theoretically proves two essential facts: 1) minimizing the MMD equals to maximize the source and target intra-class distances respectively but jointly minimize their variance with some implicit weights, so that the feature discriminability degrades; 2) the relationship between the intra-class and inter-class distances is as one falls, another rises. Based on this, we propose a novel discriminative MMD. On one hand, we consider the intra-class and inter-class distances alone to remove a redundant parameter, and the revealed weights provide their approximate optimal ranges. On the other hand, we design two different strategies to boost the feature discriminability: 1) we directly impose a trade-off parameter on the implicit intra-class distance in MMD to regulate its change; 2) we impose the similar weights revealed in MMD on inter-class distance and maximize it, then a balanced factor could be introduced to quantitatively leverage the relative importance between the feature transferability and its discriminability. The experiments on several benchmark datasets not only prove the validity of theoretical results but also demonstrate that our approach could perform better than the comparative state-of-art methods substantially.

It is always an attractive task to discover knowledge for various learning problems; however, this knowledge discovery and maintenance process usually suffers from noise, incompleteness or knowledge domain mismatch. Thus, robust knowledge discovery by removing the noisy features or samples, complementing incomplete data, and mitigating the distribution difference becomes the key. Along this line of research, low-rank modeling is widely-used to solve these challenges. This survey covers the topic of: (1) robust knowledge recovery, (2) robust knowledge transfer, (3) robust knowledge fusion, centered around several major applications. First of all, we deliver a unified formulation for robust knowledge discovery based on a given dataset. Second, we discuss robust knowledge transfer and fusion given multiple datasets with different knowledge flows, followed by practical challenges, model variations, and remarks. Finally, we highlight future research of robust knowledge discovery for incomplete, unbalance, large-scale data analysis. This would benefit AI community from literature review to future direction.

Consensus clustering fuses diverse basic partitions (i.e., clustering results obtained from conventional clustering methods) into an integrated one, which has attracted increasing attention in both academic and industrial areas due to its robust and effective performance. Tremendous research efforts have been made to thrive this domain in terms of algorithms and applications. Although there are some survey papers to summarize the existing literature, they neglect to explore the underlying connection among different categories. Differently, in this paper we aim to provide an embedding prospective to illustrate the consensus mechanism, which transfers categorical basic partitions to other representations (e.g., binary coding, spectral embedding, etc) for the clustering purpose. To this end, we not only unify two major categories of consensus clustering, but also build an intuitive connection between consensus clustering and graph embedding. Moreover, we elaborate several extensions of classical consensus clustering from different settings and problems. Beyond this, we demonstrate how to leverage consensus clustering to address other tasks, such as constrained clustering, domain adaptation, feature selection, and outlier detection. Finally, we conclude this survey with future work in terms of interpretability, learnability and theoretical analysis.

Temporal data clustering is a challenging task. Existing methods usually explore data self-representation strategy, which may hinder the clustering performance in insufficient or corrupted data scenarios. In real-world applications, we are easily accessible to a large amount of related labeled data. To this end, we propose a novel transferable subspace clustering approach by exploring useful information from relevant source data to enhance clustering performance in target temporal data. We manage to transform the original data into a shared low-dimensional and distinctive feature space by jointly seeking an effective domain-invariant projection. In this way, the well-labeled source knowledge can help obtain a more discriminative target representation. Moreover, a graph regularizer is designed to incorporate temporal information to preserve more sequence knowledge into the learned representation. Extensive experiments based on three human motion datasets illustrate that our approach is able to outperform state-of-the-art temporal data clustering methods.

Person re-identification (re-ID) is a fundamental task in automated video surveillance. In real-world visual surveillance systems, a person is often captured in quite low resolutions. So we often need to perform low-resolution person re-ID, where images captured by different cameras have great resolution divergences. Existing methods cope problem via some complicated and time-consuming strategies, making them less favorable in practice, and their performances are far from satisfactory. In this paper, we design a novel Discriminative Semi-coupled Projective Dictionary Learning (DSPDL) model to effectively and efficiently solve this problem. Specifically, we propose to jointly learn a pair of dictionaries and a mapping to bridge the gap across low(er) and high(er) resolution person images. Besides, we develop a novel graph regularizer to incorporate positive and negative image pair information in a parameterless fashion. Meanwhile, we adopt the efficient and powerful projective dictionary learning technique to boost the our efficiency. Experiments on three public datasets show the superiority of the proposed method to the state-of-the-art ones.

Identifying multi-view outliers is challenging because of the complex data distributions across different views. Existing methods cope this problem by exploiting pairwise constraints across different views to obtain new feature representations,based on which certain outlier score measurements are defined. Due to the use of pairwise constraint, it is complicated and time-consuming for existing methods to detect outliers from three or more views. In this paper, we propose a novel method capable of detecting outliers from any number of dataviews. Our method first learns latent discriminant representations for all view data and defines a novel outlier score function based on the latent discriminant representations. Specifically, we represent multi-view data by a global low-rank representation shared by all views and residual representations specific to each view. Through analyzing the view-specific residual representations of all views, we can get the outlier score for every sample. Moreover, we raise the problem of detectinga third type of multi-view outliers which are neglected by existing methods. Experiments on six datasets show our method outperforms the existing ones in identifying all types of multi-view outliers, often by large margins.

Recently the auto-encoder and its variants have demonstrated their promising results in extracting effective features. Specifically, its basic idea of encouraging the output to be as similar as input, ensures the learned representation could faithfully reconstruct the input data. However, one problem arises that not all hidden units are useful to compress the discriminative information while lots of units mainly contribute to represent the task-irrelevant patterns. In this paper, we propose a novel algorithm, Feature Selection Guided Auto-Encoder, which is a unified generative model that integrates feature selection and auto-encoder together. To this end, our proposed algorithm can distinguish the task-relevant units from the task-irrelevant ones to obtain most effective features for future classification tasks. Our model not only performs feature selection on learned high-level features, but also dynamically endows the auto-encoder to produce more discriminative units. Experiments on several benchmarks demonstrate our method's superiority over state-of-the-art approaches.

Multi-View Clustering (MVC) has garnered more attention recently since many real-world data are comprised of different representations or views. The key is to explore complementary information to benefit the clustering problem. In this paper, we present a deep matrix factorization framework for MVC, where semi-nonnegative matrix factorization is adopted to learn the hierarchical semantics of multi-view data in a layer-wise fashion. To maximize the mutual information from each view, we enforce the non-negative representation of each view in the final layer to be the same. Furthermore, to respect the intrinsic geometric structure in each view data, graph regularizers are introduced to couple the output representation of deep structures. As a non-trivial contribution, we provide the solution based on alternating minimization strategy, followed by a theoretical proof of convergence. The superior experimental results on three face benchmarks show the effectiveness of the proposed deep matrix factorization model.

Head pose estimation via embedding model has beendemonstrated its effectiveness from the recent works.However, most of the previous methods only focuson manifold relationship among poses, while overlookthe underlying global structure among subjects and poses.To build a robust and effective head pose estimator,we propose a novel Pose-dependent Low-Rank Embedding(PLRE) method, which is designed to exploita discriminative subspace to keep within-pose samplesclose while between-pose samples far away. Specifically,low-rank embedding is employed under the multitaskframework, where each subject can be naturallyconsidered as one task. Then, two novel terms are incorporatedto align multiple tasks to pursue a better posedependentembedding. One is the cross-task alignmentterm, aiming to constrain each low-rank coefficient toshare the similar structure. The other is pose-dependentgraph regularizer, which is developed to capture manifoldstructure of same pose cross different subjects. Experimentson databases CMU-PIE, MIT-CBCL, and extendedYaleB with different levels of random noise areconducted and six embedding model based baselinesare compared. The consistent superior results demonstratethe effectiveness of our proposed method.

Multi-view data is highly common nowadays, since various view-points and different sensors tend to facilitate better data representation. However, data from different views show a large divergence. Specifically, one sample lies in two kinds of structures, one is class structure and the other is view structure, which are intertwined with one another in the original feature space. To address this, we develop a Robust Multi-view Subspace Learning algorithm (RMSL) through dual low-rank decompositions, which desires to seek a low-dimensional view-invariant subspace for multi-view data. Through dual low-rank decompositions, RMSL aims to disassemble two intertwined structures from each other in the low-dimensional subspace. Furthermore, we develop two novel graph regularizers to guide dual low-rank decompositions in a supervised fashion. In this way, the semantic gap across different views would be mitigated so that RMSL can preserve more within-class information and reduce the influence of view variance to seek a more robust low-dimensional subspace. Extensive experiments on two multi-view benchmarks, e.g., face and object images, have witnessed the superiority of our proposed algorithm, by comparing it with the state-of-the-art algorithms.