Robustness to noises, outliers, and corruptions is an important issue in linear dimensionality reduction. Since the sample-specific corruptions and outliers exist, the class-special structure or the local geometric structure is destroyed, and thus, many existing methods, including the popular manifold learning- based linear dimensionality methods, fail to achieve good performance in recognition tasks. In this paper, we focus on the unsupervised robust linear dimensionality reduction on corrupted data by introducing the robust low-rank representation (LRR). Thus, a robust linear dimensionality reduction technique termed low-rank embedding (LRE) is proposed in this paper, which provides a robust image representation to uncover the potential relationship among the images to reduce the negative influence from the occlusion and corruption so as to enhance the algorithm's robustness in image feature extraction. LRE searches the optimal LRR and optimal subspace simultaneously. The model of LRE can be solved by alternatively iterating the argument Lagrangian multiplier method and the eigendecomposition. The theoretical analysis, including convergence analysis and computational complexity, of the algorithms is presented. Experiments on some well-known databases with different corruptions show that LRE is superior to the previous methods of feature extraction, and therefore, it indicates the robustness of the proposed method. The code of this paper can be downloaded from http://www.scholat.com/laizhihui.

As a popular dimensionality reduction method, nonnegative matrix factorization (NMF) has been widely used in image classification. However, the NMF does not consider discriminant information from the data themselves. In addition, most NMF-based methods use the Euclidean distance as a metric, which is sensitive to noise or outliers in data. To solve these problems, in this paper, we introduce structural incoherence and low-rank to NMF and propose a novel nonnegative factorization method, called structurally incoherent low-rank NMF (SILR-NMF), in which we jointly consider structural incoherence and low-rank properties of data for image classification. For the corrupted data, we use the L ₁ norm as a constraint to ensure the noise is sparse. SILR-NMF learns a clean data matrix from the noisy data by low-rank learning. As a result, the SILR-NMF can capture the global structure information of the data, which is more robust than local information to noise. By introducing the structural incoherence of the learned clean data, SILR-NMF ensures the clean data points from different classes are as independent as possible. To verify the performance of the proposed method, extensive experiments are conducted on six image databases. The experimental results demonstrate that our proposed method has substantial gain over existing NMF approaches.

As one of the most prevalent branches of transfer learning, domain adaptation is dedicated to generalizing the knowledge of a source domain to a target domain to perform machine learning tasks. In domain adaptation, the key strategy is to overcome the shift between different domains and learn shared features with domain invariance. However, most existing methods focus on extracting the common features of the source and target domains, and do not consider the shift problem of class center in the target domain caused by this process. Specifically, when we align the domain distributions, we often ignore the inherent feature attributes of the data, or under the guidance of false pseudo-labels, cause the target domain data to be far away from the class center after projection. This is not conducive to classification task. To address these problems, in this study, we propose a novel domain adaptation method, referred to as discriminative invariant alignment (DIA), for image representation. DIA enriches the knowledge matrix by combining the class discriminative information of the source domain and local data structure information of the target domain into a new framework. By introducing the maximum margin criterion of the source domain, the classification boundaries are expanded. To verify the performance of the proposed method, we compared DIA with several state-of-the-art methods on five benchmark databases. The experimental results show that DIA is superior to the state-of-the-art methods.

Nonnegative matrix factorization (NMF), which aims at obtaining the nonnegative low-dimensional representation of data, has received wide attention. To obtain more effective nonnegative discriminant bases from the original NMF, in this paper, a novel method called nonnegative discriminant matrix factorization (NDMF) is proposed for image classification. NDMF integrates the nonnegative constraint, orthogonality, and discriminant information in the objective function. NDMF considers the incoherent information of both factors in standard NMF and is proposed to enhance the discriminant ability of the learned base matrix. NDMF projects the low-dimensional representation of the subspace of the base matrix to regularize the NMF for discriminant subspace learning. Based on the Euclidean distance metric and the generalized Kullback-Leibler (KL) divergence, two kinds of iterative algorithms are presented to solve the optimization problem. The between- and within-class scatter matrices are divided into positive and negative parts for the update rules and the proofs of the convergence are also presented. Extensive experimental results demonstrate the effectiveness of the proposed method in comparison with the state-of-the-art discriminant NMF algorithms.

2-D neighborhood preserving projection (2DNPP) uses 2-D images as feature input instead of 1-D vectors used by neighborhood preserving projection (NPP). 2DNPP requires less computation time than NPP. However, both NPP and 2DNPP use the L₂ norm as a metric, which is sensitive to noise in data. In this paper, we proposed a novel NPP method called low-rank 2DNPP (LR-2DNPP). This method divided the input data into a component part that encoded low-rank features, and an error part that ensured the noise was sparse. Then, a nearest neighbor graph was learned from the clean data using the same procedure as 2DNPP. To ensure that the features learned by LR-2DNPP were optimal for classification, we combined the structurally incoherent learning and low-rank learning with NPP to form a unified model called discriminative LR-2DNPP (DLR-2DNPP). By encoding the structural incoherence of the learned clean data, DLR-2DNPP could enhance the discriminative ability for feature extraction. Theoretical analyses on the convergence and computational complexity of LR-2DNPP and DLR-2DNPP were presented in details. We used seven public image databases to verify the performance of the proposed methods. The experimental results showed the effectiveness of our methods for robust image representation.

As a branch of transfer learning, domain adaptation leverages useful knowledge from a source domain to a target domain for solving target tasks. Most of the existing domain adaptation methods focus on how to diminish the conditional distribution shift and learn invariant features between different domains. However, two important factors are overlooked by most existing methods: 1) the transferred features should be not only domain invariant but also discriminative and correlated, and 2) negative transfer should be avoided as much as possible for the target tasks. To fully consider these factors in domain adaptation, we propose a guided discrimination and correlation subspace learning (GDCSL) method for cross-domain image classification. GDCSL considers the domain-invariant, category-discriminative, and correlation learning of data. Specifically, GDCSL introduces the discriminative information associated with the source and target data by minimizing the intraclass scatter and maximizing the interclass distance. By designing a new correlation term, GDCSL extracts the most correlated features from the source and target domains for image classification. The global structure of the data can be preserved in GDCSL because the target samples are represented by the source samples. To avoid negative transfer issues, we use a sample reweighting method to detect target samples with different confidence levels. A semi-supervised extension of GDCSL (Semi-GDCSL) is also proposed, and a novel label selection scheme is introduced to ensure the correction of the target pseudo-labels. Comprehensive and extensive experiments are conducted on several cross-domain data benchmarks. The experimental results verify the effectiveness of the proposed methods over state-of-the-art domain adaptation methods.