Guided Discrimination and Correlation Subspace Learning for Domain Adaptation.

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.

Canonical Correlation Analysis With Low-Rank Learning for Image Representation.

As a multivariate data analysis tool, canonical correlation analysis (CCA) has been widely used in computer vision and pattern recognition. However, CCA uses Euclidean distance as a metric, which is sensitive to noise or outliers in the data. Furthermore, CCA demands that the two training sets must have the same number of training samples, which limits the performance of CCA-based methods. To overcome these limitations of CCA, two novel canonical correlation learning methods based on low-rank learning are proposed in this paper for image representation, named robust canonical correlation analysis (robust-CCA) and low-rank representation canonical correlation analysis (LRR-CCA). By introducing two regular matrices, the training sample numbers of the two training datasets can be set as any values without any limitation in the two proposed methods. Specifically, robust-CCA uses low-rank learning to remove the noise in the data and extracts the maximization correlation features from the two learned clean data matrices. The nuclear norm and L1 -norm are used as constraints for the learned clean matrices and noise matrices, respectively. LRR-CCA introduces low-rank representation into CCA to ensure that the correlative features can be obtained in low-rank representation. To verify the performance of the proposed methods, five publicly image databases are used to conduct extensive experiments. The experimental results demonstrate the proposed methods outperform state-of-the-art CCA-based and low-rank learning methods.

Weighted Correlation Embedding Learning for Domain Adaptation.

Domain adaptation leverages rich knowledge from a related source domain so that it can be used to perform tasks in a target domain. For more knowledge to be obtained under relaxed conditions, domain adaptation methods have been widely used in pattern recognition and image classification. However, most of the existing domain adaptation methods only consider how to minimize different distributions of the source and target domains, which neglects what should be transferred for a specific task and suffers negative transfer by distribution outliers. To address these problems, in this paper, we propose a novel domain adaptation method called weighted correlation embedding learning (WCEL) for image classification. In the WCEL approach, we seamlessly integrated correlation learning, graph embedding, and sample reweighting into a unified learning model. Specifically, we extracted the maximum correlated features from the source and target domains for image classification tasks. In addition, two graphs were designed to preserve the discriminant information from interclass samples and neighborhood relations in intraclass samples. Furthermore, to prevent the negative transfer problem, we developed an efficient sample reweighting strategy to predict the target with different confidence levels. To verify the performance of the proposed method in image classification, extensive experiments were conducted with several benchmark databases, verifying the superiority of the WCEL method over other state-of-the-art domain adaptation algorithms.

Low-rank discriminative regression learning for image classification.

As a famous multivariable analysis technique, regression methods, such as ridge regression, are widely used for image representation and dimensionality reduction. However, the metric of ridge regression and its variants is always the Frobenius norm (F-norm), which is sensitive to outliers and noise in data. At the same time, the performance of the ridge regression and its extensions is limited by the class number of the data. To address these problems, we propose a novel regression learning method which named low-rank discriminative regression learning (LDRL) for image representation. LDRL assumes that the input data is corrupted and thus the L1 norm can be used as a sparse constraint on the noised matrix to recover the clean data for regression, which can improve the robustness of the algorithm. Due to learn a novel project matrix that is not limited by the number of classes, LDRL is suitable for classifying the data set no matter whether there is a small or large number of classes. The performance of the proposed LDRL is evaluated on six public image databases. The experimental results prove that LDRL obtains better performance than existing regression methods.

Robust Flexible Preserving Embedding.

Neighborhood preserving embedding (NPE) has been proposed to encode overall geometry manifold embedding information. However, the class-special structure of the data is destroyed by noise or outliers existing in the data. To address this problem, in this article, we propose a novel embedding approach called robust flexible preserving embedding (RFPE). First, RFPE recovers the noisy data by low-rank learning and obtains clean data. Then, the clean data are used to learn the projection matrix. In this way, the projective learning is totally unaffected by noise or outliers. By encoding a flexible regularization term, RFPE can keep the property of the data points with a nonlinear manifold and be more flexible. RFPE searches the optimal projective subspace for feature extraction. In addition, we also extend the proposed RFPE to a kernel case and propose kernel RFPE (KRFPE). Extensive experiments on six public image databases show the superiority of the proposed methods over other state-of-the-art methods.

Low-Rank 2-D Neighborhood Preserving Projection for Enhanced Robust Image Representation.

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 L 2 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.

Structurally Incoherent Low-Rank Nonnegative Matrix Factorization for Image Classification.

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 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.

Low-Rank Preserving Projections.

As one of the most popular dimensionality reduction techniques, locality preserving projections (LPP) has been widely used in computer vision and pattern recognition. However, in practical applications, data is always corrupted by noises. For the corrupted data, samples from the same class may not be distributed in the nearest area, thus LPP may lose its effectiveness. In this paper, it is assumed that data is grossly corrupted and the noise matrix is sparse. Based on these assumptions, we propose a novel dimensionality reduction method, named low-rank preserving projections (LRPP) for image classification. LRPP learns a low-rank weight matrix by projecting the data on a low-dimensional subspace. We use the L21 norm as a sparse constraint on the noise matrix and the nuclear norm as a low-rank constraint on the weight matrix. LRPP keeps the global structure of the data during the dimensionality reduction procedure and the learned low rank weight matrix can reduce the disturbance of noises in the data. LRPP can learn a robust subspace from the corrupted data. To verify the performance of LRPP in image dimensionality reduction and classification, we compare LRPP with the state-of-the-art dimensionality reduction methods. The experimental results show the effectiveness and the feasibility of the proposed method with encouraging results.