Graph-based Semi-supervised Learning: Algorithms and Applications.

114 p.Graph-based semi-supervised learning have attracted large numbers of researchers and it is an important part of semi-supervised learning. Graph construction and semi-supervised embedding are two main steps in graph-based semi-supervised learning algorithms. In this thesis, we proposed two graph construction algorithms and two semi-supervised embedding algorithms. The main work of this thesis is summarized as follows:1. A new graph construction algorithm named Graph construction based on self-representativeness and Laplacian smoothness (SRLS) and several variants are proposed. Researches show that the coefficients obtained by data representation algorithms reflect the similarity between data samples and can be considered as a measurement of the similarity. This kind of measurement can be used for the weights of the edges between data samples in graph construction. Each column of the coefficient matrix obtained by data self-representation algorithms can be regarded as a new representation of original data. The new representations should have common features as the original data samples. Thus, if two data samples are close to each other in the original space, the corresponding representations should be highly similar. This constraint is called Laplacian smoothness.SRLS graph is based on l2-norm minimized data self-representation and Laplacian smoothness. Since the representation matrix obtained by l2 minimization is dense, a two phrase SRLS method (TPSRLS) is proposed to increase the sparsity of graph matrix. By extending the linear space to Hilbert space, two kernelized versions of SRLS are proposed. Besides, a direct solution to kernelized SRLS algorithm is also introduced.2. A new sparse graph construction algorithm named Sparse graph with Laplacian smoothness (SGLS) and several variants are proposed. SGLS graph algorithm is based on sparse representation and use Laplacian smoothness as a constraint (SGLS). A kernelized version of the SGLS algorithm and a direct solution to kernelized SGLS algorithm are also proposed. 3. SPP is a successful unsupervised learning method. To extend SPP to a semi-supervised embedding method, we introduce the idea of in-class constraints in CGE into SPP and propose a new semi-supervised method for data embedding named Constrained Sparsity Preserving Embedding (CSPE).4. The weakness of CSPE is that it cannot handle the new coming samples which means a cascade regression should be performed after the non-linear mapping is obtained by CSPE over the whole training samples. Inspired by FME, we add a regression term in the objective function to obtain an approximate linear projection simultaneously when non-linear embedding is estimated and proposed Flexible Constrained Sparsity Preserving Embedding (FCSPE).Extensive experiments on several datasets (including facial images, handwriting digits images and objects images) prove that the proposed algorithms can improve the state-of-the-art results

The Role of Riemannian Manifolds in Computer Vision: From Coding to Deep Metric Learning

A diverse number of tasks in computer vision and machine learning enjoy from representations of data that are compact yet discriminative, informative and robust to critical measurements. Two notable representations are offered by Region Covariance Descriptors (RCovD) and linear subspaces which are naturally analyzed through the manifold of Symmetric Positive Definite (SPD) matrices and the Grassmann manifold, respectively, two widely used types of Riemannian manifolds in computer vision. As our first objective, we examine image and video-based recognition applications where the local descriptors have the aforementioned Riemannian structures, namely the SPD or linear subspace structure. Initially, we provide a solution to compute Riemannian version of the conventional Vector of Locally aggregated Descriptors (VLAD), using geodesic distance of the underlying manifold as the nearness measure. Next, by having a closer look at the resulting codes, we formulate a new concept which we name Local Difference Vectors (LDV). LDVs enable us to elegantly expand our Riemannian coding techniques to any arbitrary metric as well as provide intrinsic solutions to Riemannian sparse coding and its variants when local structured descriptors are considered. We then turn our attention to two special types of covariance descriptors namely infinite-dimensional RCovDs and rank-deficient covariance matrices for which the underlying Riemannian structure, i.e. the manifold of SPD matrices is out of reach to great extent. %Generally speaking, infinite-dimensional RCovDs offer better discriminatory power over their low-dimensional counterparts. To overcome this difficulty, we propose to approximate the infinite-dimensional RCovDs by making use of two feature mappings, namely random Fourier features and the Nystrom method. As for the rank-deficient covariance matrices, unlike most existing approaches that employ inference tools by predefined regularizers, we derive positive definite kernels that can be decomposed into the kernels on the cone of SPD matrices and kernels on the Grassmann manifolds and show their effectiveness for image set classification task. Furthermore, inspired by attractive properties of Riemannian optimization techniques, we extend the recently introduced Keep It Simple and Straightforward MEtric learning (KISSME) method to the scenarios where input data is non-linearly distributed. To this end, we make use of the infinite dimensional covariance matrices and propose techniques towards projecting on the positive cone in a Reproducing Kernel Hilbert Space (RKHS). We also address the sensitivity issue of the KISSME to the input dimensionality. The KISSME algorithm is greatly dependent on Principal Component Analysis (PCA) as a preprocessing step which can lead to difficulties, especially when the dimensionality is not meticulously set. To address this issue, based on the KISSME algorithm, we develop a Riemannian framework to jointly learn a mapping performing dimensionality reduction and a metric in the induced space. Lastly, in line with the recent trend in metric learning, we devise end-to-end learning of a generic deep network for metric learning using our derivation

Graph-based Semi-supervised Learning: Algorithms and Applications.

114 p.Graph-based semi-supervised learning have attracted large numbers of researchers and it is an important part of semi-supervised learning. Graph construction and semi-supervised embedding are two main steps in graph-based semi-supervised learning algorithms. In this thesis, we proposed two graph construction algorithms and two semi-supervised embedding algorithms. The main work of this thesis is summarized as follows:1. A new graph construction algorithm named Graph construction based on self-representativeness and Laplacian smoothness (SRLS) and several variants are proposed. Researches show that the coefficients obtained by data representation algorithms reflect the similarity between data samples and can be considered as a measurement of the similarity. This kind of measurement can be used for the weights of the edges between data samples in graph construction. Each column of the coefficient matrix obtained by data self-representation algorithms can be regarded as a new representation of original data. The new representations should have common features as the original data samples. Thus, if two data samples are close to each other in the original space, the corresponding representations should be highly similar. This constraint is called Laplacian smoothness.SRLS graph is based on l2-norm minimized data self-representation and Laplacian smoothness. Since the representation matrix obtained by l2 minimization is dense, a two phrase SRLS method (TPSRLS) is proposed to increase the sparsity of graph matrix. By extending the linear space to Hilbert space, two kernelized versions of SRLS are proposed. Besides, a direct solution to kernelized SRLS algorithm is also introduced.2. A new sparse graph construction algorithm named Sparse graph with Laplacian smoothness (SGLS) and several variants are proposed. SGLS graph algorithm is based on sparse representation and use Laplacian smoothness as a constraint (SGLS). A kernelized version of the SGLS algorithm and a direct solution to kernelized SGLS algorithm are also proposed. 3. SPP is a successful unsupervised learning method. To extend SPP to a semi-supervised embedding method, we introduce the idea of in-class constraints in CGE into SPP and propose a new semi-supervised method for data embedding named Constrained Sparsity Preserving Embedding (CSPE).4. The weakness of CSPE is that it cannot handle the new coming samples which means a cascade regression should be performed after the non-linear mapping is obtained by CSPE over the whole training samples. Inspired by FME, we add a regression term in the objective function to obtain an approximate linear projection simultaneously when non-linear embedding is estimated and proposed Flexible Constrained Sparsity Preserving Embedding (FCSPE).Extensive experiments on several datasets (including facial images, handwriting digits images and objects images) prove that the proposed algorithms can improve the state-of-the-art results

Adaptive Locality Preserving Regression

This paper proposes a novel discriminative regression method, called adaptive locality preserving regression (ALPR) for classification. In particular, ALPR aims to learn a more flexible and discriminative projection that not only preserves the intrinsic structure of data, but also possesses the properties of feature selection and interpretability. To this end, we introduce a target learning technique to adaptively learn a more discriminative and flexible target matrix rather than the pre-defined strict zero-one label matrix for regression. Then a locality preserving constraint regularized by the adaptive learned weights is further introduced to guide the projection learning, which is beneficial to learn a more discriminative projection and avoid overfitting. Moreover, we replace the conventional `Frobenius norm' with the special l21 norm to constrain the projection, which enables the method to adaptively select the most important features from the original high-dimensional data for feature extraction. In this way, the negative influence of the redundant features and noises residing in the original data can be greatly eliminated. Besides, the proposed method has good interpretability for features owing to the row-sparsity property of the l21 norm. Extensive experiments conducted on the synthetic database with manifold structure and many real-world databases prove the effectiveness of the proposed method.Comment: The paper has been accepted by IEEE Transactions on Circuits and Systems for Video Technology (TCSVT), and the code can be available at https://drive.google.com/file/d/1iNzONkRByIaUhXwdEhOkkh_0d2AAXNE8/vie

Joint & Progressive Learning from High-Dimensional Data for Multi-Label Classification

Despite the fact that nonlinear subspace learning techniques (e.g. manifold learning) have successfully applied to data representation, there is still room for improvement in explainability (explicit mapping), generalization (out-of-samples), and cost-effectiveness (linearization). To this end, a novel linearized subspace learning technique is developed in a joint and progressive way, called \textbf{j}oint and \textbf{p}rogressive \textbf{l}earning str\textbf{a}teg\textbf{y} (J-Play), with its application to multi-label classification. The J-Play learns high-level and semantically meaningful feature representation from high-dimensional data by 1) jointly performing multiple subspace learning and classification to find a latent subspace where samples are expected to be better classified; 2) progressively learning multi-coupled projections to linearly approach the optimal mapping bridging the original space with the most discriminative subspace; 3) locally embedding manifold structure in each learnable latent subspace. Extensive experiments are performed to demonstrate the superiority and effectiveness of the proposed method in comparison with previous state-of-the-art methods.Comment: accepted in ECCV 201

Investigation of new learning methods for visual recognition

Visual recognition is one of the most difficult and prevailing problems in computer vision and pattern recognition due to the challenges in understanding the semantics and contents of digital images. Two major components of a visual recognition system are discriminatory feature representation and efficient and accurate pattern classification. This dissertation therefore focuses on developing new learning methods for visual recognition. Based on the conventional sparse representation, which shows its robustness for visual recognition problems, a series of new methods is proposed. Specifically, first, a new locally linear K nearest neighbor method, or LLK method, is presented. The LLK method derives a new representation, which is an approximation to the ideal representation, by optimizing an objective function based on a host of criteria for sparsity, locality, and reconstruction. The novel representation is further processed by two new classifiers, namely, an LLK based classifier (LLKc) and a locally linear nearest mean based classifier (LLNc), for visual recognition. The proposed classifiers are shown to connect to the Bayes decision rule for minimum error. Second, a new generative and discriminative sparse representation (GDSR) method is proposed by taking advantage of both a coarse modeling of the generative information and a modeling of the discriminative information. The proposed GDSR method integrates two new criteria, namely, a discriminative criterion and a generative criterion, into the conventional sparse representation criterion. A new generative and discriminative sparse representation based classification (GDSRc) method is then presented based on the derived new representation. Finally, a new Score space based multiple Metric Learning (SML) method is presented for a challenging visual recognition application, namely, recognizing kinship relations or kinship verification. The proposed SML method, which goes beyond the conventional Mahalanobis distance metric learning, not only learns the distance metric but also models the generative process of features by taking advantage of the score space. The SML method is optimized by solving a constrained, non-negative, and weighted variant of the sparse representation problem. To assess the feasibility of the proposed new learning methods, several visual recognition tasks, such as face recognition, scene recognition, object recognition, computational fine art analysis, action recognition, fine grained recognition, as well as kinship verification are applied. The experimental results show that the proposed new learning methods achieve better performance than the other popular methods