$\ell _{2,p}$ -Norm Based PCA for Image Recognition.

Recently, many ℓ1-norm-based PCA approaches have been developed to improve the robustness of PCA. However, most existing approaches solve the optimal projection matrix by maximizing ℓ1-norm-based variance and do not best minimize the reconstruction error, which is the true goal of PCA. Moreover, they do not have rotational invariance. To handle these problems, we propose a generalized robust metric learning for PCA, namely, ℓ2,p-PCA, which employs ℓ2,p -norm as the distance metric for reconstruction error. The proposed method not only is robust to outliers but also retains PCA's desirable properties. For example, the solutions are the principal eigenvectors of a robust covariance matrix and the low-dimensional representation have rotational invariance. These properties are not shared by ℓ1-norm-based PCA methods. A new iteration algorithm is presented to solve ℓ2,p-PCA efficiently. Experimental results illustrate that the proposed method is more effective and robust than PCA, PCA-L1 greedy, PCA-L1 nongreedy, and HQ-PCA.

Local Regression and Global Information-Embedded Dimension Reduction.

A large family of algorithms for unsupervised dimension reduction is based on both the local and global structures of the data. A fundamental step in these methods is to model the local geometrical structure of the data. However, the previous methods mainly ignore two facts in this step: 1) the dimensionality of the data is usually far larger than the number of local data, which is a typical ill-posed problem and 2) the data might be polluted by noise. These facts normally may lead to an inaccurate learned local structure and may degrade the final performance. In this paper, we propose a novel unsupervised dimension reduction method with the ability to address these problems effectively while also preserving the global information of the input data. Specifically, we first denoise the local data by preserving their principal components and we then apply a regularization term to the local modeling function to solve the illposed problem. Then, we use a linear regression model to capture the local geometrical structure, which is demonstrated to be insensitive to the parameters. Finally, we propose two criteria to simultaneously model both the local and the global information. Theoretical analyses for the relations between the proposed methods and some classical dimension-reduction methods are presented. The experimental results from various databases demonstrate the effectiveness of our methods.

Auto-Weighted Multi-View Learning for Image Clustering and Semi-Supervised Classification.

Due to the efficiency of learning relationships and complex structures hidden in data, graph-oriented methods have been widely investigated and achieve promising performance. Generally, in the field of multi-view learning, these algorithms construct informative graph for each view, on which the following clustering or classification procedure are based. However, in many real-world data sets, original data always contain noises and outlying entries that result in unreliable and inaccurate graphs, which cannot be ameliorated in the previous methods. In this paper, we propose a novel multi-view learning model which performs clustering/semi-supervised classification and local structure learning simultaneously. The obtained optimal graph can be partitioned into specific clusters directly. Moreover, our model can allocate ideal weight for each view automatically without explicit weight definition and penalty parameters. An efficient algorithm is proposed to optimize this model. Extensive experimental results on different real-world data sets show that the proposed model outperforms other state-of-the-art multi-view algorithms.

Convex Multiview Semi-Supervised Classification.

In many practical applications, there are a great number of unlabeled samples available, while labeling them is a costly and tedious process. Therefore, how to utilize unlabeled samples to assist digging out potential information about the problem is very important. In this paper, we study a multiclass semi-supervised classification task in the context of multiview data. First, an optimization method named Parametric multiview semi-supervised classification (PMSSC) is proposed, where the built classifier for each individual view is explicitly combined with a weight factor. By analyzing the weakness of it, a new adapted weight learning strategy is further formulated, and we come to the convex multiview semi-supervised classification (CMSSC) method. Comparing with the PMSSC, this method has two significant properties. First, without too much loss in performance, the newly used weight learning technique achieves eliminating a hyperparameter, and thus it becomes more compact in form and practical to use. Second, as its name implies, the CMSSC models a convex problem, which avoids the local-minimum problem. Experimental results on several multiview data sets demonstrate that the proposed methods achieve better performances than recent representative methods and the CMSSC is preferred due to its good traits.

Fast and Orthogonal Locality Preserving Projections for Dimensionality Reduction.

The locality preserving projections (LPP) algorithm is a recently developed linear dimensionality reduction algorithm that has been frequently used in face recognition and other applications. However, the projection matrix in LPP is not orthogonal, thus creating difficulties for both reconstruction and other applications. As the orthogonality property is desirable, orthogonal LPP (OLPP) has been proposed so that an orthogonal projection matrix can be obtained based on a step by step procedure; however, this makes the algorithm computationally more expensive. Therefore, in this paper, we propose a fast and orthogonal version of LPP, called FOLPP, which simultaneously minimizes the locality and maximizes the globality under the orthogonal constraint. As a result, the computation burden of the proposed algorithm can be effectively alleviated compared with the OLPP algorithm. Experimental results on two face recognition data sets and two hyperspectral data sets are presented to demonstrate the effectiveness of the proposed algorithm.

A Non-Greedy Algorithm for L1-Norm LDA.

Recently, L1-norm-based discriminant subspace learning has attracted much more attention in dimensionality reduction and machine learning. However, most existing approaches solve the column vectors of the optimal projection matrix one by one with greedy strategy. Thus, the obtained optimal projection matrix does not necessarily best optimize the corresponding trace ratio objective function, which is the essential criterion function for general supervised dimensionality reduction. In this paper, we propose a non-greedy iterative algorithm to solve the trace ratio form of L1-norm-based linear discriminant analysis. We analyze the convergence of our proposed algorithm in detail. Extensive experiments on five popular image databases illustrate that our proposed algorithm can maximize the objective function value and is superior to most existing L1-LDA algorithms.

Learning a 3D Human Pose Distance Metric from Geometric Pose Descriptor.

Estimating 3D pose similarity is a fundamental problem on 3D motion data. Most previous work calculates L2-like distance of joint orientations or coordinates, which does not sufficiently reflect the pose similarity of human perception. In this paper, we present a new pose distance metric. First, we propose a new rich pose feature set called Geometric Pose Descriptor (GPD). GPD is more effective in encoding pose similarity by utilizing features on geometric relations among body parts, as well as temporal information such as velocities and accelerations. Based on GPD, we propose a semisupervised distance metric learning algorithm called Regularized Distance Metric Learning with Sparse Representation (RDSR), which integrates information from both unsupervised data relationship and labels. We apply the proposed pose distance metric to applications of motion transition decision and content-based pose retrieval. Quantitative evaluations demonstrate that our method achieves better results with only a small amount of human labels, showing that the proposed pose distance metric is a promising building block for various 3D-motion related applications.