Lishan Qiao

Sparsity preserving projections with applications to face recognition

Dimensionality reduction methods (DRs) have commonly been used as a principled way to understand the high-dimensional data such as face images. In this paper, we propose a new unsupervised DR method called sparsity preserving projections (SPP). Unlike many existing techniques such as local preserving projection (LPP) and neighborhood preserving embedding (NPE), where local neighborhood information is preserved during the DR procedure, SPP aims to preserve the sparse reconstructive relationship of the data, which is achieved by minimizing a L1 regularization-related objective function. The obtained projections are invariant to rotations, rescalings and translations of the data, and more importantly, they contain natural discriminating information even if no class labels are provided. Moreover, SPP chooses its neighborhood automatically and hence can be more conveniently used in practice compared to LPP and NPE. The feasibility and effectiveness of the proposed method is verified on three popular face databases (Yale, AR and Extended Yale B) with promising results.

Graph-optimized locality preserving projections

Locality preserving projections (LPP) is a typical graph-based dimensionality reduction (DR) method, and has been successfully applied in many practical problems such as face recognition. However, LPP depends mainly on its underlying neighborhood graph whose construction suffers from the following issues: (1) such neighborhood graph is artificially defined in advance, and thus does not necessary benefit subsequent DR task; (2) such graph is constructed using the nearest neighbor criterion which tends to work poorly due to the high-dimensionality of original space; (3) it is generally uneasy to assign appropriate values for the neighborhood size and heat kernel parameter involved in graph construction. To address these problems, we develop a novel DR algorithm called Graph-optimized Locality Preserving Projections (GoLPP). The idea is to integrate graph construction with specific DR process into a unified framework, which results in an optimized graph rather than predefined one. Moreover, an entropy regularization term is incorporated into the objective function for controlling the uniformity level of the edge weights in graph, so that a principled graph updating formula naturally corresponding to conventional heat kernel weights can be obtained. Finally, the experiments on several publicly available UCI and face data sets show the feasibility and effectiveness of the proposed method with encouraging results.

Sparsity preserving discriminant analysis for single training image face recognition

Single training image face recognition is one of the main challenges to appearance-based pattern recognition techniques. Many classical dimensionality reduction methods such as LDA have achieved success in face recognition field, but cannot be directly used to the single training image scenario. Recent graph-based semi-supervised dimensionality reduction (SSDR) provides a feasible strategy to deal with such problem. However, most of the existing SSDR algorithms such as semi-supervised discriminant analysis (SDA) are locality-oriented and generally suffer from the following issues: (1) they need a large number of unlabeled training samples to estimate the manifold structure in data, but such extra samples may not be easily obtained in a given face recognition task; (2) they model the local geometry of data by the nearest neighbor criterion which generally fails to obtain sufficient discriminative information due to the high-dimensionality of face image space; (3) they construct the underlying adjacency graph (or data-dependent regularizer) using a fixed neighborhood size for all the sample points without considering the actual data distribution. In this paper, we develop a new graph-based SSDR algorithm called sparsity preserving discriminant analysis (SPDA) to address these problems. More specifically, (1) the graph in SPDA is constructed by sparse representation, and thus the local structure in data is automatically modeled instead of being manually predefined. (2) With the natural discriminative power of sparse representation, SPDA can remarkably improve recognition performance only resorting to very few extra unlabeled samples. (3) A simple ensemble strategy is developed to accelerate graph construction, which results in an efficient ensemble SPDA algorithm. Extensive experiments on both toy and real face data sets are provided to validate the feasibility and effectiveness of the proposed algorithm.

A general non-local denoising model using multi-kernel-induced measures

Noises are inevitably introduced in digital image acquisition processes, and thus image denoising is still a hot research problem. Different from local methods operating on local regions of images, the non-local methods utilize non-local information (even the whole image) to accomplish image denoising. Due to their superior performance, the non-local methods have recently drawn more and more attention in the image denoising community. However, these methods generally do not work well in handling complicated noises with different levels and types. Inspired by the fact in machine learning field that multi-kernel methods are more robust and effective in tackling complex problems than single-kernel ones, we establish a general non-local denoising model based on multi-kernel-induced measures (GNLMKIM for short), which provides us a platform to analyze some existing and design new filters. With the help of GNLMKIM, we reinterpret two well-known non-local filters in the united view and extend them to their novel multi-kernel counterparts. The comprehensive experiments indicate that these novel filters achieve encouraging denoising results in both visual effect and PSNR index.

An empirical study of two typical locality preserving linear discriminant analysis methods

Laplacian linear discriminant analysis (LapLDA) and semi-supervised discriminant analysis (SDA) are two recently proposed LDA methods. They are developed independently with the aim to improve LDA by introducing a locality preserving regularization term, and they have proved their effectiveness experimentally on some benchmark datasets. However, both algorithms ignored comparison with much simpler methods such as regularized discriminant analysis (RDA). In this paper, we make an empirical and supplementary study on LapLDA and SDA, and obtain somewhat counterintuitive results: (1) although LapLDA can generally improve the classical LDA via resorting to a complex regularization term, it does not outperform RDA, which is only based on the simplest Tikhonov regularizer; (2) to reevaluate the performance of SDA, we develop purposely a new and much simpler semi-supervised algorithm called globality preserving discriminant analysis (GPDA) and make a comparison with SDA. Surprisingly, we find that GPDA tends to achieve better performance. These two points drive us to reconsider whether one should use or how to use locality preserving strategy in practice. Finally, we discuss the reasons that lead to the possible failure of the locality preserving criterion and provide alternative strategies and suggestions to address these problems.

Ordinal margin metric learning and its extension for cross-distribution image data

Propose a novel ORdinal Margin Metric Learning (ORMML) by separating the data with large margins and making them distributed in order.Extend ORMML to cope with cross-distribution application scenarios, named CD-ORMML.Extensively demonstrate the superiority of the proposed metric learning methods to related state-of-the-art methods. In machine learning and computer vision fields, a wide range of applications, such as human age estimation and head pose recognition, are related to ordinal data in which there exists an order relationship. To perform such ordinal estimations in a desired metric space, in this paper we first propose a novel ordinal margin metric learning (ORMML) method by separating the data classes with a sequence of margins, which makes the classes distribute orderly in the learned metric space. Then, to cope with more realistic scenarios where the data are sampled with each class across multiple distributions, we present a cross-distribution variant of ORMML, coined as CD-ORMML, by maximizing the correlation between distributions within each class when conducting metric learning. Finally, extensive experiments on synthetic and publicly available image datasets demonstrate the superiority of the proposed methods in performance to the state-of-the-art methods.

Dimensionality reduction with adaptive graph

Graph-based dimensionality reduction (DR) methods have been applied successfully in many practical problems, such as face recognition, where graphs play a crucial role in modeling the data distribution or structure. However, the ideal graph is, in practice, difficult to discover. Usually, one needs to construct graph empirically according to various motivations, priors, or assumptions; this is independent of the subsequent DR mapping calculation. Different from the previous works, in this paper, we attempt to learn a graph closely linked with the DR process, and propose an algorithm called dimensionality reduction with adaptive graph (DRAG), whose idea is to, during seeking projection matrix, simultaneously learn a graph in the neighborhood of a prespecified one. Moreover, the pre-specified graph is treated as a noisy observation of the ideal one, and the square Frobenius divergence is used to measure their difference in the objective function. As a result, we achieve an elegant graph update formula which naturally fuses the original and transformed data information. In particular, the optimal graph is shown to be a weighted sum of the pre-defined graph in the original space and a new graph depending on transformed space. Empirical results on several face datasets demonstrate the effectiveness of the proposed algorithm.

Robust faces manifold modeling: Most expressive Vs. most Sparse criterion

Robust face image modeling under uncontrolled conditions is crucial for the current face recognition systems in practice. One approach is to seek a compact representation of the given image set which encodes the intrinsic lower dimensional manifold of them. Among others, Local Linear Embedding (LLE) is one of the most popular method for that purpose. However, it suffers from the following problems when used for face modeling: 1) it is not robust under uncontrolled conditions (e.g., the underlying images may contain large appearance distortions such as partial occlusion or extreme illumination variations); 2) a fixed neighborhood size is used for all the local patches without considering the actual distribution of samples in the input space; 3) the modeled local structures may not contain enough discriminative information which is essential to the later recognition stage. In this paper, we introduce the Sparse Locally Linear Embedding (SLLE) to address these issues. By replacing the most-expressive type criterion in modeling local patches in LLE with a most-sparse one, SLLE essentially finds and models more discriminative patches. This gives higher model flexibility in the sense of less sensitiveness to incorrect model and higher robustness to outliers. The feasibility and effectiveness of the proposed method is verified with encouraging results on a publicly available face database.

Sparse representation: extract adaptive neighborhood for multilabel classification

Unlike traditional classification tasks, multilabel classification allows a sample to associate with more than one label. This generalization naturally arises the difficulty in classification. Similar to the single label classification task, neighborhood-based algorithms relying on the nearest neighbor have attracted lots of attention and some of them show positive results. In this paper, we propose an Adaptive Neighborhood algorithm for multilabel classification. Constructing an adaptive neighborhood is challenging because specified information about the neighborhood, e.g. similarity measurement, should be determined automatically during construction rather than provided by the user beforehand. Few literature has covered this topic and we address this difficulty by solving an optimization problem based on the theory of sparse representation. Taking advantage of the extracted adaptive neighborhood, classification can be readily done using weighted sum of labels of training data. Extensive experiments show our proposed method outperforms the state-of-the-art.

Selecting label-dependent features for multi-label classification

Abstract An instance is often represented from different aspects (views or modalities), which leads to high-dimensional features and even multiple labels. In this paper, we focus on the feature selection problem in multi-label classification, for which a trivial solution is handling the labels dividedly. Obviously, such a scheme may not work well by leaving the label relationship out of consideration. Recently, several research works conduct feature selection directly under a multi-label framework by implicitly or explicitly modeling label relationship. However, these works assume that all labels share the same feature subset or subspace, which is not reasonable enough for some scenarios since different labels tend to convey different semantics. To address this problem, we develop a novel approach in this paper to select label-dependent features for multi-label classification. Specifically, we (1) formulate a convex model based on a more general and practical assumption that different labels convey different semantics with specific features; (2) design an alternating optimization algorithm based on Nesterovs method and L1-ball projection for efficiently finding the optimal solution, which can realize multi-label classification, feature selection, and label relationship estimation simultaneously. Finally, experiments on publicly available datasets show that the proposed algorithm achieves better performance than several related methods.