How to Solve Classification and Regression Problems on High-Dimensional Data with a Supervised Extension of Slow Feature Analysis

Supervised learning from high-dimensional data, e.g., multimedia data, is a challenging task. We propose an extension of slow feature analysis (SFA) for supervised dimensionality reduction called graph-based SFA (GSFA). The algorithm extracts a label-predictive low-dimensional set of features that can be post-processed by typical supervised algorithms to generate the final label or class estimation. GSFA is trained with a so-called training graph, in which the vertices are the samples and the edges represent similarities of the corresponding labels. A new weighted SFA optimization problem is introduced, generalizing the notion of slowness from sequences of samples to such training graphs. We show that GSFA computes an optimal solution to this problem in the considered function space, and propose several types of training graphs. For classification, the most straightforward graph yields features equivalent to those of (nonlinear) Fisher discriminant analysis. Emphasis is on regression, where four different graphs were evaluated experimentally with a subproblem of face detection on photographs. The method proposed is promising particularly when linear models are insufficient, as well as when feature selection is difficult

Deep Adaptive Feature Embedding with Local Sample Distributions for Person Re-identification

Person re-identification (re-id) aims to match pedestrians observed by disjoint camera views. It attracts increasing attention in computer vision due to its importance to surveillance system. To combat the major challenge of cross-view visual variations, deep embedding approaches are proposed by learning a compact feature space from images such that the Euclidean distances correspond to their cross-view similarity metric. However, the global Euclidean distance cannot faithfully characterize the ideal similarity in a complex visual feature space because features of pedestrian images exhibit unknown distributions due to large variations in poses, illumination and occlusion. Moreover, intra-personal training samples within a local range are robust to guide deep embedding against uncontrolled variations, which however, cannot be captured by a global Euclidean distance. In this paper, we study the problem of person re-id by proposing a novel sampling to mine suitable \textit{positives} (i.e. intra-class) within a local range to improve the deep embedding in the context of large intra-class variations. Our method is capable of learning a deep similarity metric adaptive to local sample structure by minimizing each sample's local distances while propagating through the relationship between samples to attain the whole intra-class minimization. To this end, a novel objective function is proposed to jointly optimize similarity metric learning, local positive mining and robust deep embedding. This yields local discriminations by selecting local-ranged positive samples, and the learned features are robust to dramatic intra-class variations. Experiments on benchmarks show state-of-the-art results achieved by our method.Comment: Published on Pattern Recognitio

Adaptive Graph via Multiple Kernel Learning for Nonnegative Matrix Factorization

Nonnegative Matrix Factorization (NMF) has been continuously evolving in several areas like pattern recognition and information retrieval methods. It factorizes a matrix into a product of 2 low-rank non-negative matrices that will define parts-based, and linear representation of nonnegative data. Recently, Graph regularized NMF (GrNMF) is proposed to find a compact representation,which uncovers the hidden semantics and simultaneously respects the intrinsic geometric structure. In GNMF, an affinity graph is constructed from the original data space to encode the geometrical information. In this paper, we propose a novel idea which engages a Multiple Kernel Learning approach into refining the graph structure that reflects the factorization of the matrix and the new data space. The GrNMF is improved by utilizing the graph refined by the kernel learning, and then a novel kernel learning method is introduced under the GrNMF framework. Our approach shows encouraging results of the proposed algorithm in comparison to the state-of-the-art clustering algorithms like NMF, GrNMF, SVD etc.Comment: This paper has been withdrawn by the author due to the terrible writin

Design of an Adaptive Classification Procedure for the Analysis of High-Dimensional Data with Limited Training Samples

In a typical supervised classification procedure the availability of training samples has a fundamental effect on classifier performance. For a fixed number of training samples classifier performance is degraded as the number of dimensions (features) is increased. This phenomenon has a significant influence on the analysis of hyperspectral data sets where the ratio of training samples to dimensionality is small. Objectives of this research are to develop novel methods for mitigating the detrimental effects arising from this small ratio and to reduce the effort required by an analyst in terms of training sample selection. An iterative method is developed where semi-labeled samples (classification outputs) are used with the original training samples to estimate parameters and establish a positive feedback procedure wherein parameter estimation and classification enhance each other in an iterative fashion. This work is comprised of four discrete phases. First, the role of semi-labeled samples on parameter estimates is investigated. In this phase it is demonstrated that an iterative procedure based on positive feedback is achievable. Second, a maximum likelihood pixel-wise adaptive classifier is designed. Third, a family of adaptive covariance estimators is developed that combines the adaptive classifiers and covariance estimators to deal with cases where the training sample set is extremely small. Finally, to fully utilize the rich spectral and spatial information contained in hyperspectral data and enhance the performance and robustness of the proposed adaptive classifier, an adaptive Bayesian contextual classifier based on the Markov random field is developed