Statistical adaptive metric learning in visual action feature set recognition

Abstract

Great variances in visual features often present significant challenges in human action recognitions. To address this common problem, this paper proposes a statistical adaptive metric learning (SAML) method by exploring various selections and combinations of multiple statistics in a unified metric learning framework. Most statistics have certain advantages in specific controlled environments, and systematic selections and combinations can adapt them to more realistic "in the wild" scenarios. In the proposed method, multiple statistics, include means, covariance matrices and Gaussian distributions, are explicitly mapped or generated in the Riemannian manifolds. Typically, d-dimensional mean vectors in R d are mapped to a R d×d space of symmetric positive definite (SPD) matrices Sym + d . Subsequently, by embedding the heterogeneous manifolds in their tangent Hilbert space, subspaces combination with minimal deviation is selected from multiple statistics. Then Mahalanobis metrics are introduced to map them back into the Euclidean space. Unified optimizations are finally performed based on the Euclidean distances. In the proposed method, subspaces with smaller deviations are selected before metric learning. Therefore, by exploring different metric combinations, the final learning is more representative and effective than exhaustively learning from all the hybrid metrics. Experimental evaluations are conducted on human action recognitions in both static and dynamic scenarios. Promising results demonstrate that the proposed method performs effectively for human action recognitions in the wild. a feature set [1]. In addition, image sets have been commonly used in face recognitions 30 recognitions can finally be achieved by using Nearest Neighbors (NNs) method. Secondorder statistics based methods have better representation of the data, but it is hard to design a discriminant function with a unified distance measure for the manifolds. Typical subspace-based methods include Mutual Subspace Method (MSM) [11], Discriminant Canonical Correlations (DCC)[10], Manifold Discriminant Analysis (MDA) [14], Grass-35 mann Discriminant analysis (GDA)[13], Covariance Discriminative Learning (CDL)[15], Localized Multi-Kernel Metric Learning (LMKML)[16] etc. Distribution based statistics model each sample in the feature set with a distribution, which can be expressed as an expansion of the Riemannian manifold from the 2nd-order statistic space Sym + d to Sym + d+1 . Such methods are often with 3rd-order statistics and may lead to complex parametric 40 distribution comparison. Typical examples include Single Gaussian Models (SGM) [2], Gaussian Mixture Models (GMM) [3] and kernel version of ITML with DIS-based set model (DIS-ITML). Although 3rd-order statistics model sets with more consolidated representations, the hypothesis tests often require significant amount of computation in distribution comparisons. 45More adaptive forms of set modeling methods have been proposed by combining multiple statistical metrics in certain heuristic ways....