Locality Preserving Projections for Grassmann manifold

Learning on Grassmann manifold has become popular in many computer vision tasks, with the strong capability to extract discriminative information for imagesets and videos. However, such learning algorithms particularly on high-dimensional Grassmann manifold always involve with significantly high computational cost, which seriously limits the applicability of learning on Grassmann manifold in more wide areas. In this research, we propose an unsupervised dimensionality reduction algorithm on Grassmann manifold based on the Locality Preserving Projections (LPP) criterion. LPP is a commonly used dimensionality reduction algorithm for vector-valued data, aiming to preserve local structure of data in the dimension-reduced space. The strategy is to construct a mapping from higher dimensional Grassmann manifold into the one in a relative low-dimensional with more discriminative capability. The proposed method can be optimized as a basic eigenvalue problem. The performance of our proposed method is assessed on several classification and clustering tasks and the experimental results show its clear advantages over other Grassmann based algorithms.Comment: Accepted by IJCAI 201

Robust 2D Joint Sparse Principal Component Analysis with F-Norm Minimization for Sparse Modelling: 2D-RJSPCA

© 2018 IEEE. Principal component analysis (PCA) is widely used methods for dimensionality reduction and Lots of variants have been proposed to improve the robustness of algorithm, however, these methods suffer from the fact that PCA is linear combination which makes it difficult to interpret complex nonlinear data, and sensitive to outliers or cannot extract features consistently, i.e., collectively; PCA may still require measuring all input features. 2DPCA based on 1-norm has been recently used for robust dimensionality reduction in the image domain but still sensitive to noise. In this paper, we introduce robust formation of 2DPCA by centering the data using the optimized mean for two-dimensional joint sparse as well as effectively combining the robustness of 2DPCA and the sparsity-inducing lasso regularization. Optimal mean helps to improve the robustness of joint sparse PCA further. The distance in spatial dimension is measure in F-norm and sum of different datapoint uses 1-norm. 2DR-JSPCA imposes joint sparse constraints on its objective function whereas additional plenty term help to deal with outliers efficiently. Both theoretical and empirical results on six publicly available benchmark datasets shows that Optimal mean 2DR-JSPCA provides better performance for dimensionality reduction as compare to non-sparse (2DPCA and 2DPCA-L1) and sparse (SPCA, JSPCA)

Integrating joint feature selection into subspace learning: A formulation of 2DPCA for outliers robust feature selection

© 2019 Elsevier Ltd Since the principal component analysis and its variants are sensitive to outliers that affect their performance and applicability in real world, several variants have been proposed to improve the robustness. However, most of the existing methods are still sensitive to outliers and are unable to select useful features. To overcome the issue of sensitivity of PCA against outliers, in this paper, we introduce two-dimensional outliers-robust principal component analysis (ORPCA) by imposing the joint constraints on the objective function. ORPCA relaxes the orthogonal constraints and penalizes the regression coefficient, thus, it selects important features and ignores the same features that exist in other principal components. It is commonly known that square Frobenius norm is sensitive to outliers. To overcome this issue, we have devised an alternative way to derive objective function. Experimental results on four publicly available benchmark datasets show the effectiveness of joint feature selection and provide better performance as compared to state-of-the-art dimensionality-reduction methods