Extending the classical principal component analysis (PCA), the kernel PCA (Schölkopf, Smola and Müller, 1998) effectively extracts nonlinear structures of high dimensional data. But similar to PCA, the kernel PCA can be sensitive to outliers. Various approaches have been proposed in the literature to robustify the classical PCA. However, it is not immediately clear how these approaches can be ...

ABSTRACT Principal Component Analysis (PCA) is a basis transformation to diagonalize an estimate of the covariance matrix of input data and, the new coordinates in the Eigenvector basis are called principal components. Since Kernel PCA is just a PCA in feature space F , the projection of an image in input space can be reconstructed from its principal components in feature space. This enables us...

In this paper, we consider a technique called the generic Principal Component Analysis (PCA) which is based on an extension and rigorous justification of the standard PCA. The generic PCA is treated as the best weighted linear estimator of a given rank under the condition that the associated covariance matrix is singular. As a result, the generic PCA is constructed in terms of the pseudo-invers...

We introduce a novel algorithm to compute nonnegative sparse principal components of positive semidefinite (PSD) matrices. Our algorithm comes with approximation guarantees contingent on the spectral profile of the input matrix A: the sharper the eigenvalue decay, the better the quality of the approximation. If the eigenvalues decay like any asymptotically vanishing function, we can approximate...

The main shortage of principle component analysis (PCA) based anomaly detection models is their interpretability. In this paper, our goal is to propose an interpretable PCAbased model for anomaly detection and interpretation. The propose ASPCAmodel constructs principal components with sparse and orthogonal loading vectors to represent the abnormal subspace, and uses them to interpret detected a...

Sparse Principal Component Analysis (PCA) methods are efficient tools to reduce the dimension (or number of variables) of complex data. Sparse principal components (PCs) are easier to interpret than conventional PCs, because most loadings are zero. We study the asymptotic properties of these sparse PC directions for scenarios with fixed sample size and increasing dimension (i.e. High Dimension,...

A recent proposal developed to avoid some of the drawbacks presented by standard clustering algorithms is the so-called biclustering technique [1], which performs clustering of rows and columns of the data matrix simultaneously, allowing the extraction of additional information from the dataset. Since the biclustering problem is combinatorial, and ant-based systems present several advantages wh...

Face recognition is considered to be one of the most reliable biometric, when security issues are taken into concern. For this, feature extraction becomes a critical problem. Different methods are used for extraction of facial feature which are broadly classified into linear and nonlinear subspaces. Among the linear methods are Linear Discriminant Analysis (LDA), Bayesian Methods (MAP and ML), ...

Alterations of mitochondrial DNA (mtDNA) have been associated with the risk of a number of human cancers; however, the relationship between mtDNA copy number in peripheral blood leukocytes (PBLs) and the risk of prostate cancer (PCa) has not been investigated. In a case-control study of 196 PCa patients and 196 age-paired healthy controls in a Chinese Han population, the association between mtD...

To derive a precise estimation of the associations between the cytochrome P450 1B1 (CYP1B1) 4326C/G variants and prostate cancer (PCa) risk or aggressiveness, a meta-analysis was performed using all eligible published studies. Odds ratios (ORs) with 95% confidence intervals (CIs) were estimated to assess the association in seven literature studies with 2788 cases and 2968 controls. In the overa...