Related papers: Extending Kernel PCA through Dualization: Sparsity…
This paper presents new algorithms to solve the feature-sparsity constrained PCA problem (FSPCA), which performs feature selection and PCA simultaneously. Existing optimization methods for FSPCA require data distribution assumptions and are…
Kernel methods have been proven to be a powerful tool for the integration and analysis of highthroughput technologies generated data. Kernels offer a nonlinear version of any linear algorithm solely based on dot products. The kernelized…
This work addresses two main issues of the standard Kernel Entropy Component Analysis (KECA) algorithm: the optimization of the kernel decomposition and the optimization of the Gaussian kernel parameter. KECA roughly reduces to a sorting of…
We consider the problem of maximizing the variance explained from a data matrix using orthogonal sparse principal components that have a support of fixed cardinality. While most existing methods focus on building principal components (PCs)…
Since the introduction of the lasso in regression, various sparse methods have been developed in an unsupervised context like sparse principal component analysis (s-PCA), sparse canonical correlation analysis (s-CCA) and sparse singular…
Tensor robust principal component analysis (TRPCA) has received a substantial amount of attention in various fields. Most existing methods, normally relying on tensor nuclear norm minimization, need to pay an expensive computational cost…
We present an extension of sparse PCA, or sparse dictionary learning, where the sparsity patterns of all dictionary elements are structured and constrained to belong to a prespecified set of shapes. This \emph{structured sparse PCA} is…
Principal component analysis (PCA) is a fundamental tool for analyzing multivariate data. Here the focus is on dimension reduction to the principal subspace, characterized by its projection matrix. The classical principal subspace can be…
We consider a difference-of-convex formulation where one of the terms is allowed to be hypoconvex (or weakly convex). We first examine the precise behavior of a single iteration of the Difference-of-Convex algorithm (DCA), giving a tight…
Sparse Principal Components Analysis aims to find principal components with few non-zero loadings. We derive such sparse solutions by adding a genuine sparsity requirement to the original Principal Components Analysis (PCA) objective…
Due to the rapid growth of smart agents such as weakly connected computational nodes and sensors, developing decentralized algorithms that can perform computations on local agents becomes a major research direction. This paper considers the…
An efficient computational approach for optimal reconstructing parameters of binary-type physical properties for models in biomedical applications is developed and validated. The methodology includes gradient-based multiscale optimization…
Sparsity is a fundamental modeling principle in statistics, signal processing, and data science. However, optimization with sparsity constraints is notoriously difficult. We introduce a new convex relaxation framework for {sparse…
A process centric view of robust PCA (RPCA) allows its fast approximate implementation based on a special form o a deep neural network with weights shared across all layers. However, empirically this fast approximation to RPCA fails to find…
Principal component analysis (PCA) is a classical method for dimensionality reduction based on extracting the dominant eigenvectors of the sample covariance matrix. However, PCA is well known to behave poorly in the ``large $p$, small $n$''…
We propose a new sparse principal component analysis (SPCA) method in which the solutions are obtained by projecting the full cardinality principal components onto subsets of variables. The resulting components are guaranteed to explain a…
An improved version of the sparse multiway kernel spectral clustering (KSC) is presented in this brief. The original algorithm is derived from weighted kernel principal component (KPCA) analysis formulated within the primal-dual…
It is well known that Principal Component Analysis (PCA) is strongly affected by outliers and a lot of effort has been put into robustification of PCA. In this paper we present a new algorithm for robust PCA minimizing the trimmed…
Principal Component Analysis (PCA) is one of the most important unsupervised methods to handle high-dimensional data. However, due to the high computational complexity of its eigen decomposition solution, it hard to apply PCA to the…
Sparse and outlier-robust Principal Component Analysis (PCA) has been a very active field of research recently. Yet, most existing methods apply PCA to a single dataset whereas multi-source data-i.e. multiple related datasets requiring…