Related papers: An NPDo Approach for Principal Joint Block Diagona…
Principal Component Analysis (PCA) is a fundamental tool for data visualization, denoising, and dimensionality reduction. It is widely popular in Statistics, Machine Learning, Computer Vision, and related fields. However, PCA is well-known…
The cyclic block coordinate descent-type (CBCD-type) methods, which performs iterative updates for a few coordinates (a block) simultaneously throughout the procedure, have shown remarkable computational performance for solving strongly…
Recently, there has been a trend to combine independent component analysis and canonical polyadic decomposition (ICA-CPD) for an enhanced robustness for the computation of CPD, and ICA-CPD could be further converted into CPD of a 5th-order…
Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in…
The performance of principal component analysis (PCA) suffers badly in the presence of outliers. This paper proposes two novel approaches for robust PCA based on semidefinite programming. The first method, maximum mean absolute deviation…
Principal Component Analysis (PCA) is a commonly used tool for dimension reduction in analyzing high dimensional data; Multilinear Principal Component Analysis (MPCA) has the potential to serve the similar function for analyzing tensor…
Given a set $\mathcal{C}=\{C_i\}_{i=1}^m$ of square matrices, the matrix blind joint block diagonalization problem (BJBDP) is to find a full column rank matrix $A$ such that $C_i=A\Sigma_iA^\text{T}$ for all $i$, where $\Sigma_i$'s are all…
Joint diagonalization, the process of finding a shared set of approximate eigenvectors for a collection of matrices, arises in diverse applications such as multidimensional harmonic analysis or quantum information theory. This task is…
Principal component analysis (PCA), a ubiquitous dimensionality reduction technique in signal processing, searches for a projection matrix that minimizes the mean squared error between the reduced dataset and the original one. Since…
This paper introduces a new algorithm to approximate non orthogonal joint diagonalization (NOJD) of a set of complex matrices. This algorithm is based on the Frobenius norm formulation of the JD problem and takes advantage from combining…
Principal component analysis (PCA) is largely adopted for chemical process monitoring and numerous PCA-based systems have been developed to solve various fault detection and diagnosis problems. Since PCA-based methods assume that the…
Principal component analysis (PCA) is a widely used technique for dimension reduction. As datasets continue to grow in size, distributed-PCA (DPCA) has become an active research area. A key challenge in DPCA lies in efficiently aggregating…
The research detailed in this paper scrutinizes Principal Component Analysis (PCA), a seminal method employed in statistics and machine learning for the purpose of reducing data dimensionality. Singular Value Decomposition (SVD) is often…
In this paper we develop a new approach to sparse principal component analysis (sparse PCA). We propose two single-unit and two block optimization formulations of the sparse PCA problem, aimed at extracting a single sparse dominant…
PCA (Principal Component Analysis) and its variants areubiquitous techniques for matrix dimension reduction and reduced-dimensionlatent-factor extraction. One significant challenge in using PCA, is thechoice of the number of principal…
Principal Component Analysis (PCA) is a fundamental data preprocessing tool in the world of machine learning. While PCA is often thought of as a dimensionality reduction method, the purpose of PCA is actually two-fold: dimension reduction…
Principal component analysis (PCA) is a widely used method for data processing, such as for dimension reduction and visualization. Standard PCA is known to be sensitive to outliers, and thus, various robust PCA methods have been proposed.…
The approximate joint diagonalization of a set of matrices consists in finding a basis in which these matrices are as diagonal as possible. This problem naturally appears in several statistical learning tasks such as blind signal…
In this paper, we propose a gradient-based block coordinate descent (BCD-G) framework to solve the joint approximate diagonalization of matrices defined on the product of the complex Stiefel manifold and the special linear group. Instead of…
Matrix factor models have been growing popular dimension reduction tools for large-dimensional matrix time series. However, the heteroscedasticity of the idiosyncratic components has barely received any attention. Starting from the pseudo…