Related papers: Deep Kernel Principal Component Analysis for Multi…
Traditional principal component analysis (PCA) is well known in high-dimensional data analysis, but it requires to express data by a matrix with observations to be continuous. To overcome the limitations, a new method called flexible PCA…
Conventional principal component analysis (PCA) finds a principal vector that maximizes the sum of second powers of principal components. We consider a generalized PCA that aims at maximizing the sum of an arbitrary convex function of…
We consider estimation of large approximate factor models in high-dimensional panels of stationary time series using Principal Component Analysis (PCA). We review the key results establishing the necessary and sufficient conditions for…
Real-time or near real-time hyperspectral detection and identification are extremely useful and needed in many fields. These data sets can be quite large, and the algorithms can require numerous computations that slow the process down. A…
Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm…
Principal component analysis (PCA) is routinely used in population genetics to assess genetic structure. With chromosomal reference genomes and population-scale whole genome-sequencing becoming increasingly accessible, contemporary studies…
Principal component analysis (PCA) is a classical feature extraction method, but it may be adversely affected by outliers, resulting in inaccurate learning of the projection matrix. This paper proposes a robust method to estimate both the…
Tensor principal component analysis (TPCA) is a multi-linear extension of principal component analysis which converts a set of correlated measurements into several principal components. In this paper, we propose a new robust TPCA method to…
Principal component analysis (PCA) is a fundamental dimension reduction tool in statistics and machine learning. For large and high-dimensional data, computing the PCA (i.e., the singular vectors corresponding to a number of dominant…
This paper compares two neural network input selection schemes, the Principal Component Analysis (PCA) and the Automatic Relevance Determination (ARD) based on Mac-Kay's evidence framework. The PCA takes all the input data and projects it…
Feature extraction and dimensionality reduction are important tasks in many fields of science dealing with signal processing and analysis. The relevance of these techniques is increasing as current sensory devices are developed with ever…
A representative model in integrative analysis of two high-dimensional correlated datasets is to decompose each data matrix into a low-rank common matrix generated by latent factors shared across datasets, a low-rank distinctive matrix…
Tensor robust principal component analysis (RPCA), which seeks to separate a low-rank tensor from its sparse corruptions, has been crucial in data science and machine learning where tensor structures are becoming more prevalent. While…
We describe how cross-kernel matrices, that is, kernel matrices between the data and a custom chosen set of `feature spanning points' can be used for learning. The main potential of cross-kernels lies in the fact that (a) only one side of…
Principal Component Analysis (PCA) has been used to study the pathogenesis of diseases. To enhance the interpretability of classical PCA, various improved PCA methods have been proposed to date. Among these, a typical method is the…
Recently popularized randomized methods for principal component analysis (PCA) efficiently and reliably produce nearly optimal accuracy --- even on parallel processors --- unlike the classical (deterministic) alternatives. We adapt one of…
Finding informative low-dimensional representations that can be computed efficiently in large datasets is an important problem in data analysis. Recently, contrastive Principal Component Analysis (cPCA) was proposed as a more informative…
In this paper, we consider clustering based on principal component analysis (PCA) for high-dimension, low-sample-size (HDLSS) data. We give theoretical reasons why PCA is effective for clustering HDLSS data. First, we derive a geometric…
Many statistical estimation techniques for high-dimensional or functional data are based on a preliminary dimension reduction step, which consists in projecting the sample $\bX_1, \hdots, \bX_n$ onto the first $D$ eigenvectors of the…
Sparse principal component analysis (sparse PCA) is a widely used technique for dimensionality reduction in multivariate analysis, addressing two key limitations of standard PCA. First, sparse PCA can be implemented in high-dimensional low…