Related papers: Deep Kernel Principal Component Analysis for Multi…
Spectral methods have been the mainstay in several domains such as machine learning and scientific computing. They involve finding a certain kind of spectral decomposition to obtain basis functions that can capture important structures for…
Cyber security threats have been growing significantly in both volume and sophistication over the past decade. This poses great challenges to malware detection without considerable automation. In this paper, we have proposed a novel…
We present a novel approach for adaptive, differentiable parameterization of large-scale random fields. If the approach is coupled with any gradient-based optimization algorithm, it can be applied to a variety of optimization problems,…
When modeling multivariate data, one might have an extra parameter of contextual information that could be used to treat some observations as more similar to others. For example, images of faces can vary by age, and one would expect the…
Unsupervised learning makes manifest the underlying structure of data without curated training and specific problem definitions. However, the inference of relationships between data points is frustrated by the `curse of dimensionality' in…
This is a tutorial and survey paper on factor analysis, probabilistic Principal Component Analysis (PCA), variational inference, and Variational Autoencoder (VAE). These methods, which are tightly related, are dimensionality reduction and…
Data compression can be achieved by reducing the dimensionality of high-dimensional but approximately low-rank datasets, which may in fact be described by the variation of a much smaller number of parameters. It often serves as a…
One of the most powerful methods of color image recognition is the two-dimensional principle component analysis (2DQPCA) approach, which is based on quaternion representation and preserves color information very well. However, the current…
A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance…
Principal Components Analysis (PCA) is a common way to study the sources of variation in a high-dimensional data set. Typically, the leading principal components are used to understand the variation in the data or to reduce the dimension of…
Multiway data are becoming more and more common. While there are many approaches to extending principal component analysis (PCA) from usual data matrices to multiway arrays, their conceptual differences from the usual PCA, and the…
Single-cell RNA sequencing (scRNA-seq) has revolutionized our ability to analyze gene expression at the cellular level. By providing data on gene expression for each individual cell, scRNA-seq generates large datasets with thousands of…
We present an unsupervised learning analysis of correlation hierarchies in the quarter-filled simple and extended Hubbard models by applying principal component analysis (PCA) to exact-diagonalization (ED) data on 3x4 and 4x4 cylindrical…
Robust principal component analysis (RPCA) is a widely used technique for recovering low-rank structure from matrices with missing entries and sparse, possibly large-magnitude corruptions. Although numerous algorithms achieve accurate point…
Because of high dimensionality, correlation among covariates, and noise contained in data, dimension reduction (DR) techniques are often employed to the application of machine learning algorithms. Principal Component Analysis (PCA), Linear…
This paper introduces the Class-wise Principal Component Analysis, a supervised feature extraction method for hyperspectral data. Hyperspectral Imaging (HSI) has appeared in various fields in recent years, including Remote Sensing.…
Principal component analysis (PCA) is a statistical technique commonly used in multivariate data analysis. However, PCA can be difficult to interpret and explain since the principal components (PCs) are linear combinations of the original…
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…
We revisit the problem of fair principal component analysis (PCA), where the goal is to learn the best low-rank linear approximation of the data that obfuscates demographic information. We propose a conceptually simple approach that allows…
Of particular interest is to discover useful representations solely from observations in an unsupervised generative manner. However, the question of whether existing normalizing flows provide effective representations for downstream tasks…