Related papers: ALPCAH: Sample-wise Heteroscedastic PCA with Tail …
Methodologies for multidimensionality reduction aim at discovering low-dimensional manifolds where data ranges. Principal Component Analysis (PCA) is very effective if data have linear structure. But fails in identifying a possible…
Robust Principal Component Analysis (RPCA) aims at recovering a low-rank subspace from grossly corrupted high-dimensional (often visual) data and is a cornerstone in many machine learning and computer vision applications. Even though RPCA…
Principal component analysis (PCA) is a popular dimension reduction technique often used to visualize high-dimensional data structures. In genomics, this can involve millions of variables, but only tens to hundreds of observations.…
This paper examines in detail the geometric structure of principal component analysis (PCA) by considering in detail the distributions of both unrotated and rotated MNIST digits in the space defined by the lowest order PCA components. Since…
Principal component analysis (PCA) is fundamental to statistical machine learning. It extracts latent principal factors that contribute to the most variation of the data. When data are stored across multiple machines, however, communication…
Sparse Principal Component Analysis (sparse PCA) is a fundamental dimension-reduction tool that enhances interpretability in various high-dimensional settings. An important variant of sparse PCA studies the scenario when samples are…
Mining useful clusters from high dimensional data has received significant attention of the computer vision and pattern recognition community in the recent years. Linear and non-linear dimensionality reduction has played an important role…
A system with many degrees of freedom can be characterized by a covariance matrix; principal components analysis (PCA) focuses on the eigenvalues of this matrix, hoping to find a lower dimensional description. But when the spectrum is…
Data quality (DQ) remains a fundamental concern in big data pipelines, especially when aggregations occur at multiple hierarchical levels. Traditional DQ validation rules often fail to scale or generalize across dimensions such as user…
Principal component analysis (PCA) is one of the most fundamental tools in machine learning with broad use as a dimensionality reduction and denoising tool. In the later setting, while PCA is known to be effective at subspace recovery and…
We develop asymptotic theory for principal component analysis (PCA) of a high-dimensional factor model in which the working dimension $R$ is fixed and only required to satisfy $R \ge r$, where $r$ is the true number of factors. Building on…
We develop a new principal components analysis (PCA) type dimension reduction method for binary data. Different from the standard PCA which is defined on the observed data, the proposed PCA is defined on the logit transform of the success…
Principal component analysis (PCA) is by far the most widespread tool for unsupervised learning with high-dimensional data sets. Its application is popularly studied for the purpose of exploratory data analysis and online process…
PCA is widely used in health and care research to analyze complex HD datasets, such as patient health records, genetic data, and medical imaging. By reducing dimensionality, PCA helps identify key patterns and trends, which can aid in…
Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse…
Commonly used in computer vision and other applications, robust PCA represents an algorithmic attempt to reduce the sensitivity of classical PCA to outliers. The basic idea is to learn a decomposition of some data matrix of interest into…
This paper introduces a novel sparse latent factor modeling framework using sparse asymptotic Principal Component Analysis (APCA) to analyze the co-movements of high-dimensional panel data over time. Unlike existing methods based on sparse…
Sparse versions of principal component analysis (PCA) have imposed themselves as simple, yet powerful ways of selecting relevant features of high-dimensional data in an unsupervised manner. However, when several sparse principal components…
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…
We consider the problem of learning a mixture of Random Utility Models (RUMs). Despite the success of RUMs in various domains and the versatility of mixture RUMs to capture the heterogeneity in preferences, there has been only limited…