Related papers: Tutorial on principal component analysis, with app…
Principal Subspace Analysis (PSA) -- and its sibling, Principal Component Analysis (PCA) -- is one of the most popular approaches for dimensionality reduction in signal processing and machine learning. But centralized PSA/PCA solutions are…
Dimensionality reduction techniques play important roles in the analysis of big data. Traditional dimensionality reduction approaches, such as principal component analysis (PCA) and linear discriminant analysis (LDA), have been studied…
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…
A relaxed two dimensional principal component analysis (R2DPCA) approach is proposed for face recognition. Different to the 2DPCA, 2DPCA-$L_1$ and G2DPCA, the R2DPCA utilizes the label information (if known) of training samples to calculate…
We study non-equilibrium quantum dynamics by performing principal component analysis on the data sets of wavefunction snapshots. We show that a specific transformation of the data sets maximizes the information content in the largest…
Covariance operators of random functions are crucial tools to study the way random elements concentrate over their support. The principal component analysis of a random function X is well-known from a theoretical viewpoint and extensively…
Combining principles with pragmatism, a new approach and accompanying algorithm are presented to a longstanding problem in applied statistics: the interpretation of principal components. Following Rousson and Gasser [53 (2004) 539--555]…
This work presents a guide for the use of some of the functions of the R package "multiColl" for the detection of near multicollinearity. The main contribution, in comparison to other existing packages in R or other econometric software, is…
High-dimensional time series analysis has become increasingly important in fields such as finance, economics, and biology. The two primary tasks for high-dimensional time series analysis are modeling and statistical inference, which aim to…
The matrixdist R package provides a comprehensive suite of tools for the statistical analysis of matrix distributions, including phase-type, inhomogeneous phase-type, discrete phase-type, and related multivariate distributions. This paper…
Compositional data represent a specific family of multivariate data, where the information of interest is contained in the ratios between parts rather than in absolute values of single parts. The analysis of such specific data is…
The kernel matrix used in kernel methods encodes all the information required for solving complex nonlinear problems defined on data representations in the input space using simple, but implicitly defined, solutions. Spectral analysis on…
collapse is a large C/C++-based infrastructure package facilitating complex statistical computing, data transformation, and exploration tasks in R - at outstanding levels of performance and memory efficiency. It also implements a…
Principal component analysis (PCA) is often used to analyze multivariate data together with cluster analysis, which depends on the number of principal components used. It is therefore important to determine the number of significant…
Simulated high-dimensional data is useful for testing, validating, and improving algorithms used in dimension reduction, supervised and unsupervised learning. High-dimensional data is characterized by multiple variables that are dependent…
In this work, we develop a novel principal component analysis (PCA) for semimartingales by introducing a suitable spectral analysis for the quadratic variation operator. Motivated by high-dimensional complex systems typically found in…
In this paper, we consider the problem of forming machine cell in cellular manufacturing (CM). The major problem in the design of a CM system is to identify the part families and machine groups and consequently to form manufacturing cells.…
Principal Component Analysis (PCA) is a cornerstone of dimensionality reduction, yet its classical formulation relies critically on second-order moments and is therefore fragile in the presence of heavy-tailed data and impulsive noise.…
Principal component analysis is a ubiquitous tool in exploratory data analysis. It is widely used by applied scientists for visualization and interpretability purposes. We raise an important issue (the curse of isotropy) about 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…