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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…

Principal component analysis (PCA) has achieved great success in unsupervised learning by identifying covariance correlations among features. If the data collection fails to capture the covariance information, PCA will not be able to…

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…

An improved mixture of probabilistic principal component analysis (PPCA) has been introduced for nonlinear data-driven process monitoring in this paper. To realize this purpose, the technique of a mixture of probabilistic principal…

It is well known that Principal Component Analysis (PCA) is strongly affected by outliers and a lot of effort has been put into robustification of PCA. In this paper we present a new algorithm for robust PCA minimizing the trimmed…

Network data are commonly collected in a variety of applications, representing either directly measured or statistically inferred connections between features of interest. In an increasing number of domains, these networks are collected…

Complexity is often exhibited in dynamical systems, where certain parameters evolve with time in a strange and chaotic nature. These systems lack predictability and are common in the physical world. Dissipative systems are one of such…

Asymmetric Tensor PCA (ATPCA) is a prototypical model for studying the trade-offs between sample complexity, computation, and memory. Existing algorithms for this problem typically require at least…

In statistical learning, high covariate dimensionality poses challenges for robust prediction and inference. To address this challenge, supervised dimension reduction is often performed, where dependence on the outcome is maximized for a…

The statistical analysis of tree structured data is a new topic in statistics with wide application areas. Some Principal Component Analysis (PCA) ideas were previously developed for binary tree spaces. In this study, we extend these ideas…

Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. This paper considers both minimax and adaptive estimation of the principal subspace in the high dimensional…

Identifying low-dimensional latent structures within high-dimensional data has long been a central topic in the machine learning community, driven by the need for data compression, storage, transmission, and deeper data understanding.…

A powerful study design in the fields of genomics and metabolomics is the 'replicated time course experiment' where individual time series are observed for a sample of biological units, such as human patients, termed replicates. Standard…

Principal components analysis (PCA) is a standard tool for identifying good low-dimensional approximations to data in high dimension. Many data sets of interest contain private or sensitive information about individuals. Algorithms which…

Principal component analysis (PCA) defines a reduced space described by PC axes for a given multidimensional-data sequence to capture the variations of the data. In practice, we need multiple data sequences that accurately obey individual…

We present quasicyclic principal component analysis (QPCA), a generalization of principal component analysis (PCA), that determines an optimized basis for a dataset in terms of families of shift-orthogonal principal vectors. This is of…

This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employs principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to…

We propose a novel Decentralized Differentially Private Power Method (D-DP-PM) for performing Principal Component Analysis (PCA) in networked multi-agent settings. Unlike conventional decentralized PCA approaches where each agent accesses…

In this paper, we propose a novel approach named by Discriminative Principal Component Analysis which is abbreviated as Discriminative PCA in order to enhance separability of PCA by Linear Discriminant Analysis (LDA). The proposed method…

When working with large biological data sets, exploratory analysis is an important first step for understanding the latent structure and for generating hypotheses to be tested in subsequent analyses. However, when the number of variables is…