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Principal component analysis (PCA) frequently suffers from the disturbance of outliers and thus a spectrum of robust extensions and variations of PCA have been developed. However, existing extensions of PCA treat all samples equally even…

We study the robust principal component analysis (RPCA) problem in a distributed setting. The goal of RPCA is to find an underlying low-rank estimation for a raw data matrix when the data matrix is subject to the corruption of gross sparse…

In the context of sparse principal component detection, we bring evidence towards the existence of a statistical price to pay for computational efficiency. We measure the performance of a test by the smallest signal strength that it can…

In recent times, functional data analysis (FDA) has been successfully applied in the field of high dimensional data classification. In this paper, we present a novel classification framework using functional data and classwise Principal…

Machine learning and quantum computing are being progressively explored to shed light on possible computational approaches to deal with hitherto unsolvable problems. Classical methods for machine learning are ubiquitous in pattern…

In quantum kernel learning, the primary method involves using a quantum computer to calculate the inner product between feature vectors, thereby obtaining a Gram matrix used as a kernel in machine learning models such as support vector…

Sparse Principal Component Analysis (SPCA) is an important technique for high-dimensional data analysis, improving interpretability by imposing sparsity on principal components. However, existing methods often fail to simultaneously…

Principal component analysis (PCA), the most popular dimension-reduction technique, has been used to analyze high-dimensional data in many areas. It discovers the homogeneity within the data and creates a reduced feature space to capture as…

In medical image segmentation, limited external validity remains a critical obstacle when models are deployed across unseen datasets, an issue particularly pronounced in the ultrasound image domain. Existing solutions-such as domain…

We present a new technique called contrastive principal component analysis (cPCA) that is designed to discover low-dimensional structure that is unique to a dataset, or enriched in one dataset relative to other data. The technique is a…

For multimode processes, one generally establishes local monitoring models corresponding to local modes. However, the significant features of previous modes may be catastrophically forgotten when a monitoring model for the current mode is…

We present qrpca, a fast and scalable QR-decomposition principal component analysis package. The software, written in both R and python languages, makes use of torch for internal matrix computations, and enables GPU acceleration, when…

We introduce the Kernel-Elastic Autoencoder (KAE), a self-supervised generative model based on the transformer architecture with enhanced performance for molecular design. KAE is formulated based on two novel loss functions: modified…

Principal component analysis (PCA) is a widely employed statistical tool used primarily for dimensionality reduction. However, it is known to be adversely affected by the presence of outlying observations in the sample, which is quite…

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…

Principal component analysis (PCA) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain…

Operator learning provides methods to approximate mappings between infinite-dimensional function spaces. Deep operator networks (DeepONets) are a notable architecture in this field. Recently, an extension of DeepONet based on model…

An increasing number of data science and machine learning problems rely on computation with tensors, which better capture the multi-way relationships and interactions of data than matrices. When tapping into this critical advantage, a key…

This study presents a scalable data-driven algorithm designed to efficiently address the challenging problem of reachability analysis. Analysis of cyber-physical systems (CPS) relies typically on parametric physical models of dynamical…

Principal component analysis (PCA), along with its extensions to manifolds and outlier contaminated data, have been indispensable in computer vision and machine learning. In this work, we present a unifying formalism for PCA and its…