Related papers: Compressing Large Language Models with PCA Without…

When the dimension of data is comparable to or larger than the number of data samples, Principal Components Analysis (PCA) may exhibit problematic high-dimensional noise. In this work, we propose an Empirical Bayes PCA method that reduces…

Robust principal component analysis (RPCA) is a critical tool in modern machine learning, which detects outliers in the task of low-rank matrix reconstruction. In this paper, we propose a scalable and learnable non-convex approach for…

Revisiting PCA for Time Series Reduction in Temporal Dimension; Jiaxin Gao, Wenbo Hu, Yuntian Chen; Deep learning has significantly advanced time series analysis (TSA), enabling the extraction of complex patterns for tasks like…

In datasets where the number of parameters is fixed and the number of samples is large, principal component analysis (PCA) is a powerful dimension reduction tool. However, in many contemporary datasets, when the number of parameters is…

In this paper, we study the problem of computing a Principal Component Analysis of data affected by Poisson noise. We assume samples are drawn from independent Poisson distributions. We want to estimate principle components of a fixed…

We use Principal Component Analysis (PCA) to study the gas dynamics in numerical simulations of typical MCs. Our simulations account for the non-isothermal nature of the gas and include a simplified treatment of the time-dependent gas…

Machine learning (ML) can process large sets of data generated from complex systems, which is ideal for classification tasks as often appeared in critical phenomena. Meanwhile ML techniques have been found effective in detecting critical…

Generalized principal component analysis (GLM-PCA) facilitates dimension reduction of non-normally distributed data. We provide a detailed derivation of GLM-PCA with a focus on optimization. We also demonstrate how to incorporate…

Principal Component Analysis (PCA) is known to be the most widely applied dimensionality reduction approach. A lot of improvements have been done on the traditional PCA, in order to obtain optimal results in the dimensionality reduction of…

We consider the Principal Component Analysis problem for large tensors of arbitrary order $k$ under a single-spike (or rank-one plus noise) model. On the one hand, we use information theory, and recent results in probability theory, to…

Machine Learning models are prone to fail when test data are different from training data, a situation often encountered in real applications known as distribution shift. While still valid, the training-time knowledge becomes less…

Data reconciliation (DR) and Principal Component Analysis (PCA) are two popular data analysis techniques in process industries. Data reconciliation is used to obtain accurate and consistent estimates of variables and parameters from…

Principal Component Analysis (PCA) is a widely used technique in machine learning, data analysis and signal processing. With the increase in the size and complexity of datasets, it has become important to develop low-space usage algorithms…

Probabilistic principal component analysis (PPCA) is currently one of the most used statistical tools to reduce the ambient dimension of the data. From multidimensional scaling to the imputation of missing data, PPCA has a broad spectrum of…

Recent advances in deep learning have made available large, powerful convolutional neural networks (CNN) with state-of-the-art performance in several real-world applications. Unfortunately, these large-sized models have millions of…

Principal component analysis (PCA) is a powerful data reductionmethod for Structural Health Monitoring. However, its computa-tional cost and data memory footprint pose a significant challengewhen PCA has to run on limited capability…

Principle Component Analysis PCA is a classical feature extraction and data representation technique widely used in pattern recognition. It is one of the most successful techniques in face recognition. But it has drawback of high…

Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in…

Principal Component Analysis is a novel way of of dimensionality reduction. This problem essentially boils down to finding the top k eigen vectors of the data covariance matrix. A considerable amount of literature is found on algorithms…

Principal component analysis (PCA) is often used for analyzing data in the most diverse areas. In this work, we report an integrated approach to several theoretical and practical aspects of PCA. We start by providing, in an intuitive and…