Related papers: Maximally Correlated Principal Component Analysis
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 a transform for finding the principal components (PCs) that represent features of random data. PCA also provides a reconstruction of the PCs to the original data. We consider an extension of PCA which…
Principal component analysis (PCA) is widely used for dimensionality reduction, with well-documented merits in various applications involving high-dimensional data, including computer vision, preference measurement, and bioinformatics. In…
Principal Component Analysis (PCA) is one of the most commonly used statistical methods for data exploration, and for dimensionality reduction wherein the first few principal components account for an appreciable proportion of the…
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…
Multivariate Functional Principal Component Analysis (MFPCA) is a valuable tool for exploring relationships and identifying shared patterns of variation in multivariate functional data. However, controlling the roughness of the extracted…
Kernel Principal Component Analysis (KPCA) is a key machine learning algorithm for extracting nonlinear features from data. In the presence of a large volume of high dimensional data collected in a distributed fashion, it becomes very…
We propose a new data-driven method to select the optimal number of relevant components in Principal Component Analysis (PCA). This new method applies to correlation matrices whose time autocorrelation function decays more slowly than an…
Principal component analysis (PCA) is an important tool in exploring data. The conventional approach to PCA leads to a solution which favours the structures with large variances. This is sensitive to outliers and could obfuscate interesting…
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 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…
Sparse principal component analysis (SPCA) has emerged as a powerful technique for modern data analysis, providing improved interpretation of low-rank structures by identifying localized spatial structures in the data and disambiguating…
Dynamic inner principal component analysis (DiPCA) is a powerful method for the analysis of time-dependent multivariate data. DiPCA extracts dynamic latent variables that capture the most dominant temporal trends by solving a large-scale,…
This article focuses on the robust principal component analysis (PCA) of high-dimensional data with elliptical distributions. We investigate the PCA of the sample spatial-sign covariance matrix in both nonsparse and sparse contexts,…
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 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) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…
Principal component analysis (PCA) is a classical and ubiquitous method for reducing data dimensionality, but it is suboptimal for heterogeneous data that are increasingly common in modern applications. PCA treats all samples uniformly so…
Data integration is the problem of combining multiple data groups (studies, cohorts) and/or multiple data views (variables, features). This task is becoming increasingly important in many disciplines due to the prevalence of large and…
Retrieval-Augmented Generation (RAG) has emerged as a powerful paradigm for grounding large language models in external knowledge sources, improving the precision of agents responses. However, high-dimensional language model embeddings,…