Related papers: Dynamic Functional Principal Component
Data can be assumed to be continuous functions defined on an infinite-dimensional space for many phenomena. However, the infinite-dimensional data might be driven by a small number of latent variables. Hence, factor models are relevant for…
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 the workhorse tool for dimensionality reduction in this era of big data. While often overlooked, the purpose of PCA is not only to reduce data dimensionality, but also to yield features that are…
Principal component analysis (PCA) is perhaps the most widely used method for data dimensionality reduction. A key question in PCA is deciding how many factors to retain. This manuscript describes a new approach to automatically selecting…
Of particular interest is to discover useful representations solely from observations in an unsupervised generative manner. However, the question of whether existing normalizing flows provide effective representations for downstream tasks…
In this paper we analyze approximate methods for undertaking a principal components analysis (PCA) on large data sets. PCA is a classical dimension reduction method that involves the projection of the data onto the subspace spanned by the…
Dimensionality reduction represents a critical preprocessing step in order to increase the efficiency and the performance of many hyperspectral imaging algorithms. However, dimensionality reduction algorithms, such as the Principal…
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 largely adopted for chemical process monitoring and numerous PCA-based systems have been developed to solve various fault detection and diagnosis problems. Since PCA-based methods assume that the…
Principal Components Analysis (PCA) is one of the most widely used dimension reduction techniques. Robust PCA (RPCA) refers to the problem of PCA when the data may be corrupted by outliers. Recent work by Cand{\`e}s, Wright, Li, and Ma…
Artificial neural networks that learn to perform Principal Component Analysis (PCA) and related tasks using strictly local learning rules have been previously derived based on the principle of similarity matching: similar pairs of inputs…
The purpose of this article is to develop the dimension reduction techniques in panel data analysis when the number of individuals and indicators is large. We use Principal Component Analysis (PCA) method to represent large number of…
Often the relation between the variables constituting a multivariate data space might be characterized by one or more of the terms: ``nonlinear'', ``branched'', ``disconnected'', ``bended'', ``curved'', ``heterogeneous'', or, more general,…
Despite the fact that they do not consider the temporal nature of data, classic dimensionality reduction techniques, such as PCA, are widely applied to time series data. In this paper, we introduce a factor decomposition specific for time…
Modern empirical analysis often relies on high-dimensional panel datasets with non-negligible cross-sectional and time-series correlations. Factor models are natural for capturing such dependencies. A tensor factor model describes the…
Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm…
Stochastic principal component analysis (SPCA) has become a popular dimensionality reduction strategy for large, high-dimensional datasets. We derive a simplified algorithm, called Lazy SPCA, which has reduced computational complexity and…
To interpret molecular dynamics simulations of biomolecular systems, systematic dimensionality reduction methods are commonly employed. Among others, this includes principal component analysis (PCA) and time-lagged independent component…
Many dimension reduction techniques have been developed for independent data, and most have also been extended to time series. However, these methods often fail to account for the dynamic dependencies both within and across series. In this…
In a fully-Bayesian Functional Principal Components Analysis (FPCA) the principal components are treated as unknown infinite-dimensional parameters. By projecting the functional principal components on a rich orthonormal spline basis, we…