Principal component analysis
About: Principal component analysis is a(n) research topic. Over the lifetime, 22148 publication(s) have been published within this topic receiving 691657 citation(s). The topic is also known as: PCA & principal components analysis.
Papers published on a yearly basis
•01 May 1986
Abstract: Introduction * Properties of Population Principal Components * Properties of Sample Principal Components * Interpreting Principal Components: Examples * Graphical Representation of Data Using Principal Components * Choosing a Subset of Principal Components or Variables * Principal Component Analysis and Factor Analysis * Principal Components in Regression Analysis * Principal Components Used with Other Multivariate Techniques * Outlier Detection, Influential Observations and Robust Estimation * Rotation and Interpretation of Principal Components * Principal Component Analysis for Time Series and Other Non-Independent Data * Principal Component Analysis for Special Types of Data * Generalizations and Adaptations of Principal Component Analysis
••15 Oct 2005
Abstract: When large multivariate datasets are analyzed, it is often desirable to reduce their dimensionality. Principal component analysis is one technique for doing this. It replaces the p original variables by a smaller number, q, of derived variables, the principal components, which are linear combinations of the original variables. Often, it is possible to retain most of the variability in the original variables with q very much smaller than p. Despite its apparent simplicity, principal component analysis has a number of subtleties, and it has many uses and extensions. A number of choices associated with the technique are briefly discussed, namely, covariance or correlation, how many components, and different normalization constraints, as well as confusion with factor analysis. Various uses and extensions are outlined. Keywords: dimension reduction; factor analysis; multivariate analysis; variance maximization
TL;DR: An approach to solving dimensionality reduction problems that uses easily measured local metric information to learn the underlying global geometry of a data set and efficiently computes a globally optimal solution, and is guaranteed to converge asymptotically to the true structure.
Abstract: Scientists working with large volumes of high-dimensional data, such as global climate patterns, stellar spectra, or human gene distributions, regularly confront the problem of dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. The human brain confronts the same problem in everyday perception, extracting from its high-dimensional sensory inputs-30,000 auditory nerve fibers or 10(6) optic nerve fibers-a manageably small number of perceptually relevant features. Here we describe an approach to solving dimensionality reduction problems that uses easily measured local metric information to learn the underlying global geometry of a data set. Unlike classical techniques such as principal component analysis (PCA) and multidimensional scaling (MDS), our approach is capable of discovering the nonlinear degrees of freedom that underlie complex natural observations, such as human handwriting or images of a face under different viewing conditions. In contrast to previous algorithms for nonlinear dimensionality reduction, ours efficiently computes a globally optimal solution, and, for an important class of data manifolds, is guaranteed to converge asymptotically to the true structure.
TL;DR: An efficient algorithm is proposed, which allows the computation of the ICA of a data matrix within a polynomial time and may actually be seen as an extension of the principal component analysis (PCA).
Abstract: The independent component analysis (ICA) of a random vector consists of searching for a linear transformation that minimizes the statistical dependence between its components. In order to define suitable search criteria, the expansion of mutual information is utilized as a function of cumulants of increasing orders. An efficient algorithm is proposed, which allows the computation of the ICA of a data matrix within a polynomial time. The concept of ICA may actually be seen as an extension of the principal component analysis (PCA), which can only impose independence up to the second order and, consequently, defines directions that are orthogonal. Potential applications of ICA include data analysis and compression, Bayesian detection, localization of sources, and blind identification and deconvolution.