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Our summary will be the projection of the original vectors on to q directions, the principal components, which span the sub- space. There are several equivalent ways of deriving the principal components mathe- matically. The simplest one is by finding the projections which maximize the vari- ance.
The central idea of principal component analysis (PCA) is to reduce the dimensionality of a data set consisting of a large number of interrelated variables, while retaining as much as possible of the variation present in the data set.
The task of principal component analysis (PCA) is to reduce the dimensionality of some high-dimensional data points by linearly projecting them onto a lower-dimensional space in such a way that the reconstruction error made by this projection is minimal.
Principal component analysis (PCA) is a multivariate technique that analyzes a data table in which observations are described by several inter-correlated quantitative dependent variables.
Principal Component Analysis (PCA) is the general name for a technique which uses sophis-ticated underlying mathematical principles to transforms a number of possibly correlated variables into a smaller number of variables called principal components.
Our goal is to find a weight matrix U that minimizes the mean squared difference between the input X and the output ˆX. The step from input to hidden unit can be seen as an analysis process. The X are modeled as being formed by a combination of uncorrelated sources, the components, that we want to recover.
Principal Component Analysis - Beyond practice (1) PCA is an algorithm that reduces the dimension of a cloud of points and keeps its covariance structure as much as possible.