Principal Component Analysis

Constructing new features which are the principal components of a data set. The principal components are random variables of maximal variance constructed from linear combinations of the input features. Equivalently, they are the projections onto the principal component axes, which are lines that minimize the average squared distance to each point in the data set. To ensure uniqueness, all of the principal component axes must be orthogonal. Principal Component Analysis is a maximum-likelihood technique for linear regression in the presence of Gaussian noise on both x and y. In some cases, Principal Component Analysis corresponds to a Fourier transform, such as the Discrete Cosine Transform used in JPEG image compression.

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Subjects: Mathematics Noise & Vibration