Principal component analysis

Principal component analysis (PCA) is the most popular multivariate statistical technique for dimensionality reduction. It analyzes the training data consisting of several dependent variables, which are, in general, inter-correlated, and extracts important information from the training data in the form of a set of new orthogonal variables called principal components. We can perform PCA using two methods either using eigen decomposition or using singular value decomposition (SVD).

PCA reduces the n–dimensional input data to r–dimensional input data, where r<n. In the most simple terms, PCA involves translating the origin and performing rotation of the axis such that one of the axes (principal axis) has the highest variance with data points. A reduced-dimensions dataset is obtained from the original dataset by performing this transformation and then dropping (removing) the orthogonal axes with low variance. Here we employ the SVD method...