Pattern Recognition, 4th Edition

6.7. Nonlinear Dimensionality Reduction

All the techniques that have been discussed so far in this chapter, as well as the LDA in the previous chapter, share a common goal: dimensionality reduction. In other words, given a high-dimensional data set X = {x¹, x²,…, xⁿ} ⊂ R^N of input patterns,^[4] the goal is to compute n corresponding patterns, Y = {y¹, y²,…, yⁿ} ⊂ R^m, m < N, that provide an “informative” representation of the input patterns. The word “informative” is interpreted in a different way for different methods; for example, PCA and ICA adopt different views on the issue. Another common characteristic of all the previous methods is that they respect linearity. Once a transformation matrix is computed, for each method, points in Y are ...