Linear dimensionality reduction ([CG15])

A unified framework for linear dimensionality reduction: given \(n\) points \([x_1,\ldots, x_n]\in \R^{d\times n}\), optimize \(f_X(\cdot)\) to produce a linear transformation \(P\in \R^{r\times d}\) and let \(Y=PX\in \R^{r\times n}\) be the low-dimensional transformed data.

Types of reductions

• PCA
• ICA
• CCA
• Factor analysis