ABSTRACT
In Chapter 1, we pointed out why dimensionality reduction is commonly needed in practice. On one hand, real-world data are often specified in a high-dimensional space. Direct processing of high-dimensional data is computationally expensive and the number of samples available is often small compared to their high dimensionality. On the other hand, real-world data are often highly constrained to a low-dimensional subspace. Thus, dimensionality reduction attempts to learn a mapping of high-dimensional data to a low-dimensional space, that is, a subspace.
