Spectral methods are widely used to reduce data dimensionality in order to enable a more effective use of several pattern recognition techniques such as clustering algorithms. Here we review the most popular spectral methods.
Consider a collection of sample points $ \{x_1,x_2,\cdots,x_n\} $ where $ x_i \in R^m $. We divide the methods in two categories:
- Outer Characteristics of the point cloud: These methods require the spectral analysis of a positive definite kernel of dimension m, the extrinsic dimensionality of the data.
- Inner characteristics of the point cloud: These methods require the spectral analysis of a positive definite kernel of dimension n, the number of samples in the sample cloud.
