20.4 Progressive Spectral Dimensionality Process
The main goal of introducing DP is to represent the original data in another data space via a linear transformation so that the transformed dimensions can be prioritized according to the significance of their contained information. Then, the data dimensionality in the new transformed data space can be increased or decreased by adding or removing transformed dimensions component-by-component progressively. The PI-PRPP and ID-PIPP introduced in Sections 20.3.3 and 20.3.4 are such linear transformations to satisfy the needed properties and can be used to realize DP. To be more specific, DP via PIPP is carried out by a set of pair parameters , where is a projection vector produced by a PI that is used to generate the jth PIC and ρj is the priority score calculated for the jth PICj, that is, such that
Using (20.12), all the L PIPP-generated PICs can be ranked from 1 to L according to their priorities in descending order as follows.
Let the priorities of all the PICs be arranged in descending order according to their priorities,