Optimal dimension reduction and transform coding with mixture principal components

This paper addresses the problem of resource allocation in local linear models for non-linear principal component analysis (PCA). In the local PCA model, the data space is partitioned into regions and PCA is performed in each region. Our primary result is that the advantage of these models over conventional PCA has been significantly underestimated in previous work. We apply local PCA models to the problems of image dimension reduction and transform coding. Our results show that by allocating representation or coding resources to the different image regions, instead of using a fixed arbitrary dimension everywhere, substantial increases in dimension reduced or compressed image quality can be achieved.