Fast Transformation Invariant Component Analysis
Abstract Dimensionality reduction techniques such as principal component analysis and factor analysis are used to discover a linear mapping between high dimensional data samples and points in a lower dimensional subspace. Previously, Frey and Jojic introduced transformation invariant component analysis (TCA) to learn a linear mapping, invariant to a set of known form of global transformations. However, parameter estimation in that model using the previously proposed expectation maximization (EM) algorithm required scalar operations in the order of N2 where N is the dimensionality of each training example. This is prohibitive for many applications of interest such as modeling mid to large size images, where, for instance, N may be as high as 786432 (512x512 RGB image) In this paper, we present an efficient algorithm that reduces the computational requirements to order of Nlog N. With this speedup, we show the effectiveness of transformation invariant component analysis in various applications including tracking, learning video textures, clustering, object recognition and object detection in images. Software for TCA can be downloaded from http:/www.psi.toronto.edu/fastTCA.htm.
International Journal of Computer Vision