Fast Transformation-Invariant Factor Analysis
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. In [6], Jojic and Frey introduced mixture of transformation-invariant component analyzers (MTCA) that can account for global transformations such as translations and rotations, perform clustering and learn local appearance deformations by dimensionality reduction. However, due to enormous computational requirements of the EM algorithm for learning the model, O(N2) where N is the dimensionality of a data sample, MTCA was not practical for most applications. In this paper, we demonstrate how fast Fourier transforms can reduce the computation to the order of N log N. With this speedup, we show the effectiveness of MTCA in various applications - tracking, video textures, clustering video sequences, object recognition, and object detection in images.