Fast Approximate Karhunen-Loève Transform for Three-Way Array Data

Organs, cells and microstructures in cells dealt with in biomedical image analysis are volumetric data. We are required to process and analyse these data as volumetric data without embedding into higher-dimensional vector space from the viewpoints of object oriented data analysis. Sampled values of volumetric data are expressed as three-way array data. Therefore, principal component analysis of multi-way data is an essential technique for subspace-based pattern recognition, data retrievals and data compression of volumetric data. For one-way array (the vector form) problem the discrete cosine transform matrix is a good relaxed solution of the eigenmatrix for principal component analysis. This algebraic property of principal component analysis, derives an approximate fast algorithm for PCA of three-way data arrays.