The Degrees of Freedom of Multilinear Principal Component Analysis

Abstract

We study the intrinsic model complexity of multilinear principal component analysis (mPCA), which deals with tensor objects. This model complexity, or effective degrees of freedom, is defined as the trace of the first derivative of the fitted tensor values as a function of tensor observations. The behavior of eigenvalues dispersion on each tensor mode plays a significant role in calculating the effective degrees of freedom in mPCA model. The degrees of freedom can be used for mPCA model selection.