Anatomical parts-based regression using non-negative matrix factorization

Non-negative matrix factorization (NMF) is an excellent tool for unsupervised parts-based learning, but proves to be ineffective when parts of a whole follow a specific pattern. Analyzing such local changes is particularly important when studying anatomical transformations. We propose a supervised method that incorporates a regression constraint into the NMF framework and learns maximally changing parts in the basis images, called Regression based NMF (RNMF). The algorithm is made robust against outliers by learning the distribution of the input manifold space, where the data resides. One of our main goals is to achieve good region localization. By incorporating a gradient smoothing and independence constraint into the factorized bases, contiguous local regions are captured. We apply our technique to a synthetic dataset and structural MRI brain images of subjects with varying ages. RNMF finds the localized regions which are expected to be highly changing over age to be manifested in its significant basis and it also achieves the best performance compared to other statistical regression and dimensionality reduction techniques.