Anatomical parts-based regression using non-negative matrix factorization

Abstract

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.

Intra-class multi-output regression based subspace analysis

“…For a > 0 we are guaranteed non-negative update rules. The convergence proof is similar to that in [6].…”

“…The individual high dimensional data points (vi), basis images (wi) and coefficients or low dimensional representations (hi) are represented in the columns of V, W and H matrices respectively. We use this framework to model multi-output regressions due to the efficacy of RNMF in single output parts based regression analysis [6].…”

“…These iterative update rules are obtained by building an auxiliary function from the cost function and optimizing it similar to [6].…”

“…Recently, regression based non-negative matrix factorization (RNMF) [6] aims to obtain subspaces which highlight the regression information in the low dimensional embedding. Our approach, which understands multi-dimensional intra-class regression patterns, is motivated by RNMF.…”

Neuroprediction, Violence, and the Law: Setting the Stage

“…As an alternative to using MVPA in this narrow diagnostic sense, new computational methods are under development to build classifiers that operate along a continuum, rather than as split-deciders. For example, one recently developed classifier can predict a person’s actual age within a few years, rather than simply predict if they are in a younger or older group based on an arbitrary age threshold [89]. This holds the potential for classifying a person in terms of a continuous metric of risk for future violence.…”