Locality preserving non-negative basis learning with graph embedding

Abstract

The high dimensionality of connectivity networks necessitates the development of methods identifying the connectivity building blocks that not only characterize the patterns of brain pathology but also reveal representative population patterns. In this paper, we present a non-negative component analysis framework for learning localized and sparse sub-network patterns of connectivity matrices by decomposing them into two sets of discriminative and reconstructive bases. In order to obtain components that are designed towards extracting population differences, we exploit the geometry of the population by using a graphtheoretical scheme that imposes locality-preserving properties as well as maintaining the underlying distance between distant nodes in the original and the projected space. The effectiveness of the proposed framework is demonstrated by applying it to two clinical studies using connectivity matrices derived from DTI to study a population of subjects with ASD, as well as a developmental study of structural brain connectivity that extracts gender differences.

Fig. 1

Illustration of a two-group multivariate point distribution on a manifold in the m-dimensional space. (a) The point distribution when projected into the direction x⃗ or y⃗. (b) The 3-nearest-neighbor graph of two selected magnified points. (c) The 3-farthest-point graph of the same two selected points as in b.

Fig. 2

The p = 5 connectivity bases (ASD study) learned by the proposed method. (a)–(b) are the q = 2 discriminatory, and (c)–(e) are the three reconstructive bases.

Fig. 3

The p = 10 connectivity bases (developmental study) learned by the proposed method. (a)–(f) are the q = 6 discriminatory, and (g)–(j) are the 4 reconstructive bases.