Perelman School of Medicine at the University of Pennsylvania

Section for Biomedical Image Analysis (SBIA)

NMF-Based Decomposition

Multivariate pattern analysis (MVPA) techniques have gained significant popularity in neuroimaging due to their ability to harness relationships across variables, which leads to increased sensitivity. However, traditional MVPA techniques, such as Principal Component Analysis (PCA) and Independent Component Analysis (ICA), produce components and expansion coefficients that take both negative and positive values, thus modeling the data through complex mutual cancelation between component regions of opposite sign. The complex modeling of the data along with the often global spatial support of the components, which tend to highly overlap, result in representations that lack specificity.


To circumvent the limitations of commonly applied MVPA techniques, we proposed to leverage upon the well-known ability of Non-Negative Matrix Factorization (NNMF) to produce highly specific representations of image data [1]. The non-negativity constraint of this decomposition has been shown to lead to a parts-based representation of the data, where parts are combined in additive way to form a whole (see Fig. 1). These parts encode regions of the brain that vary in consistent ways across individuals, achieving a highly interpretable dimensionality reduction that generalizes well to new data. Importantly, the derived representations seem to follow what we know about the underlying functional organization of the brain and also capture some pathological processes. Moreover, the NNMF representations favorably compare to descriptions obtained with more commonly used matrix factorization methods like PCA and ICA [1].

Figure 1 Non-negative parts of the brain estimated using Gray Matter RAVENS maps from a healthy elder population [1].



  1. Sotiras, Aristeidis, Susan M. Resnick, and Christos Davatzikos. "Finding imaging patterns of structural covariance via non-negative matrix factorization." NeuroImage 108 (2015): 1-16.


Aristeidis Sotiras