Robust Principal Component Analysis for Brain Imaging

Discrimination of cognitive states from functional Magnetic Resonance Images (fMRI) is a challenging task, particularly when across subjects common representation of brain states is to be detected. Among several difficulties, the huge number of features (voxels) is a major obstacle for reliable discrimination of common patterns across brains. Principal Component Analysis (PCA) is widely applied for learning of low dimensional linear data models in image processing. The main drawback of the traditional PCA is that it is a least-square technique that fails to account for outliers. Previous attempts to make PCA robust have treated the entire image as an outlier. However, the fMRIs may contain undesirable artifacts due to errors related with the brain scanning process, alignment errors or pixels that are corrupted by noise. In this paper we propose a new dimensionality reduction approach based on Robust Principal Component Analysis (RPCA) that uses an intra-sample outlier process to account for pixel outliers. The RPCA improves classification accuracy of two cognitive brain states across various subjects compared to using conventional PCA or not performing dimensionality reduction.