Spectral methods for brain imaging and text analysis

Spectral learning algorithms have recently become popular in data-rich domains because they lead to statistical estimation algorithms which are fast, useful, and have strong theoretical properties. We propose a general spectral framework for analyzing brain imaging data that uses sparse matrix factorization to learn the boundaries of and connections between brain regions, using both the imaging data and prior neuroanatomical knowledge. We determine biologically-relevant, patient-specific functional parcels, which significantly improve classification of Mild Cognitive Impairment (MCI) over state-of-the-art competing approaches. We use similar spectral algorithms to learn “word embeddings”-low dimensional real vectors (`eigenwords´) that capture the “meanings” of words from their contexts. Finally, we present preliminary results relating the words in a sentence presented to a subject (represented as eigenwords) to the subjects´ brain images, providing a step towards determining how sentences are represented in the brain.