Dimensionality Reduction Methods for Brain Imaging Data Analysis

Abstract

The past century has witnessed the grand success of brain imaging technologies, such as electroencephalography and magnetic resonance imaging, in probing cognitive states and pathological brain dynamics for neuroscience research and neurology practices. Human brain is “the most complex object in the universe,” and brain imaging data ( BID ) are routinely of multiple/many attributes and highly non-stationary. These are determined by the nature of BID as the recordings of the evolving processes of the brain(s) under examination in various views. Driven by the increasingly high demands for precision, efficiency, and reliability in neuro-science and engineering tasks, dimensionality reduction has become a priority issue in BID analysis to handle the notoriously high dimensionality and large scale of big BID sets as well as the enormously complicated interdependencies among data elements. This has become particularly urgent and challenging in this big data era. Dimensionality reduction theories and methods manifest unrivaled potential in revealing key insights to BID via offering the low-dimensional/tiny representations/features, which may preserve critical characterizations of massive neuronal activities and brain functional and/or malfunctional states of interest. This study surveys the most salient work along this direction conforming to a 3-dimensional taxonomy with respect to (1) the scale of BID , of which the design with this consideration is important for the potential applications; (2) the order of BID , in which a higher order denotes more BID attributes manipulatable by the method; and (3) linearity , in which the method’s degree of linearity largely determines the “fidelity” in BID exploration. This study defines criteria for qualitative evaluations of these works in terms of effectiveness, interpretability, efficiency, and scalability. The classifications and evaluations based on the taxonomy provide comprehensive guides to (1) how existing research and development efforts are distributed and (2) their performance, features, and potential in influential applications especially when involving big data. In the end, this study crystallizes the open technical issues and proposes research challenges that must be solved to enable further researches in this area of great potential.