A Projection free method for Generalized Eigenvalue Problem with a nonsmooth Regularizer

Integrating Multimodal and Longitudinal Neuroimaging Data with Multi-Source Network Representation Learning

Uncovering the complex network of the brain is of great interest to the field of neuroimaging. Mining from these rich datasets, scientists try to unveil the fundamental biological mechanisms in the human brain. However, neuroimaging data collected for constructing brain networks is generally costly, and thus extracting useful information from a limited sample size of brain networks is demanding. Currently, there are two common trends in neuroimaging data collection that could be exploited to gain more information: 1) multimodal data, and 2) longitudinal data. It has been shown that these two types of data provide complementary information. Nonetheless, it is challenging to learn brain network representations that can simultaneously capture network properties from multimodal as well as longitudinal datasets. Here we propose a general fusion framework for multi-source learning of brain networks - multimodal brain network fusion with longitudinal coupling (MMLC). In our framework, three layers of information are considered, including cross-sectional similarity, multimodal coupling, and longitudinal consistency. Specifically, we jointly factorize multimodal networks and construct a rotation-based constraint to couple network variance across time. We also adopt the consensus factorization as the group consistent pattern. Using two publicly available brain imaging datasets, we demonstrate that MMLC may better predict psychometric scores than some other state-of-the-art brain network representation learning algorithms. Additionally, the discovered significant brain regions are synergistic with previous literature. Our new approach may boost statistical power and sheds new light on neuroimaging network biomarkers for future psychometric prediction research by integrating longitudinal and multimodal neuroimaging data.

Multimodal Fusion of Brain Networks with Longitudinal Couplings

In recent years, brain network analysis has attracted considerable interests in the field of neuroimaging analysis. It plays a vital role in understanding biologically fundamental mechanisms of human brains. As the upward trend of multi-source in neuroimaging data collection, effective learning from the different types of data sources, e.g. multimodal and longitudinal data, is much in demand. In this paper, we propose a general coupling framework, the multimodal neuroimaging network fusion with longitudinal couplings (MMLC), to learn the latent representations of brain networks. Specifically, we jointly factorize multimodal networks, assuming a linear relationship to couple network variance across time. Experimental results on two large datasets demonstrate the effectiveness of the proposed framework. The new approach integrates information from longitudinal, multimodal neuroimaging data and boosts statistical power to predict psychometric evaluation measures.

Abundant Inverse Regression using Sufficient Reduction and its Applications

Statistical models such as linear regression drive numerous applications in computer vision and machine learning. The landscape of practical deployments of these formulations is dominated by forward regression models that estimate the parameters of a function mapping a set of p covariates, x , to a response variable, y. The less known alternative, Inverse Regression, offers various benefits that are much less explored in vision problems. The goal of this paper is to show how Inverse Regression in the "abundant" feature setting (i.e., many subsets of features are associated with the target label or response, as is the case for images), together with a statistical construction called Sufficient Reduction, yields highly flexible models that are a natural fit for model estimation tasks in vision. Specifically, we obtain formulations that provide relevance of individual covariates used in prediction, at the level of specific examples/samples - in a sense, explaining why a particular prediction was made. With no compromise in performance relative to other methods, an ability to interpret why a learning algorithm is behaving in a specific way for each prediction, adds significant value in numerous applications. We illustrate these properties and the benefits of Abundant Inverse Regression (AIR) on three distinct applications.

Coupled Harmonic Bases for Longitudinal Characterization of Brain Networks

There is a great deal of interest in using large scale brain imaging studies to understand how brain connectivity evolves over time for an individual and how it varies over different levels/quantiles of cognitive function. To do so, one typically performs so-called tractography procedures on diffusion MR brain images and derives measures of brain connectivity expressed as graphs. The nodes correspond to distinct brain regions and the edges encode the strength of the connection. The scientific interest is in characterizing the evolution of these graphs over time or from healthy individuals to diseased. We pose this important question in terms of the Laplacian of the connectivity graphs derived from various longitudinal or disease time points - quantifying its progression is then expressed in terms of coupling the harmonic bases of a full set of Laplacians. We derive a coupled system of generalized eigenvalue problems (and corresponding numerical optimization schemes) whose solution helps characterize the full life cycle of brain connectivity evolution in a given dataset. Finally, we show a set of results on a diffusion MR imaging dataset of middle aged people at risk for Alzheimer's disease (AD), who are cognitively healthy. In such asymptomatic adults, we find that a framework for characterizing brain connectivity evolution provides the ability to predict cognitive scores for individual subjects, and for estimating the progression of participant's brain connectivity into the future.