A group model for stable multi-subject ICA on fMRI datasets

Spatial Independent Component Analysis (ICA) is an increasingly used data-driven method to analyze functional Magnetic Resonance Imaging (fMRI) data. To date, it has been used to extract sets of mutually correlated brain regions without prior information on the time course of these regions. Some of these sets of regions, interpreted as functional networks, have recently been used to provide markers of brain diseases and open the road to paradigm-free population comparisons. Such group studies raise the question of modeling subject variability within ICA: how can the patterns representative of a group be modeled and estimated via ICA for reliable inter-group comparisons? In this paper, we propose a hierarchical model for patterns in multi-subject fMRI datasets, akin to mixed-effect group models used in linear-model-based analysis. We introduce an estimation procedure, CanICA (Canonical ICA), based on i) probabilistic dimension reduction of the individual data, ii) canonical correlation analysis to identify a data subspace common to the group iii) ICA-based pattern extraction. In addition, we introduce a procedure based on cross-validation to quantify the stability of ICA patterns at the level of the group. We compare our method with state-of-the-art multi-subject fMRI ICA methods and show that the features extracted using our procedure are more reproducible at the group level on two datasets of 12 healthy controls: a resting-state and a functional localizer study

CanICA: Model-based extraction of reproducible group-level ICA patterns from fMRI time series

Spatial Independent Component Analysis (ICA) is an increasingly used data-driven method to analyze functional Magnetic Resonance Imaging (fMRI) data. To date, it has been used to extract meaningful patterns without prior information. However, ICA is not robust to mild data variation and remains a parameter-sensitive algorithm. The validity of the extracted patterns is hard to establish, as well as the significance of differences between patterns extracted from different groups of subjects. We start from a generative model of the fMRI group data to introduce a probabilistic ICA pattern-extraction algorithm, called CanICA (Canonical ICA). Thanks to an explicit noise model and canonical correlation analysis, our method is auto-calibrated and identifies the group-reproducible data subspace before performing ICA. We compare our method to state-of-the-art multi-subject fMRI ICA methods and show that the features extracted are more reproducible

Modeling Covariate Effects in Group Independent Component Analysis with Applications to Functional Magnetic Resonance Imaging

Independent component analysis (ICA) is a powerful computational tool for separating independent source signals from their linear mixtures. ICA has been widely applied in neuroimaging studies to identify and characterize underlying brain functional networks. An important goal in such studies is to assess the effects of subjects' clinical and demographic covariates on the spatial distributions of the functional networks. Currently, covariate effects are not incorporated in existing group ICA decomposition methods. Hence, they can only be evaluated through ad-hoc approaches which may not be accurate in many cases. In this paper, we propose a hierarchical covariate ICA model that provides a formal statistical framework for estimating and testing covariate effects in ICA decomposition. A maximum likelihood method is proposed for estimating the covariate ICA model. We develop two expectation-maximization (EM) algorithms to obtain maximum likelihood estimates. The first is an exact EM algorithm, which has analytically tractable E-step and M-step. Additionally, we propose a subspace-based approximate EM, which can significantly reduce computational time while still retain high model-fitting accuracy. Furthermore, to test covariate effects on the functional networks, we develop a voxel-wise approximate inference procedure which eliminates the needs of computationally expensive covariance estimation. The performance of the proposed methods is evaluated via simulation studies. The application is illustrated through an fMRI study of Zen meditation.Comment: 36 pages, 5 figure

Graph-Based Decoding Model for Functional Alignment of Unaligned fMRI Data

Aggregating multi-subject functional magnetic resonance imaging (fMRI) data is indispensable for generating valid and general inferences from patterns distributed across human brains. The disparities in anatomical structures and functional topographies of human brains warrant aligning fMRI data across subjects. However, the existing functional alignment methods cannot handle well various kinds of fMRI datasets today, especially when they are not temporally-aligned, i.e., some of the subjects probably lack the responses to some stimuli, or different subjects might follow different sequences of stimuli. In this paper, a cross-subject graph that depicts the (dis)similarities between samples across subjects is used as a priori for developing a more flexible framework that suits an assortment of fMRI datasets. However, the high dimension of fMRI data and the use of multiple subjects makes the crude framework time-consuming or unpractical. To address this issue, we further regularize the framework, so that a novel feasible kernel-based optimization, which permits nonlinear feature extraction, could be theoretically developed. Specifically, a low-dimension assumption is imposed on each new feature space to avoid overfitting caused by the highspatial-low-temporal resolution of fMRI data. Experimental results on five datasets suggest that the proposed method is not only superior to several state-of-the-art methods on temporally-aligned fMRI data, but also suitable for dealing `with temporally-unaligned fMRI data.Comment: 17 pages, 10 figures, Proceedings of the Association for the Advancement of Artificial Intelligence (AAAI-20

Directional clustering through matrix factorization

This paper deals with a clustering problem where feature vectors are clustered depending on the angle between feature vectors, that is, feature vectors are grouped together if they point roughly in the same direction. This directional distance measure arises in several applications, including document classification and human brain imaging. Using ideas from the field of constrained low-rank matrix factorization and sparse approximation, a novel approach is presented that differs from classical clustering methods, such as seminonnegative matrix factorization, K-EVD, or k-means clustering, yet combines some aspects of all these. As in nonnegative matrix factorization and K-EVD, the matrix decomposition is iteratively refined to optimize a data fidelity term; however, no positivity constraint is enforced directly nor do we need to explicitly compute eigenvectors. As in k-means and K-EVD, each optimization step is followed by a hard cluster assignment. This leads to an efficient algorithm that is shown here to outperform common competitors in terms of clustering performance and/or computation speed. In addition to a detailed theoretical analysis of some of the algorithm's main properties, the approach is empirically evaluated on a range of toy problems, several standard text clustering data sets, and a high-dimensional problem in brain imaging, where functional magnetic resonance imaging data are used to partition the human cerebral cortex into distinct functional regions