High-order interactions observed in multi-task intrinsic networks are dominant indicators of aberrant brain function in schizophrenia.

Identifying the complex activity relationships present in rich, modern neuroimaging data sets remains a key challenge for neuroscience. The problem is hard because (a) the underlying spatial and temporal networks may be nonlinear and multivariate and (b) the observed data may be driven by numerous latent factors. Further, modern experiments often produce data sets containing multiple stimulus contexts or tasks processed by the same subjects. Fusing such multi-session data sets may reveal additional structure, but raises further statistical challenges. We present a novel analysis method for extracting complex activity networks from such multifaceted imaging data sets. Compared to previous methods, we choose a new point in the trade-off space, sacrificing detailed generative probability models and explicit latent variable inference in order to achieve robust estimation of multivariate, nonlinear group factors ("network clusters"). We apply our method to identify relationships of task-specific intrinsic networks in schizophrenia patients and control subjects from a large fMRI study. After identifying network-clusters characterized by within- and between-task interactions, we find significant differences between patient and control groups in interaction strength among networks. Our results are consistent with known findings of brain regions exhibiting deviations in schizophrenic patients. However, we also find high-order, nonlinear interactions that discriminate groups but that are not detected by linear, pairwise methods. We additionally identify high-order relationships that provide new insights into schizophrenia but that have not been found by traditional univariate or second-order methods. Overall, our approach can identify key relationships that are missed by existing analysis methods, without losing the ability to find relationships that are known to be important.

Independent component analysis for brain FMRI does indeed select for maximal independence.

A recent paper by Daubechies et al. claims that two independent component analysis (ICA) algorithms, Infomax and FastICA, which are widely used for functional magnetic resonance imaging (fMRI) analysis, select for sparsity rather than independence. The argument was supported by a series of experiments on synthetic data. We show that these experiments fall short of proving this claim and that the ICA algorithms are indeed doing what they are designed to do: identify maximally independent sources.

Correlated Noise: How it Breaks NMF, and What to Do About It.

Non-negative matrix factorization (NMF) is a problem of decomposing multivariate data into a set of features and their corresponding activations. When applied to experimental data, NMF has to cope with noise, which is often highly correlated. We show that correlated noise can break the Donoho and Stodden separability conditions of a dataset and a regular NMF algorithm will fail to decompose it, even when given freedom to be able to represent the noise as a separate feature. To cope with this issue, we present an algorithm for NMF with a generalized least squares objective function (glsNMF) and derive multiplicative updates for the method together with proving their convergence. The new algorithm successfully recovers the true representation from the noisy data. Robust performance can make glsNMF a valuable tool for analyzing empirical data.