Computational Methods to Analyze Functional Connectomes

Rapid advances in neuroimaging have resulted in large repositories of images with high temporal and spatial resolutions. This has motivated large-scale connectomic analyses aimed at understanding representation and processing of stimuli. Such analyses require novel computational tools that significantly extend the state-of-the-art in machine learning and data science. These studies have far-reaching implications for a variety of scientific fields, including but not limited to (i) neuroscience, the study of  computational, theoretical, behavioural and cellular aspects of the functioning of brains(ii) neuropathology, the branch of medicine dedicated to the study of brain diseases and disorders(iii) psychiatry, the branch of medicine focused on diagnosis, treatment and prevention of mental, emotional and behavioural disorders, and (iv) the design of human-computer interfaces, specifically brain-computer interfaces in advanced augmented reality (AR), virtual reality (VR), and assistive technologies such as robotic exoskeletons and prosthetics.

In this thesis, we will focus our analyses on functional neuroimages (fMRIs). We will discuss three related, yet distinct threads of work. First, we will present the problem of identifiability, where we present our method to show that two distinct fMRIs taken over different sessions of the same subject are more similar in terms of their connectomes than those from two different subjects. We will present new results that identify specific parts of resting state and task-specific connectomes that are responsible for the unique \emph{signatures}. We show that a very small part of the connectome can be used to derive features for discriminating between individuals. A network of these features is shown to achieve excellent training and test accuracy in matching imaging datasets. We show that these features are statistically significant, robust to perturbations, invariant across populations, and are localized to a small number of structural regions of the brain. Furthermore, we show that for task-specific connectomes, the regions identified by our method are consistent with their known functional characterization. We present a matrix sampling technique to derive computationally efficient and accurate methods for identifying the discriminating sub-connectome and support all of the claims using state-of-the-art statistical tests and computational techniques. We will discuss the privacy implications of brain signatures. We present a de-anonymization attack rooted in the innate uniqueness of the structure and function of the human brain. We show that the attack reveals not only the {\em identity of an individual, but also the efficacy with which they performing cognitive tasks}. Our attack relies on a matrix analyses techniques that are used to extract discriminating features in neuroimages. We will also discuss challenges associated with defending against such attacks.

The second thread of projects deal with network analyses of functional brain images. We model functional connectomes as networks where nodes have spatial coordinates associated with them. The problem of identifying brain signatures using such networks maps to the problem of identifying conserved patterns corresponds to the alignment of the networks. While traditional methods tackle the problem of alignment using structure obtained from images, we formulate a novel problem -- {\em rigid graph alignment}, which simultaneously aligns the network, as well as the underlying structure. We formally specify the problem and present a method based on alternating least squares which alternately aligns the network and the structure via rigid body transformations. We demonstrate that this approach significantly improves the quality of network alignment in synthetic graphs as well as in brain networks. The power of this approach is that it can be applied to any graph where nodes have spatial coordinates, and that it works very well with a number of state-of-the-art network aligners that admit a prior. Next, we model brain activity as dynamic correlation graphs. An important problem in the context of such dynamic correlation graphs is the discovery of sets of regions of the brain, whose activity level is temporally coherent. These manifest as temporally persistent sub-graphs that are strongly connected, referred to as coherent subgraphs. We present a model and method for identifying coherent subgraphs in dynamic correlation graphs. We show that densely connected components in correlation graphs can be effectively modeled as low-rank sub-matrices derived from the time series signals. Specifically, we derive theoretical results showing that quasi-cliques in a correlation graph can be inferred from rows of the left singular matrix of its time-series, and can be tracked in time to identify coherent subgraphs. We apply the proposed method to real-world time-series data from functional MRIs to show that signals corresponding to nodes in coherent subgraphs can accurately predict whether the subject was actively performing a cognitive task, or was at rest. We also show that the same set of nodes can predict task outcomes/ conditions (such as win v/s loss in a gambling task). 

In the final thread of projects, we develop methods to understand how humans process naturalistic visual inputs. A major problem associated with the analyses of such as audiovisual input from videos (eg, movies), is that observed neuronal responses are due to combinations of “pure” factors, many of which may be latent. We present a novel methodological framework for deconvolving the brain’s response to mixed stimuli into its constituent responses to underlying pure factors. This framework, based on archetypal analysis, is applied to the analysis of imaging data from an adult cohort watching the BBC show, Sherlock. By focusing on visual stimulus, we show strong correlation between the observed deconvolved response and third party textual video annotations–demonstrating the significant power of the analyses techniques. Building on these results, we show that this techniques can be used to predict neuronal responses in new subjects (how other individuals react to Sherlock), as well as to new visual content (how individuals react to other videos with known annotations). Next, we describe a novel effort aimed at reconstructing video frames from observed functional MRI (fMRI) images. We demonstrate that our model can predict visual objects (such as face, car, etc.) and abstract aspects relating to scenes (such as indoor/outdoor). Our multi-modal learning approach first learns a representation of the video frames using an encoder-decoder model, and then learns a mapping from observed fMRI response to corresponding latent video frame representation. We demonstrate the power of our model and methods using a number of tests: (i) we show that the latent representations of video frames and those constructed from corresponding fMRI images are highly clustered; (ii) the latent representations can be used to predict objects in video frames using just the fMRI frames with good accuracy; and (iii) fMRI responses can be used to reconstruct the original inputs with high fidelity to predict the presence or absence of objects from corresponding frames.