Danial Lashkari

Clustering is often formulated as the maximum likelihood estimation of a mixture model that explains the data. The EM algorithm widely used to solve the resulting optimization problem is inherently a gradient-descent method and is sensitive to initialization. The resulting solution is a local optimum in the neighborhood of the initial guess. This sensitivity to initialization presents a significant challenge in clustering large data sets into many clusters. In this paper, we present a different approach to approximate mixture fitting for clustering. We introduce an exemplar-based likelihood function that approximates the exact likelihood. This formulation leads to a convex minimization problem and an efficient algorithm with guaranteed convergence to the globally optimal solution. The resulting clustering can be thought of as a probabilistic mapping of the data points to the set of exemplars that minimizes the average distance and the information-theoretic cost of mapping. We present experimental results illustrating the performance of our algorithm and its comparison with the conventional approach to mixture model clustering.

In this paper we construct an atlas that captures functional characteristics of a cognitive process from a population of individuals. The functional connectivity is encoded in a low-dimensional embedding space derived from a diffusion process on a graph that represents correlations of fMRI time courses. The atlas is represented by a common prior distribution for the embedded fMRI signals of all subjects. The atlas is not directly coupled to the anatomical space, and can represent functional networks that are variable in their spatial distribution. We derive an algorithm for fitting this generative model to the observed data in a population. Our results in a language fMRI study demonstrate that the method identifies coherent and functionally equivalent regions across subjects.

We present a model that describes the structure in the responses of different brain areas to a set of stimuli in terms of stimulus categories (clusters of stimuli) and functional units (clusters of voxels). We assume that voxels within a unit respond similarly to all stimuli from the same category, and design a nonparametric hierarchical model to capture inter-subject variability among the units. The model explicitly encodes the relationship between brain activations and fMRI time courses. A variational inference algorithm derived based on the model learns categories, units, and a set of unit-category activation probabilities from data. When applied to data from an fMRI study of object recognition, the method finds meaningful and consistent clusterings of stimuli into categories and voxels into units.

We explore unsupervised, hypothesis-free methods for fMRI analysis in two different types of experiments. First, we employ clustering to identify large-scale functionally homogeneous systems. We formulate a generative mixture model, derive the EM algorithm and apply it to delineate functional systems. We also investigate spectral clustering in application to this problem and demonstrate that both methods give rise to similar partitions of the brain based on resting state fMRI data. Second, we demonstrate how to extend this approach to include information about the experimental protocol. Specifically, we formulate a mixture model in the space of possible profiles of brain response to stimuli. In both applications, our methods confirm previously known results in brain mapping and point to new research directions for exploratory analysis of fMRI data.