Modeling the Brain Connectivity for Pattern Analysis Itir Onal * , Emre Aksan * , Burak Velioglu * , Orhan Firat * , Mete Ozay † , Ilke Oztekin ‡ , Fatos T.Yarman Vural * * Department Computer Engineering, Middle East Technical University, Ankara, Turkey Emails: {itir,emre.aksan,velioglu,orhan.firat,vural}@ceng.metu.edu.tr † School of Computer Science, University of Birmingham, Birmingham, UK Email: m.ozay@cs.bham.ac.uk ‡ Department of Psychology, Koc University, Istanbul, Turkey Email: ioztekin@ku.edu.tr Abstract—An information theoretic approach is proposed to estimate the degree of connectivity for each voxel with its neighboring voxels. The neighborhood system is defined by spatial and functional connectivity metrics. Then, a local mesh of variable size is formed around each voxel using spatial or functional neighborhood. The mesh arc weights, called Mesh Arc Descriptors (MAD), are estimated by a linear regression model fitted to the voxel intensity values of the functional Magnetic Resonance Images (fMRI). Finally, the error term of the linear regression equation is used to estimate the mesh size for a voxel by optimizing Akaike’s information Criterion, Bayesian Information Criterion and Rissanen’s Minimum Description Length. fMRI measurements are obtained during a memory encoding and retrieval experiment performed on a subject who is exposed to the stimuli from 10 semantic categories. For each sample, a k- NN classifier is trained using the Mesh Arc Descriptors (MAD) having the variable mesh sizes. The classification performances reflect that the suggested variable-size Mesh Arc Descriptors represents the mental states better than the classical multi-voxel pattern representation. Moreover, we observe that the degree of connectivities in the brain greatly varies for each voxel. I. I NTRODUCTION Recent studies on modeling and analysis of fMRI data employ the full spatial pattern of brain activity and use pat- tern classification algorithms to decode the subtle information represented in a cognitive state [1]. Identification of patterns that are predictive of cognitive states and using them in classification are called Multi-voxel pattern analysis (MVPA). A pioneering study on MVPA methods to decode the cognitive states from the fMRI data was conducted by Haxby et al. [2]. Since then, many studies [3], [4], [5], [6], [1], [7] employed MVPA for various cognitive state classification problems. In classical MVPA approaches, generally, cognitive states are represented by concatenating the voxel intensity values under a feature vector and training a well-known classifier such as k-Nearest Neighbor (k-NN), Support Vector Machine (SVM) or Naive Bayes. Recently there has been interest in decoding brain states using fMRI in pattern recognition community. Plumpton et al. [8], [9] proposed two pattern recognition approaches for on- line classification of fMRI data. While the former uses linear and ensemble classifiers to decode cognitive states, the latter performs a semi-supervised ensemble update strategy. More- over, Gramfort et al. [10] used supervised learning methods to decode the visual percept formed by four letters during a word reading task. In their study Haufeld et al. [11] employed various kinds of supervised self-organizing maps (SSOM) to decode and visualize fMRI voxel patterns assigned to multiple categories. In [12], Ozay et al. propose a local mesh model in which relationships among spatially close voxels are used as features. These features, called Mesh Arc Descriptors, are shown to discriminate the cognitive states better than voxel intensities. In a further study, Firat et al. [13] model the relationships among functionally close neighbors and use the arc weights of functionally connected voxels to train a classifier. These studies show a significant improvement on the performance of the algorithms developed for cognitive state classification. In both studies, the number of neighboring voxels is fixed to form the mesh assuming that each voxel is connected to the same number of neighboring voxels to represent a cognitive process. In [14], [15], Onal et al. adopt a set of information theoretic criteria to estimate the optimal mesh size for each participant and sample. Although these approaches reflect the distributivity of information in the brain for an individual participant and sample, they form the local mesh of the same size around each voxel belonging to a sample. However, as Baldassano et al. [16] states, different sub-regions of brain have different degree of sub-connectivities among the voxels. Furthermore, according to Zalesky et al. [17], both the topology and the strength of connectivities of brain networks differ in different regions. In this study, we propose an information theoretic approach to model the spatial and functional brain connectivity among the voxels for a cognitive process. The degree of connectivity of a voxel is represented by the ”optimal” size of a local mesh, formed around each voxel. The size of the mesh is estimated by optimizing three well-known information theoretic criteria namely Akaike Information Criterion (AIC) [18], Bayesian Information Criterion (BIC) [19] and Minimum Description Length (MDL) [20]. Unlike previous approaches, this study aims to form meshes of variable sizes to detect how the information distribution varies in different parts of the brain. The local meshes are formed in two neighborhood systems, where nearest neighbors of a seed voxel are either the ones that are spatially closest to the seed voxel, or the ones whose Pearson correlations are highest among others. The Mesh Arc Descriptors extracted from meshes of vari- able sizes are used to train a k-NN classifiers to classify cognitive states. Our classification performances indicate that the proposed spatial and functional brain connectivity models represent the cognitive states with a higher accuracy than classical MVPA methods.