This paper introduces two unsupervised learning methods for analyzing functional magnetic resonance imaging (fMRI) data based on hidden Markov model (HMM). HMM approach is focused on capturing the first-order statistical evolution among the samples of a voxel time series, and it can provide a complimentary perspective of the BOLD signals. Two-state HMM is created for each voxel, and the model parameters are estimated from the voxel time series and the stimulus paradigm. Two different activation detection methods are presented in this paper. The first method is based on the likelihood and likelihood-ratio test, in which an additional Gaussian model is used to enhance the contrast of the HMM likelihood map. The second method is based on certain distance measures between the two state distributions, in which the most likely HMM state sequence is estimated through the Viterbi algorithm. The distance between the on-state and off-state distributions is measured either through a t-test, or using the Kullback-Leibler distance (KLD). Experimental results on both normal subject and brain tumor subject are presented. HMM approach appears to be more robust in detecting the supplemental active voxels comparing with SPM, especially for brain tumor subject. 1. Introduction Functional magnetic resonance imaging (fMRI) is a well-established technique to monitor brain activities in the field of cognitive neuroscience. The temporal behavior of each fMRI voxel reflects the variations in the concentration of oxyhemoglobin and deoxyhemoglobin, measured through blood oxygen level-dependent (BOLD) contrast. BOLD signal is generally considered as an indirect indicator for brain activities, because neural activations may increase blood flow in certain regions of the brain. 1.1. Characteristics of fMRI Data fMRI data are collected as a time series of 3 D images. Each point in the 3 D image volume is called a voxel. fMRI data have four important characteristics: (1) large data volume; (2) relatively low SNR; (3) hemodynamic delay and dispersion; (4) fractal properties. Typically, one fMRI data set includes over 1 0 0 -K voxels from a whole brain scan and therefore has 1 0 0 -K time series. The observed time sequences are combinations of different types of signals, such as task-related, function-related, and transiently task-related (different kinds of transiently task-related signals coming from different regions of brain). These are the signals that convey brain activation information. There are also many types of noises, which can be physiology-related, motion-related, and
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