Tree Augmented Na ve Bayesian Classifier with Feature Selection for fMRI Data Aabid Shariff aas44 pitt edu Ahmet Bakan ahb12 pitt edu Abstract Functional Magnetic Resonance Imaging of brain produces a vast amount of data that could help in understanding cognitive processes In order to achieve this the problem is cast as a classification problem Here we implement Tree Augmented Na ve Bayes to increase the accuracy of previously implemented Na ve Bayes We also use activity based feature selection and Principal Component Analysis to reduce the dimensionality of data and increase accuracy We have shown that TAN classifier performs better than NB classifier Also we have modified the activity based feature selection method and we have shown that there is a significant improvement in the classification accuracy 1 I n trod u ction Functional Magnetic Resonance Imaging fMRI is a powerful technique that is known to represent neural activity in brain indirectly Figure 1 illustrates fMRI data with an instantaneous image of a slice of the brain and change in activity in a volume of the brain Although this data does not provide us single neuron resolution of neural activity many studies have reported the use of this data to identify cognition These kind of studies are important in the understanding of cognitive processes medical diagnostics e g in Alzheimer s disease etc The basis of these studies is the existence of anatomically distinct regions in the brain for distinct functions carried out by the brain that reflect a particular cognitive process We can now use classification methods to understand the mapping of brain activity to cognition fMRI data has been very useful to implement as an input to classification algorithms Some problems with fMRI data are that they are high dimensional noisy and sparse This project aims at implementing Tree Augmented Na ve Bayes Classifier to increase the accuracy of prediction compared to na ve Bayes classifier while addressing above issues associated with data Figure 1 fMRI data from subject 05710 a Image of a slice of brain and b time change of activity in a voxel 2 R elated Work Recent work has trained several methods to classify the cognitive states of brain of a human subject by using fMRI data Mitchell 2004 The tasks defined in the study were classification of states looking at a sentence versus looking at a picture reading an ambiguous sentence versus reading an non ambiguous sentence and viewing a word describing one of several categories The study has made use of Na ve Bayes classifier NB Support Vector Machines SVM and k Nearest Neighbor kNN machine learning methods The group has also applied four different types of feature selection methods in accordance with the nature of the data These methods were based on the cognitive state discriminative ability of voxels activity of voxels at given cognitive state activity of voxels categorized by Regions of Interest in the brain and mean of active voxels for each region of interest In the first type of classification problems discriminating between looking at a picture or a sentence highest prediction accuracy at 89 was achieved by SVM when feature selection was performed Figure 2 Structure of the classifiers used in this study C is the class variable A s are features and arrows indicate dependence among variables In the above study NB classifier performed with 82 accuracy when feature selection was performed This simple classifier makes independence assumptions among all features of the data given the class variable So as one would expect that forsaking some of the irrelevant independence assumptions between some of the features may improve the accuracy of the learner One method aiming at reducing the number of such unwarranted independent assumptions is Tree Augmented Na ve Bayes TAN classifier described by Friedman et al The structure and relations between class variable and features in NB and TAN models are shown in Figure 2 The procedure described in Friedman et al s work is based on Chow and Liu s method to find dependence relations among variables so to be able to factorize a joint probability distribution among these variables The authors perform experiments on 25 different cases and show that the method provides higher accuracy than Na ve Bayes classifier in two out of three cases Construct TAN procedure described by Friedman et al and others to learn a TAN classifier has time and space complexity of the order O n 2 N where n is the number of features and N is number of examples Later Meila and Shi et al have modified the algorithm independently to decrease computational cost based on some assumptions and requirements in the data Meila s improvement accelerated the algorithm reducing the time complexity to O s 2Nlog s 2N n where s is a constant related to sparsity of data and s n So as it becomes obvious the acceleration in the algorithm takes advantage of sparsity in feature vectors of examples which can be illustrated with well known text classification problem The more recent study of Shi et al reduced the space complexity of the algorithm based on Meila s work In all these studies use of TAN is described for discrete data Yang et al has studied discretization methods for na ve Bayes classifier This is still a field of current research since performance of methods vary with the type of data Most recently Perez et al have reported TAN for continuous and normally distributed data which is the one we have chosen to use in this study due to nature of the fMRI data 3 Meth od s Before describing the methods we will point the main issue arising with this classifier and data combination The fMRI data has dimensionality of the order 10 5 The computational cost of applying this algorithm to fMRI data naturally requires considering efficient computation Since we cannot take advantage of later algorithmic improvements in Construct TAN method we are going to consider feature selection We will first describe procedures to select relevant features than continue with describing the implementation of the algorithms 3 1 F e a t u re S e l e c t i o n Since the fMRI data is high dimensional and noisy we require feature selection methods to reduce the computational time and also to reduce errors in the training 3 1 1 Activity Based One of the feature selection methods used here is the activity test method The goal of feature selection is to discriminate the target classes A method to do this is the
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