We present a method for supervised, automatic, and reliable classification of healthy controls, patients with bipolar disorder, and patients with schizophrenia using brain imaging data. The method uses four supervised classification learning machines trained with a stochastic gradient learning rule based on the minimization of KullbackLeibler divergence and an optimal model complexity search through posterior probability estimation. Prior to classification, given the high dimensionality of functional MRI (fMRI) data, a dimension reduction stage comprising two steps is performed: first, a one-sample univariate t-test mean-difference Tscore approach is used to reduce the number of significant discriminative functional activated voxels, and then singular value decomposition is performed to further reduce the dimension of the input patterns to a number comparable to the limited number of subjects available for each of the three classes. Experimental results using functional brain imaging (fMRI) data include receiver operation characteristic curves for the three-way classifier with area under curve values around 0.82, 0.89, and 0.90 for healthy control versus nonhealthy, bipolar disorder versus nonbipolar, and schizophrenia patients versus nonschizophrenia binary problems, respectively. The average three-way correct classification rate (CCR) is in the range of 70\%-72\%, for the test set, remaining close to the estimated Bayesian optimal CCR theoretical upper bound of about 80\%, estimated from the one nearest-neighbor classifier over the same data. {\^A}{\textcopyright} 2010 IEEE.

}, keywords = {Algorithms, Artificial Intelligence, Bayes Theorem, Bayesian learning, Bayesian networks, Biological, Brain, Case-Control Studies, Classifiers, Computer-Assisted, Diseases, Functional MRI (fMRI), Humans, Learning machines, Learning systems, Magnetic Resonance Imaging, Models, Operation characteristic, Optimization, ROC Curve, Reproducibility of Results, Signal Processing, Singular value decomposition, Statistical tests, Stochastic models, Student t test, area under the curve, article, bipolar disorder, classification, controlled study, functional magnetic resonance imaging, human, machine learning, major clinical study, neuroimaging, patient coding, receiver operating characteristic, reliability, schizophrenia}, issn = {00189294}, doi = {10.1109/TBME.2010.2080679}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-78649311169\&partnerID=40\&md5=d3b90f1a3ee4ef209d131ef986e142db}, author = {J I Arribas and V D Calhoun and T Adali} } @article {420, title = {A model selection algorithm for a posteriori probability estimation with neural networks}, journal = {IEEE Transactions on Neural Networks}, volume = {16}, year = {2005}, pages = {799-809}, abstract = {This paper proposes a novel algorithm to jointly determine the structure and the parameters of a posteriori probability model based on neural networks (NNs). It makes use of well-known ideas of pruning, splitting, and merging neural components and takes advantage of the probabilistic interpretation of these components. The algorithm, so called a posteriori probability model selection (PPMS), is applied to an NN architecture called the generalized softmax perceptron (GSP) whose outputs can be understood as probabilities although results shown can be extended to more general network architectures. Learning rules are derived from the application of the expectation-maximization algorithm to the GSP-PPMS structure. Simulation results show the advantages of the proposed algorithm with respect to other schemes. {\^A}{\textcopyright} 2005 IEEE.

}, keywords = {Algorithms, Automated, Biological, Breast Neoplasms, Computer simulation, Computer-Assisted, Computing Methodologies, Decision Support Techniques, Diagnosis, Estimation, Expectation-maximization, Generalized Softmax Perceptron (GSP), Humans, Mathematical models, Model selection, Models, Neural Networks (Computer), Neural networks, Numerical Analysis, Objective function, Pattern recognition, Posterior probability, Probability, Statistical, Stochastic Processes, algorithm, article, artificial neural network, automated pattern recognition, biological model, breast tumor, classification, cluster analysis, computer analysis, computer assisted diagnosis, decision support system, evaluation, human, mathematical computing, methodology, statistical model, statistics}, issn = {10459227}, doi = {10.1109/TNN.2005.849826}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-23044459586\&partnerID=40\&md5=f00e7d86a625cfc466373a2a938276d0}, author = {J I Arribas and Jes{\'u}s Cid-Sueiro} }