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} } @conference {412, title = {Estimates of constrained multi-class a posteriori probabilities in time series problems with neural networks}, booktitle = {Proceedings of the International Joint Conference on Neural Networks}, year = {1999}, publisher = {IEEE, United States}, organization = {IEEE, United States}, address = {Washington, DC, USA}, abstract = {In time series problems, where time ordering is a crucial issue, the use of Partial Likelihood Estimation (PLE) represents a specially suitable method for the estimation of parameters in the model. We propose a new general supervised neural network algorithm, Joint Network and Data Density Estimation (JNDDE), that employs PLE to approximate conditional probability density functions for multi-class classification problems. The logistic regression analysis is generalized to multiple class problems with softmax regression neural network used to model the a-posteriori probabilities such that they are approximated by the network outputs. Constraints to the network architecture, as well as to the model of data, are imposed, resulting in both a flexible network architecture and distribution modeling. We consider application of JNDDE to channel equalization and present simulation results.

}, keywords = {Approximation theory, Computer simulation, Constraint theory, Data structures, Joint network-data density estimation (JNDDE), Mathematical models, Multi-class a posteriori probabilities, Neural networks, Partial likelihood estimation (PLE), Probability density function, Regression analysis}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-0033325263\&partnerID=40\&md5=8c6134020b0b2a9c5ab05b131c070b88}, author = {J I Arribas and Jes{\'u}s Cid-Sueiro and T Adali and H Ni and B Wang and A R Figueiras-Vidal} } @conference {411, title = {Neural architectures for parametric estimation of a posteriori probabilities by constrained conditional density functions}, booktitle = {Neural Networks for Signal Processing - Proceedings of the IEEE Workshop}, year = {1999}, publisher = {IEEE, Piscataway, NJ, United States}, organization = {IEEE, Piscataway, NJ, United States}, address = {Madison, WI, USA}, abstract = {A new approach to the estimation of {\textquoteright}a posteriori{\textquoteright} class probabilities using neural networks, the Joint Network and Data Density Estimation (JNDDE), is presented in this paper. It is based on the estimation of the conditional data density functions, with some restrictions imposed by the classifier structure; the Bayes{\textquoteright} rule is used to obtain the {\textquoteright}a posteriori{\textquoteright} probabilities from these densities. The proposed method is applied to three different network structures: the logistic perceptron (for the binary case), the softmax perceptron (for multi-class problems) and a generalized softmax perceptron (that can be used to map arbitrarily complex probability functions). Gaussian mixture models are used for the conditional densities. The method has the advantage of establishing a distinction between the network parameters and the model parameters. Complexity on any of them can be fixed as desired. Maximum Likelihood gradient-based rules for the estimation of the parameters can be obtained. It is shown that JNDDE exhibits a more robust convergence characteristics than other methods of a posteriori probability estimation, such as those based on the minimization of a Strict Sense Bayesian (SSB) cost function.

}, keywords = {Asymptotic stability, Constraint theory, Data structures, Gaussian mixture models, Joint network and data density estimation, Mathematical models, Maximum likelihood estimation, Neural networks, Probability}, doi = {https://doi.org/10.1109/NNSP.1999.788145}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-0033321049\&partnerID=40\&md5=7967fa377810cc0c3e6a4d9020024b80}, author = {J I Arribas and Jes{\'u}s Cid-Sueiro and T Adali and A R Figueiras-Vidal} } @conference {410, title = {Neural networks to estimate ML multi-class constrained conditional probability density functions}, booktitle = {Proceedings of the International Joint Conference on Neural Networks}, year = {1999}, publisher = {IEEE, United States}, organization = {IEEE, United States}, address = {Washington, DC, USA}, abstract = {In this paper, a new algorithm, the Joint Network and Data Density Estimation (JNDDE), is proposed to estimate the {\textquoteleft}a posteriori{\textquoteright} probabilities of the targets with neural networks in multiple classes problems. It is based on the estimation of conditional density functions for each class with some restrictions or constraints imposed by the classifier structure and the use Bayes rule to force the a posteriori probabilities at the output of the network, known here as a implicit set. The method is applied to train perceptrons by means of Gaussian mixture inputs, as a particular example for the Generalized Softmax Perceptron (GSP) network. The method has the advantage of providing a clear distinction between the network architecture and the model of the data constraints, giving network parameters or weights on one side and data over parameters on the other. MLE stochastic gradient based rules are obtained for JNDDE. This algorithm can be applied to hybrid labeled and unlabeled learning in a natural fashion.

}, keywords = {Generalized softmax perceptron (GSP) network, Joint network and data density estimation (JNDDE), Mathematical models, Maximum likelihood estimation, Neural networks, Probability density function, Random processes}, doi = {https://doi.org/10.1109/IJCNN.1999.831174}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-0033326060\&partnerID=40\&md5=bb38c144dac0872f3a467dc12170e6b6}, author = {J I Arribas and Jes{\'u}s Cid-Sueiro and T Adali and A R Figueiras-Vidal} }