The State of the Art in Online Handwriting Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
Competitive local linear modeling
Signal Processing
Self-organizing maps
Detection, Estimation, and Modulation Theory: Radar-Sonar Signal Processing and Gaussian Signals in Noise
Neural Networks: A Comprehensive Foundation
Neural Networks: A Comprehensive Foundation
Neural and Adaptive Systems: Fundamentals through Simulations with CD-ROM
Neural and Adaptive Systems: Fundamentals through Simulations with CD-ROM
Nonlinear Biomedical Signal Processing Vol. II: Dynamic Analysis and Modeling
Nonlinear Biomedical Signal Processing Vol. II: Dynamic Analysis and Modeling
Joint estimation of time delays and directions of arrival ofmultiple reflections of a known signal
IEEE Transactions on Signal Processing
Statistical analysis and spectral estimation techniques forone-dimensional chaotic signals
IEEE Transactions on Signal Processing
Bayesian deconvolution of noisy filtered point processes
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Asymptotic maximum likelihood estimator performance for chaotic signals in noise
IEEE Transactions on Signal Processing
Universal composite hypothesis testing: a competitive minimax approach
IEEE Transactions on Information Theory
Optimal simultaneous detection and estimation under a false alarm constraint
IEEE Transactions on Information Theory
Optimal detection and estimation of straight patterns
IEEE Transactions on Image Processing
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There are many problems in science and engineering where the signals of interest depend simultaneously on continuous and q-ary parameters, i.e. parameters which can take only one out of q possible values. This problem is generally known as multiple composite hypothesis testing. The probability function of the observed data for a given hypothesis is uncertain, as it depends on the parameters of the system. When there is no statistical model for the unknown continuous parameters, the GLRT is the usual criterion for the binary case. Although the GLRT philosophy can be extended to accommodate multiple composite hypotheses, unfortunately the solution is not satisfactory in the general case. In this paper, we restrict the general scenario and consider problems with q-ary input vectors and linear dependence on a unique set of continuous parameters; i.e. all the hypotheses depend on the same set of parameters. Direct application of the GLRT is feasible in this case, but it suffers from an exponential increase in complexity with data length. In this paper, we derive a low-complexity stochastic gradient procedure for this problem. The resulting algorithm, which resembles the LMS, updates the unknown parameters only along the direction of the winning hypothesis. This approach also presents similarities with competitive learning techniques, in the sense that at each iteration the different hypotheses compete to train the parameters. The validity of the proposed approach is shown by applying it to blind system identification/equalization, and chaotic AR(1) model estimation.