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Discriminative training refers to an approach to pattern recognition based on direct minimization of a cost function commensurate with the performance of the recognition system. This is in contrast to the procedure of probability distribution estimation as conventionally required in Bayes' formulation of the statistical pattern recognition problem. Currently, most discriminative training algorithms for nonlinear classifier designs are based on gradient-descent (GD) methods for cost minimization. These algorithms are easy to derive and effective in practice, but are slow in training speed and have difficulty selecting the learning rates. To address the problem, we present our study on a fast discriminative training algorithm. The algorithm initializes the parameters by the expectation-maximization (EM) algorithm, and then uses a set of closed-form formulas derived in this paper to further optimize a proposed objective of minimizing error rate. Experiments in speech applications show that the algorithm provides better recognition accuracy in a fewer iterations than the EM algorithm and a neural network trained by hundreds of GD iterations. Although some convergent properties need further research, the proposed objective and derived formulas can benefit further study of the problem. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, an algorithm is proposed to integrate the unsupervised learning with the optimization of the Finite Mixture Models (FMM). While learning parameters of the FMM the proposed algorithm minimizes the mutual information among components of the FMM provided that the reduction in the likelihood of the FMM to fit the input data is minimized. The performance of the proposed algorithm is compared with the performances of other algorithms in the literature. Results show the superiority of the proposed algorithm over the other algorithms especially with data sets that are sparsely distributed or generated from overlapped clusters. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a new algorithm to mesh implicit surfaces which produces meshes both with a good triangle aspect ratio as well as a good approximation quality. The number of vertices of the output mesh is defined by the end-user. For this goal, we perform a two-stage processing: an initialization step followed by an iterative optimization step. The initialization step consists in capturing the surface topology and allocating the vertex budget. The optimization algorithm is based on a variational vertices relaxation and triangulation update. In addition a gradation parameter can be defined to adapt the mesh sampling to the curvature of the implicit surface. We demonstrate the efficiency of the approach on synthetic models as well as real-world acquired data, and provide comparisons with previous approaches. [Copyright &y& Elsevier]

We prove a closed-form solution to tensor voting (CFTV): Given a point set in any dimensions, our closed-form solution provides an exact, continuous, and efficient algorithm for computing a structure-aware tensor that simultaneously achieves salient structure detection and outlier attenuation. Using CFTV, we prove the convergence of tensor voting on a Markov random field (MRF), thus termed as MRFTV, where the structure-aware tensor at each input site reaches a stationary state upon convergence in structure propagation. We then embed structure-aware tensor into expectation maximization (EM) for optimizing a single linear structure to achieve efficient and robust parameter estimation. Specifically, our EMTV algorithm optimizes both the tensor and fitting parameters and does not require random sampling consensus typically used in existing robust statistical techniques. We performed quantitative evaluation on its accuracy and robustness, showing that EMTV performs better than the original TV and other state-of-the-art techniques in fundamental matrix estimation for multiview stereo matching. The extensions of CFTV and EMTV for extracting multiple and nonlinear structures are underway. [ABSTRACT FROM PUBLISHER]

A maximum-likelihood estimation of a multivariate mixture model's parameters is a difficult problem. One approach is to combine the REBMIX and EM algorithms. However, the REBMIX algorithm requires the use of histogram estimation, which is the most rudimentary approach to an empirical density estimation and has many drawbacks. Nevertheless, because of its simplicity, it is still one of the most commonly used techniques. The main problem is to estimate the optimum histogram-bin width, which is usually set by the number of non-overlapping, regularly spaced bins. For univariate problems it is usually denoted by an integer value; i.e., the number of bins. However, for multivariate problems, in order to obtain a histogram estimation, a regular grid must be formed. Thus, to obtain the optimum histogram estimation, an integer-optimization problem must be solved. The aim is therefore the estimation of optimum histogram binning, alone and in application to the mixture model parameter estimation with the REBMIX&EM strategy. As an estimator, the Knuth rule was used. For the optimization algorithm, a derivative based on the coordinate-descent optimization was composed. These proposals yielded promising results. The optimization algorithm was efficient and the results were accurate. When applied to the multivariate, Gaussian-mixture-model parameter estimation, the results were competitive. All the improvements were implemented in the rebmix R package. [ABSTRACT FROM AUTHOR]