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A family of parsimonious contaminated shifted asymmetric Laplace mixtures is developed for unsupervised classification of asymmetric clusters in the presence of outliers and noise. A series of constraints are applied to a modified factor analyzer structure of the component scale matrices, yielding a family of twelve models. Application of the modified factor analyzer structure and these parsimonious constraints makes these models effective for the analysis of high-dimensional data by reducing the number of free parameters that need to be estimated. A variant of the expectation-maximization algorithm is developed for parameter estimation with convergence issues being discussed and addressed. Popular model selection criteria like the Bayesian information criterion and the integrated complete likelihood (ICL) are utilized, and a novel modification to the ICL is also considered. Through a series of simulation studies and real data analyses, that includes comparisons to well-established methods, we demonstrate the improvements in classification performance found using the proposed family of models. [ABSTRACT FROM AUTHOR]

The probabilistic neural network (PNN) is an efficient approach that can compute nonlinear decision boundaries, widely used for classification. In this paper, the often used Gaussian distribution function is replaced by a new probability density function which provides a new variant of the PNN method. Most of the higher-dimensional data are statistically found to be not from the normal distribution, and hence, we have replaced it by the symmetric Laplace distribution. Further, the estimation of the smoothing parameter in the proposed PNN model is carried out with three different evolutionary algorithms, namely bat algorithm (BA), grey wolf optimizer (GWO), and whale optimization algorithm (WOA) with a novel fitness function. These different proposed PNN models with variable smoothing parameter estimation methods are tested on five different benchmark data sets. The performance of proposed three Laplace distribution-based variants of PNN incorporated with BA, GWO, and WOA are reported and compared with Gaussian-based variants of PNN and also other commonly used classifiers: the conventional PNN, extreme learning machine, and K-nearest neighbor in terms of measurement accuracy. The results demonstrate that the proposed approaches using evolutionary algorithms can provide as much as a ten percent increase in accuracy over the conventional PNN method. [ABSTRACT FROM AUTHOR]

Probabilistic neural network (PNN) is a single-pass feed-forward neural network with the capability of providing nonlinear decision boundaries. In this work, we propose the modifications to the existing PNN approach. Contributions are threefold: First, symmetric Laplace distribution has been used instead of Gaussian distribution in the pattern layer of the PNN approach. Second, a new weight coefficients' estimation method has been introduced between the pattern and summation layers of PNN. Third, a novel convex fitness function has been designed for the bat algorithm to obtain an optimal smoothing parameter vector. The designed fitness function maintains a balance between the sensitivity and specificity values. The performance of the proposed algorithm "bat algorithm-based weighted Laplacian probabilistic neural network" is compared with that of conventional PNN, weighted PNN, extreme learning method, optimal pruned extreme learning machine and K-nearest neighbor. Experimental evaluation is carried out on eleven benchmark data sets using different performance measures such as accuracy, sensitivity, specificity and Youden's index. The comparative performance evaluation of the proposed model has been made with the PNN, and other standard algorithms outperform the compared approaches in terms of classification accuracy. Friedman test is used for statistical evaluation of the proposed approach. [ABSTRACT FROM AUTHOR]