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In this paper, we present an algorithm for clustering multidimensional data, which we named TreeKDE. It is based on a tree structure decision associated with the optimization of the one-dimensional kernel density estimator function constructed from the orthogonal projections of the data on the coordinate axes. Among the main features of the proposed algorithm, we highlight the automatic determination of the number of clusters and their insertion in a rectangular region. Comparative numerical experiments are presented to illustrate the performance of the proposed algorithm and the results indicate that the TreeKDE is efficient and competitive when compared to other algorithms from the literature. Features such as simplicity and efficiency make the proposed algorithm an attractive and promising research field, which can be used as a basis for its improvement, and also for the development of new clustering algorithms based on the association between decision tree and kernel density estimator.

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Genomic prediction is revolutionizing plant breeding since candidate genotypes can be selected without the need to measure their trait in the field. When a reference population contains both phenotypic and genotypic information, it is trained by a statistical machine learning method that is subsequently used for making predictions of breeding or phenotypic values of candidate genotypes that were only genotyped. Nevertheless, the successful implementation of the genomic selection (GS) methodology depends on many factors. One key factor is the type of statistical machine learning method used since some are unable to capture nonlinear patterns available in the data. While kernel methods are powerful statistical machine learning algorithms that capture complex nonlinear patterns in the data, their successful implementation strongly depends on the careful tuning process of the involved hyperparameters. As such, in this paper we compare three methods of tuning (manual tuning, grid search, and Bayesian optimization) for the Gaussian kernel under a Bayesian best linear unbiased predictor model. We used six real datasets of wheat (Triticum aestivum L.) to compare the three strategies of tuning. We found that if we want to obtain the major benefits of using Gaussian kernels, it is very important to perform a careful tuning process. The best prediction performance was observed when the tuning process was performed with grid search and Bayesian optimization. However, we did not observe relevant differences between the grid search and Bayesian optimization approach. The observed gains in terms of prediction performance were between 2.1% and 27.8% across the six datasets under study.

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In this paper, we propose the MulticlusterKDE algorithm applied to classify elements of a database into categories based on their similarity. MulticlusterKDE is centered on the multiple optimization of the kernel density estimator function with multivariate Gaussian kernel. One of the main features of the proposed algorithm is that the number of clusters is an optional input parameter. Furthermore, it is very simple, easy to implement, well defined and stops at a finite number of steps and it always converges regardless of the data set. We illustrate our findings by implementing the algorithm in R software. The results indicate that the MulticlusterKDE algorithm is competitive when compared to K-means, K-medoids, CLARA, DBSCAN and PdfCluster algorithms. Features such as simplicity and efficiency make the proposed algorithm an attractive and promising research field that can be used as basis for its improvement and also for the development of new density-based clustering algorithms.

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Motor learning is associated with functional brain plasticity, involving specific functional connectivity changes in the neural networks. However, the degree of learning new motor skills varies among individuals, which is mainly due to the between-subject variability in brain structure and function captured by electroencephalographic (EEG) recordings. Here, we propose a kernel-based functional connectivity measure to deal with inter/intra-subject variability in motor-related tasks. To this end, from spatio-temporal-frequency patterns, we extract the functional connectivity between EEG channels through their Gaussian kernel cross-spectral distribution. Further, we optimize the spectral combination weights within a sparse-based ℓ2-norm feature selection framework matching the motor-related labels that perform the dimensionality reduction of the extracted connectivity features. From the validation results in three databases with motor imagery and motor execution tasks, we conclude that the single-trial Gaussian functional connectivity measure provides very competitive classifier performance values, being less affected by feature extraction parameters, like the sliding time window, and avoiding the use of prior linear spatial filtering. We also provide interpretability for the clustered functional connectivity patterns and hypothesize that the proposed kernel-based metric is promising for evaluating motor skills.

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In the recent past, estimating brain activity with magneto/electroencephalography (M/EEG) has been increasingly employed as a noninvasive technique for understanding the brain functions and neural dynamics. However, one of the main open problems when dealing with M/EEG data is its non-Gaussian and nonstationary structure. In this paper, we introduce a methodology for enhancing the data covariance estimation using a weighted combination of multiple Gaussian kernels, termed WM-MK, that relies on the Kullback-Leibler divergence for associating each kernel weight to its relevance. From the obtained results of validation on nonstationary and non-Gaussian brain activity (simulated and real-world EEG data), WM-MK proves that the accuracy of the source estimation raises by more effectively exploiting the measured nonlinear structures with high time and space complexity.

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This paper proposes a novel P1-weighted Lukasiewicz Logic based Fuzzy Similarity Classifier for classifying Denver Group of chromosomes and compares its performance with the other classifiers under study. A chromosome is classified to one of the seven groups from A to G, based on the Denver System of classification of chromosomes. Chromosomes within a particular Denver Group are difficult to identify, possessing almost identical characteristics for the extracted features. This work evaluates the performance of supervised classifiers including Naive Bayes, Support Vector Machine with Gaussian Kernel (SVM), Multilayer perceptron (MLP) and a novel, unsupervised, P1-weighted Lukasiewicz Logic based Fuzzy Similarity Classifier, in classifying the Denver Group of chromosomes. A fundamental review on fuzzy similarity based classification is presented. Experimental results clearly demonstrates that the proposed P1-weighted Lukasiewicz Logic based Fuzzy Similarity Classifier using the generalized Minkowski mean metric, produces the best classification results, almost identical to the Ground Truth values. One-way Analysis of Variance (ANOVA) at 95% and 99% level of confidence and Tukey's post-hoc analysis is performed to validate the selection of the classifier. The proposed P1-weighted Lukasiewicz Logic based Fuzzy Similarity Classifier gives the most promising classification results and can be applied to any large scale biomedical data and other applications.

Este trabalho propõe uma nova lógica P1pondera de Lukasiewicz de acordo com o classificador de similarida fuzzy para classificar cromossomas do Grupo Denver e compara o seu desempenho com os outros classificadores em estudo. Um cromossoma é classificado com um dos sete grupos de A a G, com base no Sistema de Denver de classificação de cromossomos. Cromossomos dentro de um grupo de Denver particular são difíceis de identificar, com características quase idênticas para os recursos extraídos. Este trabalho avalia o desempenho de classificadores supervisionados, incluindo Naive Bayes, Support Vector Machine com Gaussian Kernel (SVM), perceptron multicamadas (MLP) e um novo classificador sem supervisão, P1-weighted, lógica de Lukasiewicz de acordo com o classificador de similaridade Fuzzy para a classificação do Grupo Denver de cromossomos . Apresenta-se ma revisão fundamentada na classificação de acordo com similaridade difusa. Resultados experimentais demonstram claramente que Classificador Similaridade Fuzzy proposto de acordo com a lógica de Lukasiewicz P1-weighted usando a médica métrica de Minkowski para produz melhores resultados de classificação. Estes valores foram muito similares aos valores de Ground Truth . Análise de variancia (ANOVA) com 95% de grau de confiança e análise post-hoc de Tukey 99% foram realizadas para validar a seleção do classificador. Este classificador P1-weighted de lógica de Lukasiewicz está de acordo com o classificador de similaridade difusa oferecendo resultados declassificação mais promissoras. Portanto, podendo ser aplicado a dados biomédicos em larga escala além de outras aplicações.

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