In high dimension, low sample size (HDLSS) settings, classifiers based on Euclidean distances like the nearest neighbor classifier and the average distance classifier perform quite poorly if differences between locations of the underlying populations get masked by scale differences. To rectify this problem, several modifications of these classifiers have been proposed in the literature. However, existing methods are confined to location and scale differences only, and they often fail to discriminate among populations differing outside of the first two moments. In this article, we propose some simple transformations of these classifiers resulting in improved performance even when the underlying populations have the same location and scale. We further propose a generalization of these classifiers based on the idea of grouping of variables. High-dimensional behavior of the proposed classifiers is studied theoretically. Numerical experiments with a variety of simulated examples as well as an extensive analysis of benchmark data sets from three different databases exhibit advantages of the proposed methods.

Popular clustering algorithms based on usual distance functions (e.g., the Euclidean distance) often suffer in high dimension, low sample size (HDLSS) situations, where concentration of pairwise distances and violation of neighborhood structure have adverse effects on their performance. In this article, we use a new data-driven dissimilarity measure, called MADD, which takes care of these problems. MADD uses the distance concentration phenomenon to its advantage, and as a result, clustering algorithms based on MADD usually perform well for high dimensional data. We establish it using theoretical as well as numerical studies. We also address the problem of estimating the number of clusters. This is a challenging problem in cluster analysis, and several algorithms are available for it. We show that many of these existing algorithms have superior performance in high dimensions when they are constructed using MADD. We also construct a new estimator based on a penalized version of the Dunn index and prove its consistency in the HDLSS asymptotic regime. Several simulated and real data sets are analyzed to demonstrate the usefulness of MADD for cluster analysis of high dimensional data.

In this article, we develop and investigate a new classifier based on features extracted using spatial depth. Our construction is based on fitting a generalized additive model to posterior probabilities of different competing classes. To cope with possible multi-modal as well as non-elliptic nature of the population distribution, we also develop a localized version of spatial depth and use that with varying degrees of localization to build the classifier. Final classification is done by aggregating several posterior probability estimates, each of which is obtained using this localized spatial depth with a fixed scale of localization. The proposed classifier can be conveniently used even when the dimension of the data is larger than the sample size, and its good discriminatory power for such data has been established using theoretical as well as numerical results.

This paper presents a fuzzy partition and Tsallis entropy based thresholding approach for multi-level image segmentation. Image segmentation is considered as one of the most critical tasks in image processing and pattern recognition area. However, discriminating many objects present in an image automatically is the most challenging one. As a result, multilevel thresholding based methods gain importance in recent times, because of its ability to split the image into more than one segments. Efficiency of these algorithms still remains a matter of concern. Over the years, fuzzy partition of 1-D histogram has been employed successfully in bi-level image segmentation to improve the separation between object and the background. Here a fuzzy based technique is adopted in multi-level image segmentation scenario using Tsallis entropy based thresholding. Differential Evolution, a widely used meta-heuristic in recent times, is used for lesser computation time of the proposed algorithm. Both visual and statistical comparison of outcomes between Tsallis and Fuzzy - Tsallis entropy based methods are given in this paper to establish the superiority of the technique.

This paper proposes a hybrid autoregressive integrated moving average - dynamic evolving neural-fuzzy inference system (ARIMA-DENFIS) model for wind speed forecasting. The theory of ARIMA, DENFIS and the hybrid of the two are discussed. The proposed model is evaluated with NDBC wind speed data and the results show that the proposed hybrid ARIMA-DENFIS model outperforms DENFIS model in most of the cases. It has comparable or better error measures than ARIMA model. In addition, when the forecasting horizon increases, the advantage of the proposed ARIMA-DENFIS model becomes more significant.

Multilevel thresholding amounts to segmenting a gray-level image into several distinct regions. This paper presents a 2D histogram based multilevel thresholding approach to improve the separation between objects. Recent studies indicate that the results obtained with 2D histogram oriented approaches are superior to those obtained with 1D histogram based techniques in the context of bi-level thresholding. Here, a method to incorporate 2D histogram related information for generalized multilevel thresholding is proposed using the maximum Tsallis entropy. Differential evolution (DE), a simple yet efficient evolutionary algorithm of current interest, is employed to improve the computational efficiency of the proposed method. The performance of DE is investigated extensively through comparison with other well-known nature inspired global optimization techniques such as genetic algorithm, particle swarm optimization, artificial bee colony, and simulated annealing. In addition, the outcome of the proposed method is evaluated using a well known benchmark--the Berkley segmentation data set (BSDS300) with 300 distinct images.