In extending univariate outlier detection methods to higher dimension, various issues arise: limited visualization methods, inadequacy of marginal methods, lack of a natural order, limited parametric modeling, and, when using Mahalanobis distance, restriction to ellipsoidal contours. To address and overcome such limitations, we introduce nonparametric multivariate outlier identifiers based on m...

The classification of high dimensional data with kernel methods is considered in this article. Exploiting the emptiness property of high dimensional spaces, a kernel based on the Mahalanobis distance is proposed. The computation of the Mahalanobis distance requires the inversion of a covariance matrix. In high dimensional spaces, the estimated covariance matrix is ill-conditioned and its invers...

The objectives of the present study were to determine heterotic groups of germplasm lines of tropical maize by test crosses and by simple sequence repeat (SSR) markers and to compare five grouping methods of heterogeneous maize. Sixteen lines of nine populations in the S5 generation were evaluated in test crosses with three testers. The results of four experimental trials over two years were us...

The Mahalanobis Taguchi System (MTS) is considered one of the most promising binary classification algorithms to handle imbalance data. Unfortunately, MTS lacks a method for determining an efficient threshold for the binary classification. In this paper, a nonlinear optimization model is formulated based on minimizing the distance between MTS Receiver Operating Characteristics (ROC) curve and t...

This paper deals with the multiple ellipse fitting problem based on a given set of data points in a plane. The presumption is that all data points are derived from k ellipses that should be fitted. The problem is solved by means of center-based clustering, where cluster centers are ellipses. If the Mahalanobis distance-like function is introduced in each cluster, then the cluster center is repr...

This paper contains three contributions to the problem of learning a Mahalanobis distance. First, a general framework for kernelizing Mahalanobis distance learners is presented. The framework allows existing algorithms to learn a Mahalanobis distance in a feature space associated with a pre-specified kernel function. The framework is then used for kernelizing three well-known learners, namely, ...

Today, real-time fault detection and predictive maintenance based on sensor data are actively introduced in various areas such as manufacturing, aircraft, power system monitoring. Many faults motors or rotating machinery like industrial robots, aircraft engines, wind turbines can be diagnosed by analyzing signal vibration noise. In this study, to detect failures data, preprocessing was performe...

We consider the supervised classification problem of machine learning in Cayley-Klein projective geometries: We show how to learn a curved Mahalanobis metric distance corresponding to either the hyperbolic geometry or the elliptic geometry using the Large Margin Nearest Neighbor (LMNN) framework. We report on our experimental results, and further consider the case of learning a mixed curved Mah...

Support vector machines have gotten wide acceptance for their high generalization ability for real world applications. But the major drawback is slow training for classification problems with a large number of training data. To overcome this problem, in this paper, we discuss extracting boundary data from the training data and train the support vector machine using only these data. Namely, for ...