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...

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...

One of the basic problems in data analysis lies in choosing the optimal rescaling (change of coordinate system) to study properties of a given data-set Y . The classical Mahalanobis approach has its basis in the classical normalization/rescaling formula Y 3 y → Σ Y · (y − mY ), where mY denotes the mean of Y and ΣY the covariance matrix . Based on the cross-entropy we generalize this approach a...

This paper focuses on the problem of kernelizing an existing supervised Mahalanobis distance learner. The following features are included in the paper. Firstly, three popular learners, namely, “neighborhood component analysis”, “large margin nearest neighbors” and “discriminant neighborhood embedding”, which do not have kernel versions are kernelized in order to improve their classification per...

the organizations use all appropriate tools to improve their service to the customers. the detection of especial customers and the forecast of their behavior undoubtedly can play an important role in improvement of service. in this paper, a new statistical method called the mahalanobis taguchi system has been used for this purpose. this method is used for the analysis of real data of an insuran...