Topic
Mahalanobis distance
About: Mahalanobis distance is a research topic. Over the lifetime, 4616 publications have been published within this topic receiving 95294 citations.
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TL;DR: In this article, the authors proposed a center-based clustering algorithm for the multiple ellipse fitting problem, where the assumption is that all data points are derived from k ellipses that should be fitted.
Abstract: 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 represented by the corresponding Mahalanobis circle-center. The distance from a point $a \in \mathbb{R}^2$ to the Mahalanobis circle is based on the algebraic criterion. The well-known k-means algorithm has been adapted to search for a locally optimal partition of the Mahalanobis circle-centers. Several numerical examples are used to illustrate the proposed algorithm.
21 citations
01 Jan 2015
TL;DR: This work introduces the motivation and foundations of MVPA, explains how pattern analysis algorithms can be used for the analysis of neuroimaging data, and outlines the mathematical background of the most important methods: linear discriminant analysis, logistic regression, support vector machine, and Mahalanobis distance.
Abstract: The standard mass-univariate analysis of fMRI data is increasingly being complemented by multivariate approaches. Multi-voxel pattern analysis (MVPA) comprises a number of methods designed to access and assess information contained in distributed patterns of neural activity. We introduce the motivation and foundations of MVPA, explain how pattern analysis algorithms can be used for the analysis of neuroimaging data, and outline the mathematical background of the most important methods: linear discriminant analysis, logistic regression, support vector machine, and Mahalanobis distance.
21 citations
TL;DR: The relation between the stable fixed points of the GK algorithm and the datasets using Jacobian matrix analysis is revealed, and a theoretical base for selecting the fuzziness index m of GK is provided.
Abstract: In fuzzy clustering, the fuzzy c-means (FCM) is the most known algorithm. Several extensions and variations of FCM had been proposed in the literature. The first important extension to FCM was proposed by Gustafson and Kessel (GK). In the GK fuzzy clustering, they considered the effect of different cluster shapes except for spherical shapes by replacing the Euclidean distance of the FCM objective function with the Mahalanobis distance. The GK algorithm has become one of the most frequently used clustering algorithms. Just like FCM, the fuzziness index m is a parameter in which the value will greatly influence the performance of the GK algorithm. However, there is no theoretical work on the parameter selection for the fuzziness index m of GK. In this paper, we reveal the relation between the stable fixed points of the GK algorithm and the datasets using Jacobian matrix analysis, and then provide a theoretical base for selecting the fuzziness index m in the GK algorithm. Some experimental results verify the effectiveness of our theoretical results.
21 citations
20 Aug 2006
TL;DR: An online signature verification scheme based on spectrum analysis and Mahalanobis decision is proposed, and experimentation demonstrates that spectrum analysis based on windows with variable widths is effective for online signature signals.
Abstract: In this paper, an online signature verification scheme based on spectrum analysis and Mahalanobis decision is proposed We firstly divided signatures to a number of frames with variable widths according to the characteristics of the time sequences, and then employed the fast Fourier transformation (FFT) to extract the spectrum of signatures The distance between the Fourier coefficient within the corresponding frames is computed, and the Mahalanobis decision making is employed Experimentation demonstrates that spectrum analysis based on windows with variable widths is effective for online signature signals
21 citations
06 Jul 2014
TL;DR: A new fuzzy co-clustering model is proposed, which is a fuzzy variant of multinomial mixture density estimation, and the effects of tuning the degree of fuzziness comparing with its corresponding probabilistic model are demonstrated.
Abstract: Fuzzy c-Means (FCM) clustering by entropy-based regularization concept is a fuzzy variant of Gaussian mixtures density estimation. FCM was also extended to a full-parameter model by introducing Mahalanobis distance and the K-L information-based fuzzification scheme, in which the degree of fuzziness of partition is evaluated comparing with Gaussian mixtures. In this paper, a new fuzzy co-clustering model is proposed, which is a fuzzy variant of multinomial mixture density estimation. Multinomial mixtures is a probabilistic model for co-clustering of cooccurrence matrices and the proposed method extends multinomial mixtures so that the degree of fuzziness can be tuned in a similar manner to K-L information-based FCM. Several experimental results demonstrate the effects of tuning the degree of fuzziness comparing with its corresponding probabilistic model.
21 citations