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 formulate multivariate generalized BS regression models and carry out a diagnostic analysis for these models and consider the Mahalanobis distance as a global influence measure to detect multivariate outliers and use it for evaluating the adequacy of the distributional assumption.
Abstract: Birnbaum–Saunders (BS) models are receiving considerable attention in the literature. Multivariate regression models are a useful tool of the multivariate analysis, which takes into account the correlation between variables. Diagnostic analysis is an important aspect to be considered in the statistical modeling. In this paper, we formulate multivariate generalized BS regression models and carry out a diagnostic analysis for these models. We consider the Mahalanobis distance as a global influence measure to detect multivariate outliers and use it for evaluating the adequacy of the distributional assumption. We also consider the local influence approach and study how a perturbation may impact on the estimation of model parameters. We implement the obtained results in the R software, which are illustrated with real-world multivariate data to show their potential applications.
52 citations
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TL;DR: In this article, a robust methodology using multivariate quality control charts for subgroups based on generalized Birnbaum-Saunders distributions and an adapted Hotelling statistic is proposed for Phases I and II of control charts.
Abstract: Multivariate control charts are powerful and simple visual tools for monitoring the quality of a process. This multivariate monitoring is carried out by considering simultaneously several correlated quality characteristics and by determining whether these characteristics are in control or out of control. In this paper, we propose a robust methodology using multivariate quality control charts for subgroups based on generalized Birnbaum–Saunders distributions and an adapted Hotelling statistic. This methodology is constructed for Phases I and II of control charts. We estimate the corresponding parameters with the maximum likelihood method and use parametric bootstrapping to obtain the distribution of the adapted Hotelling statistic. In addition, we consider the Mahalanobis distance to detect multivariate outliers and use it to assess the adequacy of the distributional assumption. A Monte Carlo simulation study is conducted to evaluate the proposed methodology and to compare it with a standard method...
52 citations
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TL;DR: A Monte Carlo simulation used to compare Dk and D squared in terms of their hit and false alarm rates, their extent of overlap, and their effect on correlation coefficients resulting from outlier removal indicated that D squared had a higher hit rate than Dk with approximately the same false alarm rate.
Abstract: Comrey (1985) presented a statistic, Dk, to detect outliers. Its purported advantage over the more well-known Mahalanobis D squared is that it might be more sensitive to outliers that distort the correlation coefficient. The present study used a Monte Carlo simulation to compare Dk and D squared in terms of their hit and false alarm rates, their extent of overlap, and their effect on correlation coefficients resulting from outlier removal. The results indicated that D squared had a higher hit rate than Dk with approximately the same false alarm rate. The statistics identified the same cases as outliers 19 to 55 percent of the time. Surprising, the average correlations that resulted from outlier removal by D squared were closer to the population correlations than were those resulting from outlier removal by Dk. Under the conditions investigated, D squared was preferable to Dk as an outlier removal statistic.
52 citations
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TL;DR: A self‐learning framework for ground detection and classification is introduced, where the terrain model is automatically initialized at the beginning of the vehicle's operation and progressively updated online, with the additional advantage of not requiring human intervention for training or a priori assumption on the ground appearance.
Abstract: Reliable terrain analysis is a key requirement for a mobile robot to operate safely in challenging environments, such as in natural outdoor settings. In these contexts, conventional navigation systems that assume a priori knowledge of the terrain geometric properties, appearance properties, or both, would most likely fail, due to the high variability of the terrain characteristics and environmental conditions. In this paper, a self-learning framework for ground detection and classification is introduced, where the terrain model is automatically initialized at the beginning of the vehicle's operation and progressively updated online. The proposed approach is of general applicability for a robot's perception purposes, and it can be implemented using a single sensor or combining different sensor modalities. In the context of this paper, two ground classification modules are presented: one based on radar data, and one based on monocular vision and supervised by the radar classifier. Both of them rely on online learning strategies to build a statistical feature-based model of the ground, and both implement a Mahalanobis distance classification approach for ground segmentation in their respective fields of view. In detail, the radar classifier analyzes radar observations to obtain an estimate of the ground surface location based on a set of radar features. The output of the radar classifier serves as well to provide training labels to the visual classification module. Once trained, the vision-based classifier is able to discriminate between ground and nonground regions in the entire field of view of the camera. It can also detect multiple terrain components within the broad ground class. Experimental results, obtained with an unmanned ground vehicle operating in a rural environment, are presented to validate the system. It is shown that the proposed approach is effective in detecting drivable surface, reaching an average classification accuracy of about 80% on the entire video frame with the additional advantage of not requiring human intervention for training or a priori assumption on the ground appearance.
52 citations
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11 Sep 2005TL;DR: This paper proposes using Mahalanobis kernels, which are generalized RBF kernels, to solve the problem of optimizing the kernel parameter and the margin parameter by time-consuming cross validation for model selection.
Abstract: Radial basis function (RBF) kernels are widely used for support vector machines. But for model selection, we need to optimize the kernel parameter and the margin parameter by time-consuming cross validation. To solve this problem, in this paper we propose using Mahalanobis kernels, which are generalized RBF kernels. We determine the covariance matrix for the Mahalanobis kernel using the training data corresponding to the associated classes. Model selection is done by line search. Namely, first the margin parameter is optimized and then the Mahalanobis kernel parameter is optimized. According to the computer experiments for two-class problems, a Mahalanobis kernel with a diagonal covariance matrix shows better generalization ability than a Mahalanobis kernel with a full covariance matrix, and a Mahalanobis kernel optimized by line search shows comparable performance with that with an RBF kernel optimized by grid search.
52 citations