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 paper, the authors defined good and bad leverage observations in factor analysis and defined outliers as observations that deviate from the factor model, not from the center of the data cloud.
Abstract: Parallel to the development in regression diagnosis, this paper defines good and bad leverage observations in factor analysis. Outliers are observations that deviate from the factor model, not from the center of the data cloud. The effects of each kind of outlying observations on the normal distribution-based maximum likelihood estimator and the associated likelihood ratio statistic are studied through analysis. The distinction between outliers and leverage observations also clarifies the roles of three robust procedures based on different Mahalanobis distances. All the robust procedures are designed to minimize the effect of certain outlying observations. Only the robust procedure with a residual-based distance properly controls the effect of outliers. Empirical results illustrate the strength or weakness of each procedure and support those obtained in analysis. The relevance of the results to general structural equation models is discussed and formulas are provided.
74 citations
TL;DR: Wang et al. as discussed by the authors proposed a hidden Markov model (HMM)-based process monitoring model to explicitly address the nonlinear and multimodal characteristics in processes. But, the HMM-based monitoring models can be used for online process monitoring without too much human intervention, and the experimental results clearly demonstrate that the proposed approaches effectively captured the non-linear and multi-modal relationship in process variables and showed superior process monitoring performance compared to those conventional process monitoring approaches.
73 citations
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TL;DR: BoostMetric as mentioned in this paper uses rank-one positive semidefinite matrices as weak learners within an efficient and scalable boosting-based learning process to learn a valid Mahalanobis distance metric.
Abstract: The success of many machine learning and pattern recognition methods relies heavily upon the identification of an appropriate distance metric on the input data. It is often beneficial to learn such a metric from the input training data, instead of using a default one such as the Euclidean distance. In this work, we propose a boosting-based technique, termed BoostMetric, for learning a quadratic Mahalanobis distance metric. Learning a valid Mahalanobis distance metric requires enforcing the constraint that the matrix parameter to the metric remains positive definite. Semidefinite programming is often used to enforce this constraint, but does not scale well and easy to implement. BoostMetric is instead based on the observation that any positive semidefinite matrix can be decomposed into a linear combination of trace-one rank-one matrices. BoostMetric thus uses rank-one positive semidefinite matrices as weak learners within an efficient and scalable boosting-based learning process. The resulting methods are easy to implement, efficient, and can accommodate various types of constraints. We extend traditional boosting algorithms in that its weak learner is a positive semidefinite matrix with trace and rank being one rather than a classifier or regressor. Experiments on various datasets demonstrate that the proposed algorithms compare favorably to those state-of-the-art methods in terms of classification accuracy and running time.
73 citations
TL;DR: In this article, a data-driven method based on principal component analysis and Fisher discriminant analysis is presented to detect and diagnose multiple faults including fixed bias, drifting bias, complete failure of sensors, air damper stuck and water valve stuck occurred in the air handling units.
72 citations
23 Sep 2009
TL;DR: A new local spatio-temporal feature is proposed to represent the cuboids detected in video sequences that utilizes the covariance matrix to capture the self-correlation information of the low-level features within each cuboid.
Abstract: This paper presents a new action recognition approach based on local spatio-temporal features. The main contributions of our approach are twofold. First, a new local spatio-temporal feature is proposed to represent the cuboids detected in video sequences. Specifically, the descriptor utilizes the covariance matrix to capture the self-correlation information of the low-level features within each cuboid. Since covariance matrices do not lie on Euclidean space, the Log-Euclidean Riemannian metric is used for distance measure between covariance matrices. Second, the Earth Mover’s Distance (EMD) is used for matching any pair of video sequences. In contrast to the widely used Euclidean distance, EMD achieves more robust performances in matching histograms/distributions with different sizes. Experimental results on two datasets demonstrate the effectiveness of the proposed approach.
72 citations