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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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Journal Article
TL;DR: In this article, a comparison of the Mahalanobis-Taguchi System and a standard statistical technique for defect detection by identifying abnormalities is presented, with acceptable alpha and beta (probability of type I and beta) errors.
Abstract: The Mahalanobis-Taguchi System is a diagnosis and forecasting method for multivariate data. Mahalanobis distance is a measure based on correlations between the variables and different patterns that can be identified and analyzed with respect to a base or reference group. This paper presents a comparison of the Mahalanobis-Taguchi System and a standard statistical technique for defect detection by identifying abnormalities. The objective of this research is to provide a method for defect detection with acceptable alpha (probability of type I) and beta (probability of type II) errors.

31 citations

Journal ArticleDOI
TL;DR: This paper attempts to imitate the way of physical examination of palpebral conjunctiva to detect anemia, so that computers can identify anemia patients automatically in a consolidated manner for a screening process and proves the feasibility of the attempt.

31 citations

Journal ArticleDOI
TL;DR: A multiclass model based on normal observations and Mahalanobis distance for agriculture development that provides 100% accuracy, recall, precision and 0% error rate when compared with other traditional classifier models is proposed.
Abstract: Mahalanobis taguchi system (MTS) is a multi-variate statistical method extensively used for feature selection and binary classification problems. The calculation of orthogonal array and signal-to-noise ratio in MTS makes the algorithm complicated when more number of factors are involved in the classification problem. Also the decision is based on the accuracy of normal and abnormal observations of the dataset. In this paper, a multiclass model using Improved Mahalanobis Taguchi System (IMTS) is proposed based on normal observations and Mahalanobis distance for agriculture development. Twenty-six input factors relevant to crop cultivation have been identified and clustered into six main factors for the development of the model. The multiclass model is developed with the consideration of the relative importance of the factors. An objective function is defined for the classification of three crops, namely paddy, sugarcane and groundnut. The classification results are verified against the results obtained from the agriculture experts working in the field. The proposed classifier provides 100% accuracy, recall, precision and 0% error rate when compared with other traditional classifier models.

31 citations

Journal ArticleDOI
TL;DR: A multivariate time-series analysis employing a state–space embedding strategy and singular value decomposition is presented in this article to detect infrastructure damage and shows that damage occurrence and severity can be successfully identified.
Abstract: A multivariate time-series analysis employing a state–space embedding strategy and singular value decomposition is presented in this article to detect infrastructure damage. After summarizing the current state–space reconstruction method, the univariate state–space reconstruction is extended to multivariate (or global) reconstruction for observed time series at multiple locations. Under the hypothesis that reconstructed phase state geometry will change with damage, a reduced feature based on Mahalanobis distance of the most significant singular value vector, which is calculated from the reconstructed trajectory, is proposed. Both the area under receiver operating characteristic curve and deflection coefficient are used as comparison metrics to illustrate the presence and severity of damage. The advantage of this proposed approach is computational efficiency and easy implementation using state–space methodology since it does not require high-dimensional neighbor searches, as previous methods have proposed....

31 citations

Journal ArticleDOI
TL;DR: In this paper, a simple proof of the Chebyshev's inequality for random vectors is given, which provides a lower bound for the percentage of the population of an arbitrary random vector X with finite mean μ = E(X), and a positive definite covariance matrix V = Cov(X) whose Mahalanobis distance with respect to V to the mean μ is less than a fixed value.
Abstract: In this short note, a very simple proof of the Chebyshev's inequality for random vectors is given. This inequality provides a lower bound for the percentage of the population of an arbitrary random vector X with finite mean μ = E(X) and a positive definite covariance matrix V = Cov(X) whose Mahalanobis distance with respect to V to the mean μ is less than a fixed value. The main advantage of the proof is that it is a simple exercise for a first year probability course. An alternative proof based on principal components is also provided. This proof can be used to study the case of a singular covariance matrix V.

31 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20241
2023208
2022452
2021232
2020239
2019249