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In statistics, Mahalanobis distance is a distance measure introduced by P. C. Mahalanobis in 1936. It is based on correlations between variables by which different patterns can be identified and analysed. It is a useful way of determining similarity of an unknown sample set to a known one. It differs from Euclidean distance in that it takes into account the correlations of the data set. Formally, the Mahalanobis distance from a group of values with mean and covariance matrix for a multivariate vector is defined as: and of the same distribution with the covariance matrix : where

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  • Mahalanobis distance
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  • In statistics, Mahalanobis distance is a distance measure introduced by P. C. Mahalanobis in 1936. It is based on correlations between variables by which different patterns can be identified and analysed. It is a useful way of determining similarity of an unknown sample set to a known one. It differs from Euclidean distance in that it takes into account the correlations of the data set. Formally, the Mahalanobis distance from a group of values with mean and covariance matrix for a multivariate vector is defined as: and of the same distribution with the covariance matrix : where
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  • In statistics, Mahalanobis distance is a distance measure introduced by P. C. Mahalanobis in 1936. It is based on correlations between variables by which different patterns can be identified and analysed. It is a useful way of determining similarity of an unknown sample set to a known one. It differs from Euclidean distance in that it takes into account the correlations of the data set. Formally, the Mahalanobis distance from a group of values with mean and covariance matrix for a multivariate vector is defined as: Mahalanobis distance can also be defined as dissimilarity measure between two random vectors and of the same distribution with the covariance matrix : If the covariance matrix is the identity matrix then it is the same as Euclidean distance. If covariance matrix is diagonal, then it is called normalized Euclidean distance: where is the standard deviation of the over the sample set.
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