Mahalanobis distance

About: Mahalanobis distance is a research topic. Over the lifetime, 4616 publications have been published within this topic receiving 95294 citations.

Euclidean Distance as a Similarity Metric for Principal Component Analysis

Abstract: Eigentechniques, in particular principal component analysis (PCA), have been widely used in meteorological analyses since the early 1950s. Traditionally, choices for the parent similarity matrix, which are diagonalized, have been limited to correlation, covariance, or, rarely, cross products. Whereas each matrix has unique characteristic benefits, all essentially identify parameters that vary together. Depending on what underlying structure the analyst wishes to reveal, similarity matrices can be employed, other than the aforementioned, to yield different results. In this work, a similarity matrix based upon Euclidean distance, commonly used in cluster analysis, is developed as a viable alternative. For PCA, Euclidean distance is converted into Euclidean similarity. Unlike the variance-based similarity matrices, a PCA performed using Euclidean similarity identifies parameters that are close to each other in a Euclidean distance sense. Rather than identifying parameters that change together, the r...

Fault diagnosis of rolling bearings using multifractal detrended fluctuation analysis and Mahalanobis distance criterion

Abstract: Vibrations of a defective rolling bearing often exhibit nonstationary and nonlinear characteristics which are submerged in strong noise and interference components. Thus, diagnostic feature extraction is always a challenge and has aroused wide concerns for a long time. In this paper, the multifractal detrended fluctuation analysis (MF-DFA) is applied to uncover the multifractality buried in nonstationary time series for exploring rolling bearing fault data. Subsequently, a new approach for fault diagnosis is proposed based on MF-DFA and Mahalanobis distance criterion. The multifractality of bearing data is estimated with the generalized the Hurst exponent and the multifractal spectrum. Five characteristic parameters which are sensitive to changes of bearing fault conditions are extracted from the spectrum for diagnosis of fault sizes. For benchmarking this new method, the empirical mode decomposition (EMD) method is also employed to analyze the same dataset. The results show that MF-DFA outperforms EMD in revealing the nature of rolling bearing fault data.

PSMATCH2: Stata module to perform full Mahalanobis and propensity score matching, common support graphing, and covariate imbalance testing

Abstract: psmatch2 implements full Mahalanobis and propensity score matching, common support graphing, and covariate imbalance testing. This routine supersedes the previous 'psmatch' routine of B. Sianesi. The April 2012 revision of pstest changes the syntax of that command.

A multivariate outlier detection method

Abstract: A method for the detection of multivariate outliers is proposed which accounts for the data structure and sample size. The cut-off value for identifying outliers is defined by a measure of deviation of the empirical distribution function of the robust Mahalanobis distance from the theoretical distribution function. The method is easy to implement and fast to compute.