The Mahalanobis distance is a key tool in multivariate chemometrics, aiding in multivariate calibration, pattern recognition, and process control.

The Mahalanobis distance

The hesitant Mahalanobis distance measure effectively measures deviation between hesitant fuzzy sets, allowing adaptive weighting and eliminating correlation between attributes in hesitant fuzzy environments.

Hesitant Mahalanobis distance with applications to estimating the optimal number of clusters

The Mahalanobis distance is an appropriate measure of distance between elliptic distributions with different locations but a common shape, and can also be used for multivariate normal distributions differing only in location.

The Mahalanobis distance and elliptic distributions

The Choquet-Mahalanobis integral is a generalization of the Choquet integral and the Mahalanobis distance, useful for representing dependence between variables in probability-density functions.

On a comparison between Mahalanobis distance and Choquet integral: The Choquet-Mahalanobis operator

A residual-based Mahalanobis distance measure is the most effective in identifying and downweighting aberrant item response patterns, improving scale reliability and unidimensionality.

Three Mahalanobis distances and their role in assessing unidimensionality.

The relationship between squared Mahalanobis distance, T2, and leverage statistics in WinISI and The Unscrambler simplifies the translation of these distance measures for spectral outlier detection in near infrared calibration.

A note on Mahalanobis and related distance measures in WinISI and The Unscrambler

The reduced Mahalanobis distance, with fewer retained principal components, outperforms the full rank model for discriminating via soft models.

Re‐evaluating the role of the Mahalanobis distance measure

Cross-validated Mahalanobis distances can effectively assess representational similarity in neural activity patterns measured by fMRI, enabling efficient comparisons with computational models.

On the distribution of cross-validated Mahalanobis distances

The generalized Mahalanobis distance (MD) is a useful measure for evaluating distance between data points and distribution mean in statistics and pattern recognition.

On the Generalization of the Mahalanobis Distance

This paper explores optimal distance bounds for the Mahalanobis distance, enabling efficient spatial pruning techniques in feature-based similarity search.

Optimal Distance Bounds for the Mahalanobis Distance

This paper presents a unified approach for obtaining exact confidence intervals for the Mahalanobis distance and related measures in statistical problems involving comparing two multivariate normal populations.

CONFIDENCE INTERVALS FOR THE MAHALANOBIS DISTANCE

Organizing similar coordinates in clusters can improve the construction of the Mahalanobis distance between samples, allowing the recovery of Euclidean distances in hidden spaces.

Mahalanonbis Distance Informed by Clustering

The proposed dynamic time warping measure improves multivariate time series classification accuracy by aligning out-of-synchronization or different length MTS, and learning accurate Mahalanobis distance functions using a LogDet divergence-based metric learning with triplet constraint model.

Learning a Mahalanobis Distance-Based Dynamic Time Warping Measure for Multivariate Time Series Classification

The Mahalanobis distance technique can be used to model ecological niches, habitat suitability, species distributions, and resource selection functions, but a common error in converting distances into probabilities needs to be addressed.

Mahalanobis distances and ecological niche modelling: correcting a chi-squared probability error

Mahalanobis distances are a useful niche modeling technique, but their effectiveness depends on individual data and question, with the minimum covariance determinant and minimum volume ellipsoid methods performing best at larger sample sizes.

Mahalanobis distances for ecological niche modelling and outlier detection: implications of sample size, error, and bias for selecting and parameterising a multivariate location and scatter method

The MADIFA method, which considers environmental availability, provides a more accurate method for estimating ecological suitability maps and identifying basic habitat requirements for species.

The factorial decomposition of the Mahalanobis distances in habitat selection studies.

The Weighted Euclidean distance measure outperformed the other three distance measures for long-time text-independent speaker identification, with the Mahalanobis distance measure showing the least performance.

Comparison of Four Distance Measures for Long Time Text-Independent Speaker Identification

The modified sum square error (SSE)-based distance is among the best distance measures for PCA-based face recognition, requiring less images for 100% cumulative recognition compared to other tested measures.

Distance measures for PCA-based face recognition

The Mahalanobis distance is a useful measure in chemometrics, but its relationship to principal components analysis is poorly understood.

The Mahalanobis distance and its relationship to principal component scores

Mahalanobis distance is a powerful tool for achievement analysis in education and educational psychology, with potential for rapid adoption in the field.

Application of Mahalanobis Distance in Education and Educational Psychology: A Mini Review

What are the distance measures that can be compared to the Mahalanobis distance?

These studies suggest that distance measures comparable to the Mahalanobis distance include hesitant Mahalanobis distance, Choquet-Mahalanobis integral, residual-based Mahalanobis distance, reduced Mahalanobis distance, cross-validated Mahalanobis distances, and generalized Mahalanobis distance.