The Mahalanobis distance
Chemometrics and Intelligent Laboratory SystemsPublished 1 January 2000
Roy De Maesschalck, D. Jouan-Rimbaud, D.L. Massart
Citations2,226
SJR quartileQ2
SJR score0.65
SNIP1.20
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
The Mahalanobis distance, in the original and principal component (PC) space, will be examined and interpreted in relation with the Euclidean distance (ED).
Abstract
The theory of many multivariate chemometrical methods is based on the measurement of distances. The Mahalanobis distance (MD), in the original and principal component (PC) space, will be examined and interpreted in relation with the Euclidean distance (ED). Techniques based on the MD and applied in different fields of chemometrics such as in multivariate calibration, pattern recognition and process control are explained and discussed.
Keywords
ChemistryDecision SciencesEngineering
TechnometricsRobust Regression and Outlier Detection
6,183 Citations1989Gregory F. Piepel, Peter J. Rousseeuw +1 more
Statistics for Analytical Chemistry
3,580 Citations1993Jane C. Miller, Jane Miller +1 more
TechnometricsA User's Guide to Principal Components
3,347 Citations1993Stefan D. Leigh, J. Edward Jackson
TechnometricsCross-Validatory Estimation of the Number of Components in Factor and Principal Components Models
2,496 Citations1978Svante Wold
Journal of the American Statistical AssociationRegularized Discriminant Analysis
2,238 Citations1989Jerome H. Friedman
Alternatives to the usual maximum likelihood estimates for the covariance matrices are proposed, characterized by two parameters, the values of which are customized to individual situations by jointly minimizing a sample-based estimate of future misclassification risk.
TechnometricsFactor Analysis in Chemistry
2,217 Citations1994Larry G. Blackwood, Edmund R. Malinowski
TechnometricsMultivariate SPC Charts for Monitoring Batch Processes
1,380 Citations1995Paul Nomikos, John F. MacGregor
The problem of using time-varying trajectory data measured on many process variables over the finite duration of a batch process is considered and multiway principal-component analysis is used to compress the information contained in the data trajectories into low-dimensional spaces that describe the operation of past batches.
Control Engineering PracticeStatistical process control of multivariate processes
1,240 Citations1995John F. MacGregor, Theodora Kourti
An overview of multivariate statistical methods use for the statistical process control of both continuous and batch multivariate processes and examples are provided of their use for analysing the operations of a mineral processing plant, for on-line monitoring and fault diagnosis of a continuous polymerization process and for the on- line monitoring of an industrial batch polymerization reactor.
Journal of the American Statistical AssociationRegularized Discriminant Analysis
867 Citations1989Jerome H. Friedman
Journal of the American Statistical AssociationStatistical Methods for Quality Improvement
758 Citations2000SRJ, Thomas P. Ryan
Chemometrics and Intelligent Laboratory SystemsProcess analysis, monitoring and diagnosis, using multivariate projection methods
738 Citations1995Theodora Kourti, John F. MacGregor
Applications are provided on the analysis of historical data from the catalytic cracking section of a large petroleum refinery, on the monitoring and diagnosis of a continuous polymerization process and on the Monitoring of an industrial batch process.
Crop SciencePopulation Definition, Sample Selection, and Calibration Procedures for Near Infrared Reflectance Spectroscopy
718 Citations1991J. S. Shenk, Mark O. Westerhaus
The MPLSR calibration method gave an overall 18% improvement in standard error of performance (SEP) compared with the MSR calibrationmethod, which provided acceptable validation statistics for crude protein, acid detergent fiber, and in vitro dry matter disappearance.
ACS symposium seriesSIMCA: A Method for Analyzing Chemical Data in Terms of Similarity and Analogy
586 Citations1977Svante Wold, Michael Sjöstróm
Journal of Quality TechnologyMultivariate Control Charts for Individual Observations
581 Citations1992Nola D. Tracy, John C. Young +1 more
P correlated process characteristics are being measured simultaneously and special causes of variation are identified in order to establish control and to obtain control.
TechnometricsCross-Validatory Estimation of the Number of Components in Factor and Principal Components Models
578 Citations1978Svante Wold
TechnometricsExtension of Sample Sizes and Percentage Points for Significance Tests of Outlying Observations
512 Citations1972Frank E. Grubbs, Glenn Beck
Journal of Quality TechnologyPrincipal Components and Factor Analysis: Part I—Principal Components
373 Citations1980J. Edward Jackson
TechnometricsQuality Control Methods for Several Related Variables
256 Citations1959J. Edward Jackson
The methods described in an earlier article devoted to control methods for more than two related variables are extended and the concept of matrix notation is introduced because of the resultant simplification in multivariate analysis.
TechnometricsMultivariate SPC Charts for Monitoring Batch Processes
230 Citations1995Paul Nomikos, John F. MacGregor
Analytica Chimica ActaComparison of regularized discriminant analysis linear discriminant analysis and quadratic discriminant analysis applied to NIR data
224 Citations1996W. Wu, Y. Mallet +5 more
It is concluded that in many cases, LDA or QDA should be recommended for practical use, depending on the characteristics of the data, but in those cases where even small gains in classification quality are important, the application of RDA might be useful.
Analytical ChemistryQualitative near-infrared reflectance analysis using Mahalanobis distances
222 Citations1985Howard Mark, David. Tunnell
The Data Analysis Handbook
221 Citations1994Ildiko E. Frank, Roberto Todeschini
Analytica Chimica ActaCharacterization of fatty acids composition in vegetable oils by gas chromatography and chemometrics
187 Citations1998Dong‐Sun Lee, Bong‐Soo Noh +2 more
Chemometrics and Intelligent Laboratory SystemsDecision criteria for soft independent modelling of class analogy applied to near infrared data
164 Citations1999Roy De Maesschalck, Andrea Candolfi +2 more
SIMCA modified with the Mahalanobis distance was found to be a good alternative of the original SIMCA which, for the presented NIR data set, seems to be more robust for finding outliers when the exact number of PCs to build the model is not known.
Analytica Chimica ActaUNEQ: a disjoint modelling technique for pattern recognition based on normal distribution
158 Citations1986M. P. Derde, D.L. Massart
The UNEQ method can be very useful for classification purposes but requires the populations to be homogeneous as is the case for other techniques.
TechnometricsExtension of Sample Sizes and Percentage Points for Significance Tests of Outlying Observations
124 Citations1972Frank E. Grubbs, Glenn Beck
Management ScienceEconomic Design of <i>T</i><sup>2</sup> Control Charts to Maintain Current Control of a Process
114 Citations1972Douglas C. Montgomery, Phillip J. Klatt
Analytica Chimica ActaClassification of vegetable oils by linear discriminant analysis of Electronic Nose data
94 Citations1999Yolanda González Martı́n, José Luis Pérez Pavón +2 more
TechnometricsMultivariate Profile Charts for Statistical Process Control
85 Citations1994Camil Fuchs, Yoav Benjamini
Computers and Biomedical ResearchUse of a microcomputer for the definition of multivariate confidence regions in medical diagnosis based on clinical laboratory profiles
78 Citations1984D. Coomans, I. Broeckaert +4 more
It is shown that related procedures can produce results of very different quality and that the multivariate region approach is attractive for the clinician's daily practice since the methods are easily implemented on a microcomputer.
Applied SpectroscopyOn-Line Monitoring of Powder Blending with Near-Infrared Spectroscopy
73 Citations1998Roy De Maesschalck, F. Cuesta Sánchez +3 more
Journal of Quality TechnologyPrincipal Components and Factor Analysis: Part II—Additional Topics Related to Principal Components
72 Citations1981J. Edward Jackson
Analytical ChemistryNear-IR Detection of Polymorphism and Process-Related Substances
72 Citations1996Paul K. Aldridge, Christine L. Evans +4 more
Analytical ChemistryClassification of Near-Infrared Spectra Using Wavelength Distances: Comparison to the Mahalanobis Distance and Residual Variance Methods
62 Citations1995Paul J. Gemperline, Nichole R. Boyer
Chemometrics and Intelligent Laboratory SystemsMultivariate statistical process control in chromatography
48 Citations1997Arend Nijhuis, S. De Jong +1 more
Handbook of statistics5 Introduction to positive-breakdown methods
48 Citations1997Peter J. Rousseeuw
Analytical ChemistryUse of Mahalanobis distances to evaluate sample preparation methods for near-infrared reflectance analysis
47 Citations1987Howard Mark
The AnalystPrincipal component outlier detection and SIMCA: a synthesis
46 Citations1994Bart Mertens, Michael P. Thompson +1 more
Chemometrics and Intelligent Laboratory SystemsLeverage and influence measures for principal component regression
44 Citations1989Tormod Næs
Analytica Chimica ActaCharacterisation of the representativity of selected sets of samples in multivariate calibration and pattern recognition
44 Citations1997D. Jouan-Rimbaud, D.L. Massart +2 more
The presented results show that two statistical tests, to compare two data sets, and estimate their representativity, can be used as a diagnostic for the determination of representativity.
Journal of ChemometricsImprovements to the classification performance of RDA
40 Citations1993S. Aeberhard, D. Coomans +1 more
By means of an extensive simulation it was shown that the new model selection procedure performs better than the original one and one of the control parameters of regularized discriminant analysis is allowed to take on negative values, which leads to an improved performance in certain situations.
Analytica Chimica ActaDetection of inhomogeneities in sets of NIR spectra
39 Citations1996V. Centner, D.L. Massart +1 more
Methods for the detection of outliers and clusters in data sets for multivariate calibration are discussed and the Cochran test applied to the sum of absorbances is shown to identify outlying replicates.
Analytica Chimica ActaApplication of pattern recognition to the discrimination of roasted coffees
34 Citations1996Marı́a J. Martı́n, Fernando Pablos +1 more
Chemometrics and Intelligent Laboratory SystemsDetermination of the representativity between two multidimensional data sets by a comparison of their structure
23 Citations1998D. Jouan-Rimbaud, D.L. Massart +2 more
An approach for the investigation and comparison of the data structure in the multidimensional space is proposed, based on three properties, namely, the direction of theData sets, the variance–covariance ofThe data points, and the location of thedata sets' centroids.
TechnometricsMultivariate Profile Charts for Statistical Process Control
21 Citations1994Camil Fuchs, Yoav Benjamini
Journal of ChemometricsPattern recognition analysis of near‐infrared spectra by robust distance method
15 Citations1995Junghwan Cho, Paul J. Gemperline
The properties of a robust distance method are examined using near‐infrared spectra of sulfamethoxazole and mixtures with its major degradation products, sulfanilic acid and sulfanilamide and it successfully detected unacceptable samples even when they were inadvertently included in the training data set.
Analytical ChemistryComposite multivariate quality control using a system of univariate, bivariate, and multivariate quality control rules
13 Citations1991S. Jay. Smith, S. P. Caudill +2 more
A composite multivariate quality control (CMQC) system to control simultaneously measured variables to detect unacceptable trends and systematic error, unacceptable random error, and unacceptable changes in the correlation structure in any pair of variables is proposed.
Journal of AOAC INTERNATIONALOutlier Detection in Collaborative Studies
12 Citations1990Patrick C. Kelly
Extended tables of critical values for the reduction in standard deviation tests for single and paired outliers recommended for collaborative studies suggest a confidence interval approach is suggested as a means to treat all sizes of collaborative studies in a uniform manner.
Chemometrics and Intelligent Laboratory SystemsClassification of detectors for ion chromatography using principal components regression and linear discriminant analysis
8 Citations1998Ziad Ramadan, M. Mulholland +1 more
The ability of these numerically-oriented methods to classify discrete, non-numerical data, is surprisingly good and compares with induction methods, neural networks and expert systems reported previously.
Analytical ChemistryPerformance characteristics of a composite multivariate quality control system
7 Citations1992Samuel P. Caudill, S. Jay. Smith +2 more
The various components of the CMQC system have adequate statistical power to detect systematic errors, random errors, and correlation changes under the conditions likely to be encountered with multivariate analytical measurement systems.
Biometrical JournalUsing Generalized Distances in Classification of Groups
5 Citations1991P. Dagnelie, A. Merckx
With a set of nearly 12,000 biometrical data, comprising populations of 14 different species of clover, four methods to cluster those populations are tried, in order to compare their results and to see whether the numerical classification obtained agrees with the botanical taxonomy.