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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.


Papers
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Journal ArticleDOI
TL;DR: In this paper, the authors propose a method to identify statistical outliers, which are candidates for interpretation as true geochemical anomalies, and isolate a multi-element subset that is representative of the geochemical background.

114 citations

Book
30 Aug 2000
TL;DR: This chapter discusses the development of the Fault Diagnosis Program (FDP) and its applications in Health Care, Mechanical Industry, Space Industry, and Software Industry.
Abstract: Preface Acknoledgements Chapter 1: Introduction 1.1 Lives Versus Machines 1.2 What Is MTS? 1.3 Where MTS Can Be Applied 1.4 An Important Issue Chapter 2: A Detailed Example of MTS 2.1 Clutch Disc Defects 2.2 Visual Inspection Method 2.3 Differential and Integral Characteristics 2.4 Raw Data Collection 2.5 Normalization 2.6 Matrix Construction 2.7 Mahalanobis Distance 2.8 Results of Recognition 2.9 Selection of Threshold Value 2.10 Selection of Characteristics 2.11 Confirmation Chapter 3: Business-Process Forecasting 3.1 A Problem in Business Systems 3.2 Preparation of the Database 3.3 Calculation of the Database 3.4 Mahalanobis Distance 3.5 Estimation of the Unpaid Amount and its Estimating Error by Using the SN Ratio 3.6 Rationalization of Item Selection 3.7 Design of a Business System Section One -- Health Care Chapter 4: Diagnosis of a Special Health Checking 4.1 Diagnosis of Liver Function 4.2 Selection of Characteristics 4.3 The Loss Function of Health Checkups (Determination of Threshold) Chapter 5: Application for Medical Treatment 5.1 Problems in Clinical Research 5.2 Mahalanobis Distance and Treatment Effect 5.3 The Study Using One Patient 5.4 Comparison Treatment Methods Section Two -- Mechanical Industry Chapter 6: Wafer Yield Prediction 6.1 Objective 6.2 Base Space 6.3 Relatinship Between Mahalanobis Distance and Yield 6.4 Selection of Characteristics Chapter 7: Inkject Quality Inspection 7.1 Introduction 7.2 Camera Inspection System 7.3 Mahalanobis Distance Results 7.4 Measurement System Cost Reduction 7.5 Conclusions Chapter 8: Prevention of Driving Accidents 8.1 Introduction 8.2 Measuring System 8.3 Base Space 8.4 Base Data Collection 8.5 Base Space Construction and Mahalanobis Distance Distribution 8.6 Mahalanaobis Distance Under Dangerous Situations 8.7 Evaluation of Functionality 8.8 Conclusion Section Three -- Electrical Industry Chapter 9: Solder Joint Appearance Inspection 9.1 Introduction 9.2 Data Collection and Mahalanobis Distance Calculation 9.3 Mahalanobis Distance Using Inspection-Logic Characteristics 9.4 Mahalanobis Distance Using Reflection Characteristics Chapter 10: Fire Alarm System Optimization 10.1 Introduction 10.2 Data Collection 10.3 Calculation of Mahalanobis Space 10.4 Calculation of Mahalanobis Distance 10.5 Selection of Sensors Section Four -- Chemical Industry Chapter 11: Diagnosis of Photographic Processing Solution 11.1 Introduction 11.2 Processing of Photo-Sensitive Materials 11.3 Selection of the Base Space 11.4 Mahalanobis Distance of Rejected Solutions and Their Photographic Quality 11.5 Factorial Effects 11.6 Discussions Chapter 12: Pattern Recognition for Infrared Absorption Spectrum Analysis 12.1 Introduction 12.2 Experiment 12.3 Selection of Characteristics 12.4 Results Section Five -- Space Industry Chapter 13: Fault Analysis 13.1 Introduction 13.2 Outline of the Fault Diagnosis Program (FDP) 13.3 Observer and Residual 13.4 Process of Fault Diagnosis by Using Residuals 13.5 Collection of Normal Data 13.6 The Standard Space of a Normal Group 13.7 Fault Detection by Mahalanobis Distance 13.8 Fault Identification by Mahalanobis Distance 13.9 Fault Identification by Estimation Errors Section Six -- Software Industry Chapter 14: Valuation of a Programmer's Capability 14.1 Introduction 14.2 Data Collection 14.3 The MTS Method 14.4 Analysis 14.5 Factor Reductin 14.6 Effective Factors 14.7 Results Chapter 15: Handwriting Recognition 15.1 Introduction 15.2 Extraction of Character Elements 15.3 Procedures of Character Recognition 15.4 Calculation of Mahalanobis Distance 15.5 Hand-Written Character Recognition Section Seven -- Government Chapter 16: U.S. Dollar Bill Inspection 16.1 Patterns of U.S. Dollar Bills 16.2 Characteristics of One-Dollar Bills 16.3 Differentiation of One-Dollar Bills Index

113 citations

Journal ArticleDOI
TL;DR: An efficient algorithm for evaluating the (weighted bipartite graph of) associations between two sets of data with Gaussian error, e.g., between a set of measured state vectors and aSet of estimated state vectors is described.
Abstract: An efficient algorithm for evaluating the (weighted bipartite graph of) associations between two sets of data with Gaussian error, e.g., between a set of measured state vectors and a set of estimated state vectors, is described. A general method is developed for determining, from the covariance matrix, minimal d-dimensional error ellipsoids for the state vectors which always overlap when a gating criterion is satisfied. Circumscribing boxes, or d-ranges, for the data ellipsoids are then found and whenever they overlap the association probability is computed. For efficiently determining the intersections of the d-ranges, a multidimensional search tree method is used to reduce the overall scaling of the evaluation of associations. Very few associations that lie outside the predetermined error threshold or gate are evaluated. The search method developed is a fixed Mahalanobis distance search. Empirical tests for variously distributed data in both three and eight dimensions indicate that the scaling is significantly reduced. Computational loads for many large-scale data association tasks can therefore be significantly reduced by this or related methods. >

111 citations

Journal ArticleDOI
TL;DR: In this article, the Mahalanobis distance classifier was employed to determine the best eight-band combination for two multispectral, multitemporal and multisensor image datasets.
Abstract: Determination of the 'best' bands that are assigned to the input neurons of an artificial neural network (ANN) is one of the critical steps in designing the ANN for a particular problem. A large number of inputs reduces the network's generalization capabilities and introduces redundant and perhaps irrelevant information, while a small number of inputs could be insufficient for the network to learn the characteristics of the training data. The number of input bands defines the complexity of the problem. Methods used to select the optimum inputs are known as feature selection techniques. Their use in the context of artificial neural networks was investigated in this study. Statistical separability measures, specifically Wilks' v and Hotelling's T 2, and separability indices were employed to determine the best eight-band combination for two multispectral, multitemporal and multisensor image datasets. The Mahalanobis distance classifier was employed in the determination of the 'best' subset solution. In the s...

111 citations


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