Weighted Mahalanobis Distance Research Articles

Gaussian Derivative Change-point Detection for early warnings of industrial system failures

An early warning of future system failure is essential for conducting predictive maintenance and enhancing system availability. This paper introduces a three-step framework for assessing system health to predict imminent system breakdowns. First, the Gaussian Derivative Change-Point Detection (GDCPD) algorithm is proposed for detecting changes in the high-dimensional feature space. GDCPD conducts a multivariate Change-Point Detection (CPD) by implementing Gaussian derivative processes for identifying change locations on critical system features, as these changes eventually will lead to system failure. To assess the significance of these changes, Weighted Mahalanobis Distance (WMD) is applied in both offline and online analyses. In the offline setting, WMD helps establish a threshold that determines significant system variations, while in the online setting, it facilitates real-time monitoring, issuing alarms for potential future system breakdowns. Utilizing the insights gained from the GDCPD and monitoring scheme, Long Short-Term Memory (LSTM) network is then employed to estimate the Remaining Useful Life (RUL) of the system. The experimental study of a real-world system demonstrates the effectiveness of the proposed methodology in accurately forecasting system failures well before they occur. By integrating CPD with real-time monitoring and RUL prediction, this methodology significantly advances system health monitoring and early warning capabilities.

Generalized Weighted Mahalanobis Distance Improved VIKOR Model for Rockburst Classification Evaluation

Rockbursts are hazardous phenomena of sudden and violent rock failure in deep underground excavations under high geostress conditions, which poses a serious threat to geotechnical engineering. The occurrence of rockbursts is influenced by a combination of factors. Therefore, it is necessary to find an efficient method to assess rockburst grades. In this paper, we propose a novel method that enhances the VIKOR method using a novel combination of weight and generalized weighted Mahalanobis distance. The combination weights of the evaluation indicators were calculated using game theory by combining subjective experience and objective data statistical characteristics. By introducing the generalized weighted Mahalanobis distance, the VIKOR method is improved to address the issues of inconsistent dimensions, different importance, and inconsistent correlation among indicators. The proposed method can deal with the complexity of the impact factors of rockburst evaluation and classify the rockburst intensity level. The results show that the accuracy of the improved VIKOR method with the distance formula is higher than that of the unimproved VIKOR method; the evaluation accuracy of the improved VIKOR method with the generalized weighted Mahalanobis distance is 91.67%, which outperforms the improved VIKOR methods with the Euclidean and Canberra distances. This assessment method can be easily implemented and does not depend on the discussion of the rockburst occurrence mechanism, making it widely applicable for engineering rockburst evaluation.

Potential causes analysis of abnormal observations diagnosed by improved Mahalanobis-Taguchi system

Mahalanobis-Taguchi system (MTS) was proposed by Genichi Taguchi for the study of multidimensional systems and has been effectively applied in many fields. The traditional MTS method focuses on the dimensionality reduction of multidimensional systems and the measurement of abnormal degree of observations. In order to further improve the effectiveness of the MTS method, many studies related to the MTS method have been conducted, including the construction of Mahalanobis space, threshold determination, selection of useful variables, and so on. However, only four studies have been conducted to analyze the potential causes of abnormal observations diagnosed by the MTS method. Meanwhile, these studies ignore the counter-correlations between variables, which will make it impossible to find the potential causes of some abnormal observations and therefore unable to effectively improve these abnormal observations. This paper aims to improve the traditional MTS method and then propose an effective method to analyze the potential causes of abnormal observations diagnosed by the improved MTS method. First, this paper proposes to divide the traditional MTS method into two phases. In phase one, the scaled Mahalanobis distance function is still used to measure the abnormal degree of observation, while in phase two the weighted Mahalanobis distance function should be used to make the diagnosis more reasonable and accurate. Second, a new decomposition method of weighted Mahalanobis distance is proposed to identify potential causes of abnormal observations based on Mason-Young-Tracy (MYT) decomposition method. The method focuses not only on whether individual variables are outside their reference ranges, but also on whether the linear relationships between variables are consistent with the reference group, which makes the analysis of abnormal causes more comprehensive and reliable. Finally, the blood viscosity diagnosis system in a hospital was improved using the improved MTS method. The results showed that the variables in the diagnosis system decreased by 37.5%, and the differentiation between the abnormal conditions and the health group increased by 102%. At the same time, the potential causes of an abnormal observation were identified based on the MYT decomposition method of weighted Mahalanobis distance. The above results verified the feasibility and effectiveness of the method in this paper.

Spectral Clustering Approach with K-Nearest Neighbor and Weighted Mahalanobis Distance for Data Mining

This paper proposes a spectral clustering method using k-means and weighted Mahalanobis distance (Referred to as MDLSC) to enhance the degree of correlation between data points and improve the clustering accuracy of Laplacian matrix eigenvectors. First, we used the correlation coefficient as the weight of the Mahalanobis distance to calculate the weighted Mahalanobis distance between any two data points and constructed the weighted Mahalanobis distance matrix of the data set; then, based on the weighted Mahalanobis distance matrix, we used the K-nearest neighborhood (KNN) algorithm construct similarity matrix. Secondly, the regularized Laplacian matrix was calculated according to the similarity matrix, normalized and decomposed, and the feature space for clustering was obtained. This method fully considered the degree of linear correlation between data and special spatial structure and achieved accurate clustering. Finally, various spectral clustering algorithms were used to conduct multi-angle comparative experiments on artificial and UCI data sets. The experimental results show that MDLSC has certain advantages in each clustering index and the clustering quality is better. The distribution results of the eigenvectors also show that the similarity matrix calculated by MDLSC is more reasonable, and the calculation of the eigenvectors of the Laplacian matrix maximizes the retention of the distribution characteristics of the original data, thereby improving the accuracy of the clustering algorithm.

Early Warning of Abnormal Bridge Frequencies Based on a Local Correlation Model under Multiple Environmental Conditions

The accuracy of frequency prediction is markedly affected by the nonlinearity and model degradation caused by multiple environmental conditions, which may hinder the prediction accuracy and detectability of damage. Therefore, this paper proposes a local correlation model (LCM) between multiorder bridge frequencies and multiple environmental factors for early warning of abnormal frequencies. First, partial least-squares analysis was conducted to extract several environmental principal components sensitive to modal frequencies. The most relevant local data set for each online environmental sample was selected according to similarity measurements based on Euclidean distance metrics. On this basis, more accurate environment–frequency relation models were formed using relatively simple local linear regression models. To filter out the residual environmental variability not suppressed by the LCM and to enlarge slightly abnormal frequency variation, a warning index (i.e., the weighted Mahalanobis distance) was defined using the residual subspatial reconstruction of principal component analysis. Finally, the validity of the proposed method was verified on a cable-stayed bridge. The results show that in contrast to conventional methods, the proposed LCM can accurately describe complicated frequency variations under changing environmental conditions by considering both the nonlinearity of environmental conditions and the time-varying properties of relation models. The detectability of frequency anomalies induced by sudden events can be effectively improved.

Early Warning Method of Structural Damage Using Localized Frequency Cointegration under Changing Environments

Modal frequencies are widely used to capture dynamics and reveal possible failures of bridge structures. However, the non-Gaussianity and nonlinearity of nonstationary modal frequencies associated with the actual structure under changing environmental conditions often restrict the application in structural health monitoring. Therefore, a new localized frequency cointegration without environmental measurements for the elimination of environmental interference and damage warning is proposed in this paper. The k-nearest neighbor rule is first employed to search for sufficient nearest neighbors for each modal feature based on similarity measurements over a wide range of training data. After that, the cointegration analysis associated with the Johansen procedure is performed to remove environmental trends and obtain multivariable cointegration residuals. Then, the defined early warning index (i.e., the weighted Mahalanobis distance) derived from the exponentially weighted moving average is adopted with respect to the identification of subtle damage. Eight groups of cointegration models between nonstationary modal variables are constructed and validated on the Z24 bridge case. The results demonstrate that the proposed approach can successfully discard spurious influences of environmental variations and identify the occurrence of real structural damage compared to traditional methods. Additionally, this approach is not constrained by the statistical distribution of observation samples, and the selection and combination of different modal orders are crucial in capturing the changes in frequency anomalies for the bridge condition assessment.

Research and Application of Warship Multiattribute Threat Assessment Based on Improved TOPSIS Gray Association Analysis

Multitarget threat evaluation of warship air attacks is one of the most urgent problems in warship defense operations. To evaluate the target threat quickly and accurately, an air attack multitarget threat evaluation method based on improved TOPSIS gray relational analysis is proposed. This method establishes threat assessment system of five attributes of target type, anti-jamming ability, heading angle, altitude, and speed. The weight coefficient of each index of the warship is obtained by combining the entropy weight method with the analytic hierarchy process. Topsis can make full use of the information of the original data, and its results can accurately reflect the gap between various evaluation schemes. The weighted Mahalanobis distance and comprehensive gray correlation between the attribute to be evaluated and the positive and negative ideal states are calculated by the improved TOPSIS gray correlation method. The target threat degree to be evaluated is obtained by combining the two methods. Finally, an example is given to prove the effectiveness of the evaluation model.

Single Infrared Image Stripe Removal via Residual Attention Network.

The non-uniformity of the readout circuit response in the infrared focal plane array unit detector can result in fixed pattern noise with stripe, which seriously affects the quality of the infrared images. Considering the problems of existing non-uniformity correction, such as the loss of image detail and edge blurring, a multi-scale residual network with attention mechanism is proposed for single infrared image stripe noise removal. A multi-scale feature representation module is designed to decompose the original image into varying scales to obtain more image information. The product of the direction structure similarity parameter and the Gaussian weighted Mahalanobis distance is used as the similarity metric; a channel spatial attention mechanism based on similarity (CSAS) ensures the extraction of a more discriminative channel and spatial feature. The method is employed to eliminate the stripe noise in the vertical and horizontal directions, respectively, while preserving the edge texture information of the image. The experimental results show that the proposed method outperforms four state-of-the-art methods by a large margin in terms of the qualitative and quantitative assessments. One hundred infrared images with different simulated noise intensities are applied to verify the performance of our method, and the result shows that the average peak signal-to-noise ratio and average structural similarity of the corrected image exceed 40.08 dB and 0.98, respectively.

Prediction of the Remaining Useful Life of a Switch Machine, Based on Multi-Source Data

Aimed at the shortcomings of a single feature to characterize the health status and accurately predict the remaining life span of the equipment, a prediction method for a switch machine, based on the weighted Mahalanobis distance (WDMD), is proposed. The method consists of two parts: the construction of a health indicator, based on the weighted Markov distance and the prediction of the remaining useful life, based on the hidden Markov model (HMM). Firstly, a kernel principal component analysis (KPCA) is used to extract the characteristics of the power curve data of the switch machine, and the characteristics with a high correlation with the degradation process are screened, according to the trend indicators. Secondly, the resulting features are combined with multi-source information, as the input, and a comprehensive health indicator (HI) is constructed by the weighted fusion of the WDMD algorithm, to characterize the degradation process of the switch machine. The degradation model of this HI is established and trained by the HMM, so as to predict the remaining life span of the equipment. Finally, the actual operation data of the railway field is selected to verify the prediction method proposed in the paper. The results show that the state recognition and the life prediction accuracy of the proposed method is higher, which can provide effective opinions for the predictive maintenance of the switch machine equipment.

A robust hybrid method using dynamic network analysis and Weighted Mahalanobis distance for modeling systemic risk in the international energy market

This paper proposes a novel hybrid method called Weighted Turbulence, which combines the dynamic network and weighted Mahalanobis distance to measure the overall systemic risk level of the international energy markets system. We simultaneously capture two essential drivers of systemic risk on international energy markets, including the abnormal price behavior of the single market and the interconnectedness among different energy markets, as the fundamental points of our modeling. It makes our proposed model can characterize the larger influential level of the abnormal behavior of the core energy market than that of the periphery markets on the systemic risk level and eliminate the negative impact of the non-systematic markets of the targeted markets system on the systemic risk measuring, which few existing schemes can achieve that. The empirical study further confirms the effectiveness and robustness of our proposed model. It can accurately detect the spikes of systemic risk in international energy markets, and the measuring results are unaffected by the interference of the noise data. The proposed method is applicable in practical systemic risk measurement, which has valuable theoretical and practical implications for related energy market participants.

Battlefield Target Grouping by a Hybridization of an Improved Whale Optimization Algorithm and Affinity Propagation

Target grouping, which is essentially a data clustering problem, is a research hotspot in the field of battlefield situation assessment. To address an unknown battlefield environment, affinity propagation based on an improved whale optimization algorithm (APBWOA) is proposed from the perspective of clustering. First, we propose a whale optimization algorithm based on a chaotic map and nonlinear inertia weight improvement called CPIW-WOA, which uses an improved circle map to generate initial populations and introduces nonlinear inertia weights to improve its convergence efficiency. The test results on nine benchmark functions show that the CPIW-WOA algorithm has superior performance to existing methods. Second, based on the fact that it fully considers the weights of the attributes in a given sample, the weighted Mahalanobis distance is adopted to replace the Euclidean distance. In addition, the silhouette index is introduced to determine the optimal number of clusters. By iteratively updating through CPIW-WOA to search for the optimal settings, the limitation of manually entering specified parameters can be overcome. Test results on real-world datasets show that the new method is more accurate and effective than other methods; therefore, it can provide effective solutions with respect to battlefield target grouping.

PCAmatchR: a flexible R package for optimal case-control matching using weighted principal components.

A concern when conducting genome-wide association studies (GWAS) is the potential for population stratification, i.e. ancestry-based genetic differences between cases and controls, that if not properly accounted for, could lead to biased association results. We developed PCAmatchR as an open source R package for performing optimal case-control matching using principal component analysis (PCA) to aid in selecting controls that are well matched by ancestry to cases. PCAmatchR takes user supplied PCA outputs and selects matching controls for cases by utilizing a weighted Mahalanobis distance metric which weights each principal component by the percentage of genetic variation explained. Results from the 1000 Genomes Project data demonstrate both the functionality and performance of PCAmatchR for selecting matching controls for case populations as well as reducing inflation of association test statistics. PCAmatchR improves genomic similarity between matched cases and controls, which minimizes the effects of population stratification in GWAS analyses. PCAmatchR is freely available for download on GitHub (https://github.com/machiela-lab/PCAmatchR) or through CRAN (https://CRAN.R-project.org/package=PCAmatchR). Supplementary data are available at Bioinformatics online.

Weighted L1-norm Logistic Regression for Gene Selection of Microarray Gene Expression Classification

The classification of cancer is a significant application of the DNA microarray data. Gene selection methods are ordinarily used handle the issue of high-dimensionality of microarray data to enable experts to diagnose and classify cancer with high accuracy. The penalized logistic regression (PLR) technique is usually used in the dimensionality reduction of the high-dimensional gene expression data sets to remove irrelevant and redundant predictors from the binary logistic regression model. One of the regularization techniques used to achieve this goal is the least absolute shrinkage and selection operator (Lasso). However, this technique has been criticized for being biased in the selection of genes. The adaptive Lasso was usually proposed by assigning an initial weight to each gene to address the selection bias. This paper is concerned with adapting PLR to improve its capability in classification and gene selection, in the sense of accuracy, by introducing the one-dimensional weighted Mahalanobis distance (1-DWM) for each gene as an initial weight inside L1-norm. By experiments, this proposed method, denoted by adaptive penalized logistic regression (APLR), gives more accurate results compared with other famous methods in this regard. The proposed method is applied to some real high-dimensional gene expression data sets in order to demonstrate its efficiency in terms of classification accuracy and selection of gene. Therefore, the proposed method could be utilized in other studies implementing gene selection in the area of classification of high dimensional cancer data sets.

2-stage modified random forest model for credit risk assessment of P2P network lending to “Three Rurals” borrowers

With the rapid growth of the P2P online loan industry in the “Three Rurals” (agriculture, rural areas, and farmers) sector, it is imperative to manage the borrowing risk of borrowers in the rural areas. A credit risk assessment model is proposed to classify the credit worthiness of the “Three Rurals” borrowers. We select the loan data of the Pterosaur Loan platform as the research sample, and establish a 2-stage Syncretic Cost-sensitive Random Forest (SCSRF) model to evaluate the credit risk of the borrowers. From the random forest, we construct a cost relationship from the actual distribution of the data categories, introduce a weighted Mahalanobis distance using the entropy weight method in the cost function, and adopt a weighted voting for the cost-sensitive decision tree base classifier. The parameters of the SCSRF model are optimized via a grid search. We validate the SCSRF classification model against several established credit evaluation models.

A resilience evaluation method for a combined regional agricultural water and soil resource system based on Weighted Mahalanobis distance and a Gray-TOPSIS model

Continuous urbanization, development of the economy, and the unrestrained exploitation and use of natural resources, the earth's ecosystems have been severely damaged by various types of frequently occurring natural and man-made disasters. Agricultural water and soil resources as a basic national strategic resources, a conflict is increasingly prominent between the available supply of and the increasing demand for these resources. Under such circumstances, the need for a quantitative diagnosis of the resilience of these types of has drawn increasing attention in China and abroad. A Technique for the Order of Preference by Similarity to an Ideal Solution (TOPSIS) evaluation model based on weighted Mahalanobis distance and gray relational analysis (MTS-GRA-TOPSIS) was proposed to evaluate the resilience of a combined regional agricultural water and soil resource (CRAWSR) system. For this purpose, a case study of the Jiansanjiang Administration of Agricultural Reclamation in Heilongjiang Province, China, was conducted. A total of 15 farms under its administration were used as evaluation objects, using information substitutability to screen out 12 indicators used to evaluate resilience. A MTS-GRA-TOPSIS model was used to evaluate the resilience rating of a CRAWSR system for 15 farms. The results show that the current resilience level of Jiansanjiang was rather low and that it should be improved. Specific countermeasures and suggestions were proposed, including increasing the utilization ratio of water and soil resources, returning farmland to forests, reducing groundwater use for agricultural irrigation, balancing the development of various industries, and improving the level of agricultural water conservation and mechanization. Verification of the rationality and reliability of the evaluation results obtained by the MTS-GRA-TOPSIS model was conducted which may be valuable for the formulation of related resource development strategies.

Remaining useful life prediction of the ball screw system based on weighted Mahalanobis distance and an exponential model

The ball screw system is one of the crucial components of machine tools and predicting its remaining useful life (RUL) can enhance the reliability and safety of the entire machine tool and reduce maintenance costs. Although quite a few techniques have been developed for the fault diagnosis of the ball screw system, forecasting the RUL of the ball screw system is a remaining challenge. To make up for this deficiency, we present a model-based method to predict the RUL of the ball screw system, which consists of two parts: health indicator (HI) construction and RUL prediction. First, we develop a novel HI, weighted Mahalanobis distance (WDMD). Unlike the Mahalanobis distance (MD), which is constructed by fusing original features directly, the WDMD is formed with some selected features only, and the features are weighted before integration. Second, an exponential model is developed to describe the degradation path of the ball screw system. Then, the particle filtering algorithm is employed to combine the WDMD and the degradation model for state estimation and RUL prediction. The proposed approach is verified by a dataset obtained from an experimental system designed for accelerated life tests of the ball screw system. The results show that the WDMD has a more apparent deterioration trend than the MD and the proposed exponential model performs better than both the linear model and the nonlinear model in RUL prediction.

Comparison of joint control schemes for multivariate normal i.i.d. output

The performance of a product frequently relies on more than one quality characteristic. In such a setting, joint control schemes are used to determine whether or not we are in the presence of unfavorable disruptions in the location ( $${\varvec{\mu }}$$ ) and spread ( $${\varvec{\varSigma }}$$ ) of a vector of quality characteristics. A common joint scheme for multivariate output comprises two charts: one for $${\varvec{\mu }}$$ based on a weighted Mahalanobis distance between the vector of sample means and the target mean vector; another one for $${\varvec{\varSigma }}$$ depending on the ratio between the determinants of the sample covariance matrix and the target covariance matrix. Since we are well aware that there are plenty of quality control practitioners who are still reluctant to use sophisticated control statistics, this paper tackles Shewhart-type charts for $${\varvec{\mu }}$$ and $${\varvec{\varSigma }}$$ based on three pairs of control statistics depending on the nominal mean vector and covariance matrix, $${\varvec{\mu }}_0$$ and $${\varvec{\varSigma }}_0$$ . We either capitalize on existing results or derive the joint probability density functions of these pairs of control statistics in order to assess the ability of the associated joint schemes to detect shifts in $${\varvec{\mu }}$$ or $${\varvec{\varSigma }}$$ for various out-of-control scenarios. A comparison study relying on extensive numerical and simulation results leads to the conclusion that none of the three joints schemes for $${\varvec{\mu }}$$ and $${\varvec{\varSigma }}$$ is uniformly better than the others. However, those results also suggest that the joint scheme with the control statistics $$n \, ( \bar{\mathbf {X}}-{\varvec{\mu }}_0 )^\top \, {\varvec{\varSigma }}_0^{-1} \, ( \bar{\mathbf {X}}-{\varvec{\mu }}_0 )$$ and $$\hbox {det} \left( (n-1) \mathbf{S} \right) / \hbox {det} \left( {\varvec{\varSigma }}_0 \right) $$ has the best overall average run length performance.

Covariance effect analysis of similarity measurement methods for early construction cost estimation using case-based reasoning

Abstract Quality source data are essential to secure the reliability of early cost estimation, accuracy, and transparency of the estimation process. To improve the reliability of cost estimation results using CBR, a recurring issue in similarity measurement has been to accurately compute the distance among attributes and cases for the retrieval of the most similar singular or plural cases. However, these existing similarity measures have limitations in taking the covariance among attributes into consideration, and reflecting the effects of covariance in the computation of distances among attributes. To deal with this challenging issue, this research examines the weighted Mahalanobis distance based similarity measure applied to CBR cost estimation, and carries out comparative research on the existing distance measurement methods of CBR. To validate the suggested CBR cost model, simulation data test and case studies using 99 multi-family housing complexes are carried out. As a consequence, this research is expected to improve academic value and mathematical and statistical logicality of similarity measurement, especially in application to CBR cost estimation. The results can be further referenced to not only the area of construction cost estimation, but also international market selection, planning and scheduling, noise control and management, and energy management where case-based reasoning can be applied.

An adaptive dose-finding method using a change-point model for molecularly targeted agents in phase I trials.

The paradigm of oncology drug development is expanding from developing cytotoxic agents to developing biological or molecularly targeted agents (MTAs). Although it is common for the efficacy and toxicity of cytotoxic agents to increase monotonically with dose escalation, the efficacy of some MTAs may exhibit non-monotonic patterns in their dose-efficacy relationships. Many adaptive dose-finding approaches in the available literature account for the non-monotonic dose-efficacy behavior by including additional model parameters. In this study, we propose a novel adaptive dose-finding approach based on binary efficacy and toxicity outcomes in phase I trials for monotherapy using an MTA. We develop a dose-efficacy model, the parameters of which are allowed to change in the vicinity of the change point of the dose level, in order to consider the non-monotonic pattern of the dose-efficacy relationship. The change point is obtained as the dose that maximizes the log-likelihood of the assumed dose-efficacy and dose-toxicity models. The dose-finding algorithm is based on the weighted Mahalanobis distance, calculated using the posterior probabilities of efficacy and toxicity outcomes. We compare the operating characteristics between the proposed and existing methods and examine the sensitivity of the proposed method by simulation studies under various scenarios. Copyright © 2016 John Wiley & Sons, Ltd.

Improved SDA based on mixed weighted Mahalanobis distance

We propose an improved subclass discriminant analysis based on the mixed weighted Mahalanobis distance, with the aim of resolving the classification problem that samples are multi-subclass distributed and the computed vectors are sub-optimal. There are three contributions in this paper. First, we used some theoretical support to improve the traditional discriminant criterion function in subclass discriminant analysis. Second, we propose a new distance measure called the mixed weighted Mahalanobis distance (MWMD), which considers the influence of the sample size and sample scatter. Finally, inspired by approximate weighted linear discriminant analysis, we applied MWMD to the improved criterion function. Our experimental results confirmed that the proposed method has a better classification performance than other discriminant analysis methods, using an artificial dataset and some benchmark databases.