Mahalanobis Distance

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Liangpei Zhang - One of the best experts on this subject based on the ideXlab platform.

  • a low rank and sparse matrix decomposition based Mahalanobis Distance method for hyperspectral anomaly detection
    IEEE Transactions on Geoscience and Remote Sensing, 2016
    Co-Authors: Yuxiang Zhang, Liangpei Zhang, Shugen Wang
    Abstract:

    Anomaly detection is playing an increasingly important role in hyperspectral image (HSI) processing. The traditional anomaly detection methods mainly extract knowledge from the background and use the difference between the anomalies and the background to distinguish them. Anomaly contamination and the inverse covariance matrix problem are the main difficulties with these methods. The low-rank and sparse matrix decomposition (LRaSMD) technique may have the potential to solve the aforementioned hyperspectral anomaly detection problem since it can extract knowledge from both the background and the anomalies. This paper proposes an LRaSMD-based Mahalanobis Distance method for hyperspectral anomaly detection (LSMAD). This approach has the following capabilities: 1) takes full advantage of the LRaSMD technique to set the background apart from the anomalies; 2) explores the low-rank prior knowledge of the background to compute the background statistics; and 3) applies the Mahalanobis Distance differences to detect the probable anomalies. Extensive experiments were carried out on four HSIs, and it was found that LSMAD shows a better detection performance than the current state-of-the-art hyperspectral anomaly detection methods.

  • a support vector conditional random fields classifier with a Mahalanobis Distance boundary constraint for high spatial resolution remote sensing imagery
    IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2014
    Co-Authors: Yanfei Zhong, Liangpei Zhang
    Abstract:

    In this paper, a modified conditional random fields (CRFs) classifier, namely the support vector conditional random fields classifier with a Mahalanobis Distance boundary constraint (SVRFMC), is proposed to perform the task of classification for high spatial resolution (HSR) remote sensing imagery. In SVRFMC, the CRFs model has the intrinsic ability of incorporating the contextual information in both the observation and labeling fields. Support vector machine (SVM) is set as the spectral term to get a more precise estimation of each pixel's probability of belonging to each possible class. To preserve the spatial details in the classification result, a Mahalanobis Distance boundary constraint is considered as the spatial term to undertake appropriate spatial smoothing. By integrating SVM and a Mahalanobis Distance boundary constraint, SVRFMC can not only avoid the explicit modeling of observed data, but can also undertake appropriate smoothing with the consideration of contextual information, thereby exhibiting more universality and validity in the application of HSR image classification, especially when the image has a complex land-cover class distribution and the training samples are limited. Three HSR images comprising QuickBird, IKONOS, and HYDICE imagery were utilized to evaluate the performance of the proposed algorithm in comparison to other image classification approaches: noncontextual multiclass SVM, a traditional object-oriented classifier (OOC), an object-oriented classification based on fractal net evolution approach (FNEA) segmentation (OO-FNEA), a simplified CRF model with boundary constraint (BC-CRF), and a recently proposed contextual classifier combining SVM and Markov random fields (Markovian support vector classifier). The experimental results demonstrate that the SVRFMC algorithm is superior to the other methods, providing a satisfactory classification result for HSR imagery, including both multispectral HSR imagery and hyperspectral HSR imagery, even with limited training samples, from both the visualization and quantitative evaluations.

  • a support vector conditional random fields classifier with a Mahalanobis Distance boundary constraint for high spatial resolution remote sensing imagery
    IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2014
    Co-Authors: Yanfei Zhong, Liangpei Zhang
    Abstract:

    In this paper, a modified conditional random fields (CRFs) classifier, namely the support vector conditional random fields classifier with a Mahalanobis Distance boundary constraint (SVRFMC), is proposed to perform the task of classification for high spatial resolution (HSR) remote sensing imagery. In SVRFMC, the CRFs model has the intrinsic ability of incorporating the contextual information in both the observation and labeling fields. Support vector machine (SVM) is set as the spectral term to get a more precise estimation of each pixel's probability of belonging to each possible class. To preserve the spatial details in the classification result, a Mahalanobis Distance boundary constraint is considered as the spatial term to undertake appropriate spatial smoothing. By integrating SVM and a Mahalanobis Distance boundary constraint, SVRFMC can not only avoid the explicit modeling of observed data, but can also undertake appropriate smoothing with the consideration of contextual information, thereby exhibiting more universality and validity in the application of HSR image classification, especially when the image has a complex land-cover class distribution and the training samples are limited. Three HSR images comprising QuickBird, IKONOS, and HYDICE imagery were utilized to evaluate the performance of the proposed algorithm in comparison to other image classification approaches: noncontextual multiclass SVM, a traditional object-oriented classifier (OOC), an object-oriented classification based on fractal net evolution approach (FNEA) segmentation (OO-FNEA), a simplified CRF model with boundary constraint (BC-CRF), and a recently proposed contextual classifier combining SVM and Markov random fields (Markovian support vector classifier). The experimental results demonstrate that the SVRFMC algorithm is superior to the other methods, providing a satisfactory classification result for HSR imagery, including both multispectral HSR imagery and hyperspectral HSR imagery, even with limited training samples, from both the visualization and quantitative evaluations.

Yanfei Zhong - One of the best experts on this subject based on the ideXlab platform.

  • a support vector conditional random fields classifier with a Mahalanobis Distance boundary constraint for high spatial resolution remote sensing imagery
    IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2014
    Co-Authors: Yanfei Zhong, Liangpei Zhang
    Abstract:

    In this paper, a modified conditional random fields (CRFs) classifier, namely the support vector conditional random fields classifier with a Mahalanobis Distance boundary constraint (SVRFMC), is proposed to perform the task of classification for high spatial resolution (HSR) remote sensing imagery. In SVRFMC, the CRFs model has the intrinsic ability of incorporating the contextual information in both the observation and labeling fields. Support vector machine (SVM) is set as the spectral term to get a more precise estimation of each pixel's probability of belonging to each possible class. To preserve the spatial details in the classification result, a Mahalanobis Distance boundary constraint is considered as the spatial term to undertake appropriate spatial smoothing. By integrating SVM and a Mahalanobis Distance boundary constraint, SVRFMC can not only avoid the explicit modeling of observed data, but can also undertake appropriate smoothing with the consideration of contextual information, thereby exhibiting more universality and validity in the application of HSR image classification, especially when the image has a complex land-cover class distribution and the training samples are limited. Three HSR images comprising QuickBird, IKONOS, and HYDICE imagery were utilized to evaluate the performance of the proposed algorithm in comparison to other image classification approaches: noncontextual multiclass SVM, a traditional object-oriented classifier (OOC), an object-oriented classification based on fractal net evolution approach (FNEA) segmentation (OO-FNEA), a simplified CRF model with boundary constraint (BC-CRF), and a recently proposed contextual classifier combining SVM and Markov random fields (Markovian support vector classifier). The experimental results demonstrate that the SVRFMC algorithm is superior to the other methods, providing a satisfactory classification result for HSR imagery, including both multispectral HSR imagery and hyperspectral HSR imagery, even with limited training samples, from both the visualization and quantitative evaluations.

  • a support vector conditional random fields classifier with a Mahalanobis Distance boundary constraint for high spatial resolution remote sensing imagery
    IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2014
    Co-Authors: Yanfei Zhong, Liangpei Zhang
    Abstract:

    In this paper, a modified conditional random fields (CRFs) classifier, namely the support vector conditional random fields classifier with a Mahalanobis Distance boundary constraint (SVRFMC), is proposed to perform the task of classification for high spatial resolution (HSR) remote sensing imagery. In SVRFMC, the CRFs model has the intrinsic ability of incorporating the contextual information in both the observation and labeling fields. Support vector machine (SVM) is set as the spectral term to get a more precise estimation of each pixel's probability of belonging to each possible class. To preserve the spatial details in the classification result, a Mahalanobis Distance boundary constraint is considered as the spatial term to undertake appropriate spatial smoothing. By integrating SVM and a Mahalanobis Distance boundary constraint, SVRFMC can not only avoid the explicit modeling of observed data, but can also undertake appropriate smoothing with the consideration of contextual information, thereby exhibiting more universality and validity in the application of HSR image classification, especially when the image has a complex land-cover class distribution and the training samples are limited. Three HSR images comprising QuickBird, IKONOS, and HYDICE imagery were utilized to evaluate the performance of the proposed algorithm in comparison to other image classification approaches: noncontextual multiclass SVM, a traditional object-oriented classifier (OOC), an object-oriented classification based on fractal net evolution approach (FNEA) segmentation (OO-FNEA), a simplified CRF model with boundary constraint (BC-CRF), and a recently proposed contextual classifier combining SVM and Markov random fields (Markovian support vector classifier). The experimental results demonstrate that the SVRFMC algorithm is superior to the other methods, providing a satisfactory classification result for HSR imagery, including both multispectral HSR imagery and hyperspectral HSR imagery, even with limited training samples, from both the visualization and quantitative evaluations.

Lei Wang - One of the best experts on this subject based on the ideXlab platform.

  • scalable large margin Mahalanobis Distance metric learning
    IEEE Transactions on Neural Networks, 2010
    Co-Authors: Chunhua Shen, Junae Kim, Lei Wang
    Abstract:

    For many machine learning algorithms such as k-nearest neighbor ( k-NN) classifiers and k-means clustering, often their success heavily depends on the metric used to calculate Distances between different data points. An effective solution for defining such a metric is to learn it from a set of labeled training samples. In this work, we propose a fast and scalable algorithm to learn a Mahalanobis Distance metric. The Mahalanobis metric can be viewed as the Euclidean Distance metric on the input data that have been linearly transformed. By employing the principle of margin maximization to achieve better generalization performances, this algorithm formulates the metric learning as a convex optimization problem and a positive semidefinite (p.s.d.) matrix is the unknown variable. Based on an important theorem that a p.s.d. trace-one matrix can always be represented as a convex combination of multiple rank-one matrices, our algorithm accommodates any differentiable loss function and solves the resulting optimization problem using a specialized gradient descent procedure. During the course of optimization, the proposed algorithm maintains the positive semidefiniteness of the matrix variable that is essential for a Mahalanobis metric. Compared with conventional methods like standard interior-point algorithms or the special solver used in large margin nearest neighbor , our algorithm is much more efficient and has a better performance in scalability. Experiments on benchmark data sets suggest that, compared with state-of-the-art metric learning algorithms, our algorithm can achieve a comparable classification accuracy with reduced computational complexity.

  • scalable large margin Mahalanobis Distance metric learning
    arXiv: Computer Vision and Pattern Recognition, 2010
    Co-Authors: Chunhua Shen, Junae Kim, Lei Wang
    Abstract:

    For many machine learning algorithms such as $k$-Nearest Neighbor ($k$-NN) classifiers and $ k $-means clustering, often their success heavily depends on the metric used to calculate Distances between different data points. An effective solution for defining such a metric is to learn it from a set of labeled training samples. In this work, we propose a fast and scalable algorithm to learn a Mahalanobis Distance metric. By employing the principle of margin maximization to achieve better generalization performances, this algorithm formulates the metric learning as a convex optimization problem and a positive semidefinite (psd) matrix is the unknown variable. a specialized gradient descent method is proposed. our algorithm is much more efficient and has a better performance in scalability compared with existing methods. Experiments on benchmark data sets suggest that, compared with state-of-the-art metric learning algorithms, our algorithm can achieve a comparable classification accuracy with reduced computational complexity.

Michael Pecht - One of the best experts on this subject based on the ideXlab platform.

  • Anomaly detection for IGBTs using Mahalanobis Distance
    Microelectronics Reliability, 2015
    Co-Authors: Nishad Patil, Diganta Das, Michael Pecht
    Abstract:

    Abstract In this study, a Mahalanobis Distance (MD)-based anomaly detection approach has been evaluated for non-punch through (NPT) and trench field stop (FS) insulated gate bipolar transistors (IGBTs). The IGBTs were subjected to electrical–thermal stress under a resistive load until their failure. Monitored on-state collector–emitter voltage and collector–emitter currents were used as input parameters to calculate MD. The MD values obtained from the healthy data were transformed using a Box–Cox transform, and three standard deviation limits were obtained from the transformed data. The upper three standard deviation limits of the transformed MD healthy data were used as a threshold for anomaly detection. The anomaly detection times obtained by using the MD approach were compared to the detection times obtained by using a fixed percentage change threshold for the on-state collector–emitter voltage.

  • online anomaly detection for hard disk drives based on Mahalanobis Distance
    IEEE Transactions on Reliability, 2013
    Co-Authors: Yu Wang, Qiang Miao, Eden W M, Kwokleung Tsui, Michael Pecht
    Abstract:

    A hard disk drive (HDD) failure may cause serious data loss and catastrophic consequences. Online health monitoring provides information about the degradation trend of the HDD, and hence the early warning of failures, which gives us a chance to save the data. This paper developed an approach for HDD anomaly detection using Mahalanobis Distance (MD). Critical parameters were selected using failure modes, mechanisms, and effects analysis (FMMEA), and the minimum redundancy maximum relevance (mRMR) method. A self-monitoring, analysis, and reporting technology (SMART) data set is used to evaluate the performance of the developed approach. The result shows that about 67% of the anomalies of failed drives can be detected with zero false alarm rate, and most of them can provide users with at least 20 hours during which to backup the data.

  • health monitoring of cooling fans based on Mahalanobis Distance with mrmr feature selection
    IEEE Transactions on Instrumentation and Measurement, 2012
    Co-Authors: Xiaohang Jin, Eden W M, L L Cheng, Michael Pecht
    Abstract:

    Cooling fans are widely used for thermal management in electronic products. The failure of cooling fans may cause electronic products to overheat, which can shorten the product's life, cause electronic components to burn, and even result in catastrophic consequences. Thus, there is a growing interest in health monitoring and anomaly detection for cooling fans in electronic products. A novel method for the health monitoring of cooling fans based on Mahalanobis Distance with minimum redundancy maximum relevance features is proposed in this paper. A case study of anomaly detection in cooling fans is carried out. The proposed method helps to avoid multicollinearity and tracks the degradation trends of the cooling fans. The results show that the proposed approach is feasible.

  • health monitoring of hard disk drive based on Mahalanobis Distance
    Prognostics and System Health Management Conference, 2011
    Co-Authors: Yu Wang, Qiang Miao, Michael Pecht
    Abstract:

    A hard disk drive (HDD) is one of the core components of most computer systems. A failure of HDD may cause serious data loss and catastrophic consequences. Thus, health monitoring and anomaly prediction for HDD are critical to prevent data loss and make strategies for data backup. This paper analyzed the potential failure modes and failure mechanisms influencing on HDD reliability by FMMEA (Failure Modes, Mechanisms and Effects Analysis) method and performed the prioritization by estimating the risk priority numbers. The Head Disk Interface (HDI) and head stack assembly related failure and relevant performance parameters are identified as the dominant failure mode and health monitoring parameters. A novel strategy for anomaly prediction of hard disk based on Mahalanobis Distance using SMART attributes is also suggested in this paper. Furthermore, a case study of HDD anomaly prediction based on the methodology presented in this paper is carried out. The experiment results showed that the proposed method is feasible.

  • health monitoring of electronic products based on Mahalanobis Distance and weibull decision metrics
    Microelectronics Reliability, 2011
    Co-Authors: Gang Niu, Michael Pecht, Satnam Singh, Steven W Holland
    Abstract:

    Abstract This paper presents a novel approach for health monitoring of electronic products using the Mahalanobis Distance (MD) and Weibull distribution. The MD value is used as a health index, which has the advantage of both summarizing the multivariate operating parameters and reducing the data set into a fused Distance index. The Weibull distribution is used to determine health decision metrics, which are useful in characterizing distributions of MD values. Furthermore, a case study of notebook computer health monitoring system is carried out. The experimental results show that the proposed method is valuable.

Chunhua Shen - One of the best experts on this subject based on the ideXlab platform.

  • scalable large margin Mahalanobis Distance metric learning
    IEEE Transactions on Neural Networks, 2010
    Co-Authors: Chunhua Shen, Junae Kim, Lei Wang
    Abstract:

    For many machine learning algorithms such as k-nearest neighbor ( k-NN) classifiers and k-means clustering, often their success heavily depends on the metric used to calculate Distances between different data points. An effective solution for defining such a metric is to learn it from a set of labeled training samples. In this work, we propose a fast and scalable algorithm to learn a Mahalanobis Distance metric. The Mahalanobis metric can be viewed as the Euclidean Distance metric on the input data that have been linearly transformed. By employing the principle of margin maximization to achieve better generalization performances, this algorithm formulates the metric learning as a convex optimization problem and a positive semidefinite (p.s.d.) matrix is the unknown variable. Based on an important theorem that a p.s.d. trace-one matrix can always be represented as a convex combination of multiple rank-one matrices, our algorithm accommodates any differentiable loss function and solves the resulting optimization problem using a specialized gradient descent procedure. During the course of optimization, the proposed algorithm maintains the positive semidefiniteness of the matrix variable that is essential for a Mahalanobis metric. Compared with conventional methods like standard interior-point algorithms or the special solver used in large margin nearest neighbor , our algorithm is much more efficient and has a better performance in scalability. Experiments on benchmark data sets suggest that, compared with state-of-the-art metric learning algorithms, our algorithm can achieve a comparable classification accuracy with reduced computational complexity.

  • scalable large margin Mahalanobis Distance metric learning
    arXiv: Computer Vision and Pattern Recognition, 2010
    Co-Authors: Chunhua Shen, Junae Kim, Lei Wang
    Abstract:

    For many machine learning algorithms such as $k$-Nearest Neighbor ($k$-NN) classifiers and $ k $-means clustering, often their success heavily depends on the metric used to calculate Distances between different data points. An effective solution for defining such a metric is to learn it from a set of labeled training samples. In this work, we propose a fast and scalable algorithm to learn a Mahalanobis Distance metric. By employing the principle of margin maximization to achieve better generalization performances, this algorithm formulates the metric learning as a convex optimization problem and a positive semidefinite (psd) matrix is the unknown variable. a specialized gradient descent method is proposed. our algorithm is much more efficient and has a better performance in scalability compared with existing methods. Experiments on benchmark data sets suggest that, compared with state-of-the-art metric learning algorithms, our algorithm can achieve a comparable classification accuracy with reduced computational complexity.