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Showing papers on "Mahalanobis distance published in 2016"


Journal ArticleDOI
TL;DR: In this paper, the authors compare the reliability of three classes of dissimilarity measures: classification accuracy, Euclidean/Mahalanobis distance, and Pearson correlation distance, using simulations and four real functional magnetic resonance imaging (fMRI) datasets.

416 citations


Journal ArticleDOI
TL;DR: This paper proposes an LRaSMD-based Mahalanobis distance method for hyperspectral anomaly detection (LSMAD), and it was found that LSMAD shows a better detection performance than the current state-of-the-art hyperspectRAL anomaly detection methods.
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.

331 citations


Journal ArticleDOI
TL;DR: T theoretical analyses and empirical observations across wide spectrum multi-class imbalanced benchmarks indicate that MDO is the method of choice by offering statistical superior MAUC and precision compared to the popular over-sampling techniques.
Abstract: Class imbalance problem is quite pervasive in our nowadays human practice. This problem basically refers to the skewness in the data underlying distribution which, in turn, imposes many difficulties on typical machine learning algorithms. To deal with the emerging issues arising from multi-class skewed distributions, existing efforts are mainly divided into two categories: model-oriented solutions and data-oriented techniques. Focusing on the latter, this paper presents a new over-sampling technique which is inspired by Mahalanobis distance. The presented over-sampling technique, called MDO (Mahalanobis Distance-based Over-sampling technique), generates synthetic samples which have the same Mahalanobis distance from the considered class mean as other minority class examples. By preserving the covariance structure of the minority class instances and intelligently generating synthetic samples along the probability contours, new minority class instances are modelled better for learning algorithms. Moreover, MDO can reduce the risk of overlapping between different class regions which are considered as a serious challenge in multi-class problems. Our theoretical analyses and empirical observations across wide spectrum multi-class imbalanced benchmarks indicate that MDO is the method of choice by offering statistical superior MAUC and precision compared to the popular over-sampling techniques.

272 citations


Posted ContentDOI
25 Jul 2016-bioRxiv
TL;DR: It is found that pcadapt and hapflk are the most powerful software in scenarios of population divergence and range expansion and it is a valuable tool for data analysis in molecular ecology.
Abstract: The R package pcadapt performs genome scans to detect genes under selection based on population genomic data. It assumes that candidate markers are outliers with respect to how they are related to population structure. Because population structure is ascertained with principal component analysis, the package is fast and works with large-scale data. It can handle missing data and pooled sequencing data. By contrast to population-based approaches, the package handle admixed individuals and does not require grouping individuals into populations. Since its first release, pcadapt has evolved both in terms of statistical approach and software implementation. We present results obtained with robust Mahalanobis distance, which is a new statistic for genome scans available in the 2.0 and later versions of the package. When hierarchical population structure occurs, Mahalanobis distance is more powerful than the communality statistic that was implemented in the first version of the package. Using simulated data, we compare pcadapt to other software for genome scans (BayeScan, hapflk, OutFLANK, sNMF). We find that the proportion of false discoveries is around a nominal false discovery rate set at 10% with the exception of BayeScan that generates 40% of false discoveries. We also find that the power of BayeScan is severely impacted by the presence of admixed individuals whereas pcadapt is not impacted. Last, we find that pcadapt and hapflk are the most powerful software in scenarios of population divergence and range expansion. Because pcadapt handles next-generation sequencing data, it is a valuable tool for data analysis in molecular ecology.

158 citations


Book ChapterDOI
08 Oct 2016
TL;DR: In this article, a metric learning formulation called Weighted Approximate Rank Component Analysis (WARCA) is proposed to optimize the precision at top ranks by combining the WARP loss with a regularizer that favors orthonormal linear mappings and avoids rank-deficient embeddings.
Abstract: We are interested in the large-scale learning of Mahalanobis distances, with a particular focus on person re-identification. We propose a metric learning formulation called Weighted Approximate Rank Component Analysis (WARCA). WARCA optimizes the precision at top ranks by combining the WARP loss with a regularizer that favors orthonormal linear mappings and avoids rank-deficient embeddings. Using this new regularizer allows us to adapt the large-scale WSABIE procedure and to leverage the Adam stochastic optimization algorithm, which results in an algorithm that scales gracefully to very large data-sets. Also, we derive a kernelized version which allows to take advantage of state-of-the-art features for re-identification when data-set size permits kernel computation. Benchmarks on recent and standard re-identification data-sets show that our method beats existing state-of-the-art techniques both in terms of accuracy and speed. We also provide experimental analysis to shade lights on the properties of the regularizer we use, and how it improves performance.

142 citations


Journal ArticleDOI
TL;DR: A LogDet divergence-based metric learning with triplet constraint model which can learn Mahalanobis matrix with high precision and robustness is established.
Abstract: Multivariate time series (MTS) datasets broadly exist in numerous fields, including health care, multimedia, finance, and biometrics. How to classify MTS accurately has become a hot research topic since it is an important element in many computer vision and pattern recognition applications. In this paper, we propose a Mahalanobis distance-based dynamic time warping (DTW) measure for MTS classification. The Mahalanobis distance builds an accurate relationship between each variable and its corresponding category. It is utilized to calculate the local distance between vectors in MTS. Then we use DTW to align those MTS which are out of synchronization or with different lengths. After that, how to learn an accurate Mahalanobis distance function becomes another key problem. This paper establishes a LogDet divergence-based metric learning with triplet constraint model which can learn Mahalanobis matrix with high precision and robustness. Furthermore, the proposed method is applied on nine MTS datasets selected from the University of California, Irvine machine learning repository and Robert T. Olszewski’s homepage, and the results demonstrate the improved performance of the proposed approach.

140 citations


Journal ArticleDOI
TL;DR: In this article, the authors showed that the computation of distance covariance and distance correlation of real-valued random variables can be done in O(n log n) time using a U-statistic.
Abstract: Distance covariance and distance correlation have been widely adopted in measuring dependence of a pair of random variables or random vectors If the computation of distance covariance and distance correlation is implemented directly accordingly to its definition then its computational complexity is O(n2), which is a disadvantage compared to other faster methods In this article we show that the computation of distance covariance and distance correlation of real-valued random variables can be implemented by an O(nlog n) algorithm and this is comparable to other computationally efficient algorithms The new formula we derive for an unbiased estimator for squared distance covariance turns out to be a U-statistic This fact implies some nice asymptotic properties that were derived before via more complex methods We apply the fast computing algorithm to some synthetic data Our work will make distance correlation applicable to a much wider class of problems A supplementary file to this article, available on

117 citations


Posted Content
TL;DR: In this paper, a metric learning formulation called Weighted Approximate Rank Component Analysis (WARCA) is proposed to optimize the precision at top ranks by combining the WARP loss with a regularizer that favors orthonormal linear mappings, and avoids rank-deficient embeddings.
Abstract: We are interested in the large-scale learning of Mahalanobis distances, with a particular focus on person re-identification. We propose a metric learning formulation called Weighted Approximate Rank Component Analysis (WARCA). WARCA optimizes the precision at top ranks by combining the WARP loss with a regularizer that favors orthonormal linear mappings, and avoids rank-deficient embeddings. Using this new regularizer allows us to adapt the large-scale WSABIE procedure and to leverage the Adam stochastic optimization algorithm, which results in an algorithm that scales gracefully to very large data-sets. Also, we derive a kernelized version which allows to take advantage of state-of-the-art features for re-identification when data-set size permits kernel computation. Benchmarks on recent and standard re-identification data-sets show that our method beats existing state-of-the-art techniques both in term of accuracy and speed. We also provide experimental analysis to shade lights on the properties of the regularizer we use, and how it improves performance.

117 citations


Journal ArticleDOI
TL;DR: In this article, a joint approach to estimate the number of mixture components and identify cluster-relevant variables simultaneously as well as to obtain an identified model is presented, which consists in specifying sparse hierarchical priors on the mixture weights and component means.
Abstract: In the framework of Bayesian model-based clustering based on a finite mixture of Gaussian distributions, we present a joint approach to estimate the number of mixture components and identify cluster-relevant variables simultaneously as well as to obtain an identified model. Our approach consists in specifying sparse hierarchical priors on the mixture weights and component means. In a deliberately overfitting mixture model the sparse prior on the weights empties superfluous components during MCMC. A straightforward estimator for the true number of components is given by the most frequent number of non-empty components visited during MCMC sampling. Specifying a shrinkage prior, namely the normal gamma prior, on the component means leads to improved parameter estimates as well as identification of cluster-relevant variables. After estimating the mixture model using MCMC methods based on data augmentation and Gibbs sampling, an identified model is obtained by relabeling the MCMC output in the point process representation of the draws. This is performed using $$K$$K-centroids cluster analysis based on the Mahalanobis distance. We evaluate our proposed strategy in a simulation setup with artificial data and by applying it to benchmark data sets.

104 citations


Journal ArticleDOI
TL;DR: Binary Tree is integrated with Support Vector Data Description to address multi-classification issues with unbalanced datasets in machinery fault diagnosis and yields higher classification accuracy comparing with conventional models.
Abstract: Binary Tree is integrated with Support Vector Data Description to address multi-classification issues with unbalanced datasets.Separability measure based on Mahalanobis distance is proposed to construct Binary Tree.The parameters of Support Vector Data Description are optimized using Particle Swarm Optimization to eliminate the error caused by manually selection. In machinery fault diagnosis area, the obtained data samples under faulty conditions are usually far less than those under normal condition, resulting in unbalanced dataset issue. The commonly used machine learning techniques including Neural Network, Support Vector Machine, and Fuzzy C-Means, etc. are subject to high misclassification with unbalanced datasets. On the other hand, Support Vector Data Description is suitable for unbalanced datasets, but it is limited for only two class classification. To address the aforementioned issues, Support Vector Data Description based machine learning model is formulated with Binary Tree for multi-classification problems (e.g. multi fault classification or fault severity recognition, etc.) in machinery fault diagnosis. The binary tree structure of multiple clusters is firstly drawn based on the order of cluster-to-cluster distances calculated by Mahalanobis distance. Support Vector Data Description model is then applied to Binary Tree structure from top to bottom for classification. The parameters of Support Vector Data Description are optimized by Particle Swarm Optimization algorithm taking the recognition accuracy as objective function. The effectiveness of presented method is validated in the rotor unbalance severity classification, and the presented method yields higher classification accuracy comparing with conventional models.

96 citations


Journal ArticleDOI
TL;DR: Three methods for the identification of multivariate outliers are compared based on the Mahalanobis distance that will be made resistant against outliers and model deviations by robust estimation of location and covariance.
Abstract: Three methods for the identification of multivariate outliers (Rousseeuw and Van Zomeren, 1990; Becker and Gather, 1999; Filzmoser et al, 2005) are compared They are based on the Mahalanobis distance that will be made resistant against outliers and model deviations by robust estimation of location and covariance The comparison is made by means of a simulation study Not only the case of multivariate normally distributed data, but also heavy tailed and asymmetric distributions will be considered The simulations are focused on low dimensional ( p = 5 ) and high dimensional ( p = 30 ) data

Journal ArticleDOI
TL;DR: A novel unsupervised and nonparametric genetic algorithm for decision boundary analysis (GADBA) to support the structural damage detection process, even in the presence of linear and nonlinear effects caused by operational and environmental variability is proposed.

Journal ArticleDOI
TL;DR: To use deterministic methods to select the feature-channels pairs that best classify the hand postures at different limb positions, EMG data from 10 able-bodied subjects were acquired and 10 time-domain and frequency-domain features were extracted.

Journal ArticleDOI
TL;DR: In this article, the authors formulate multivariate generalized BS regression models and carry out a diagnostic analysis for these models and consider the Mahalanobis distance as a global influence measure to detect multivariate outliers and use it for evaluating the adequacy of the distributional assumption.
Abstract: Birnbaum–Saunders (BS) models are receiving considerable attention in the literature. Multivariate regression models are a useful tool of the multivariate analysis, which takes into account the correlation between variables. Diagnostic analysis is an important aspect to be considered in the statistical modeling. In this paper, we formulate multivariate generalized BS regression models and carry out a diagnostic analysis for these models. We consider the Mahalanobis distance as a global influence measure to detect multivariate outliers and use it for evaluating the adequacy of the distributional assumption. We also consider the local influence approach and study how a perturbation may impact on the estimation of model parameters. We implement the obtained results in the R software, which are illustrated with real-world multivariate data to show their potential applications.

Proceedings ArticleDOI
09 Oct 2016
TL;DR: A new concept called multimodal typicality, τMM is proposed in this paper, which offers a closed analytical form that represents ensemble properties derived entirely from the empirical observations of data and is applicable to data streams and online algorithms.
Abstract: In this paper, a novel empirical data analysis approach (abbreviated as EDA) is introduced which is entirely data-driven and free from restricting assumptions and pre-defined problem- or user-specific parameters and thresholds. It is well known that the traditional probability theory is restricted by strong prior assumptions which are often impractical and do not hold in real problems. Machine learning methods, on the other hand, are closer to the real problems but they usually rely on problem- or user-specific parameters or thresholds making it rather art than science. In this paper we introduce a theoretically sound yet practically unrestricted and widely applicable approach that is based on the density in the data space. Since the data may have exactly the same value multiple times we distinguish between the data points and unique locations in the data space. The number of data points, k is larger or equal to the number of unique locations, l and at least one data point occupies each unique location. The number of different data points that have exactly the same location in the data space (equal value), ƒ can be seen as frequency. Through the combination of the spatial density and the frequency of occurrence of discrete data points, a new concept called multimodal typicality, τMM is proposed in this paper. It offers a closed analytical form that represents ensemble properties derived entirely from the empirical observations of data. Moreover, it is very close (yet different) from the histograms, from the probability density function (pdf) as well as from fuzzy set membership functions. Remarkably, there is no need to perform complicated pre-processing like clustering to get the multimodal representation. Moreover, the closed form for the case of Euclidean, Mahalanobis type of distance as well as some other forms (e.g. cosine-based dissimilarity) can be expressed recursively making it applicable to data streams and online algorithms. Inference/estimation of the typicality of data points that were not present in the data so far can be made. This new concept allows to rethink the very foundations of statistical and machine learning as well as to develop a series of anomaly detection, clustering, classification, prediction, control and other algorithms.

Posted Content
TL;DR: Analytical expressions for the means and covariances of the sample distribution of the cross-validated Mahalanobis distance allow us to construct a normal approximation to the estimated distances, which enables powerful inference on the measured statistics.
Abstract: We present analytical expressions for the means and covariances of the sample distribution of the cross-validated Mahalanobis distance. This measure has proven to be especially useful in the context of representational similarity analysis (RSA) of neural activity patterns as measured by means of functional magnetic resonance imaging (fMRI). These expressions allow us to construct a normal approximation to the estimated distances, which in turn enables powerful inference on the measured statistics. Using the results, the difference between two distances can be statistically assessed, and the measured structure of the distances can be efficiently compared to predictions from computational models.

Proceedings ArticleDOI
08 Dec 2016
TL;DR: A DGA Botnet detection scheme based on DNS traffic analysis which utilizes semantic measures such as entropy, meaning the level of the domain, frequency of n-gram appearances and Mahalanobis distance for domain classification is proposed.
Abstract: Botnets play major roles in a vast number of threats to network security, such as DDoS attacks, generation of spam emails, information theft. Detecting Botnets is a difficult task in due to the complexity and performance issues when analyzing the huge amount of data from real large-scale networks. In major Botnet malware, the use of Domain Generation Algorithms allows to decrease possibility to be detected using white list - blacklist scheme and thus DGA Botnets have higher survival. This paper proposes a DGA Botnet detection scheme based on DNS traffic analysis which utilizes semantic measures such as entropy, meaning the level of the domain, frequency of n-gram appearances and Mahalanobis distance for domain classification. The proposed method is an improvement of Phoenix botnet detection mechanism, where in the classification phase, the modified Mahalanobis distance is used instead of the original for classification. The clustering phase is based on modified k-means algorithm for archiving better effectiveness. The effectiveness of the proposed method was measured and compared with Phoenix, Linguistic and SVM Light methods. The experimental results show the accuracy of proposed Botnet detection scheme ranges from 90 to 99,97% depending on Botnet type.

Journal ArticleDOI
TL;DR: The results show the Mahalanobis Typicality model had more high scoring areas and greater overall similarity than Maxent to the MCE outputs, suggesting, for this case study, it was the most appropriate SDM for aquaculture site selection.

Journal ArticleDOI
TL;DR: In this paper, an efficient and effective damage detection algorithm is proposed using transmissibility along with Mahalanobis distance and Hotelling T-square for long-term health monitoring for structures.
Abstract: Accurate and efficient damage detection in long-term health monitoring for structures still encounters many difficulties due to the effect of environment. Furthermore, recorded big data requires efficient damage detection algorithm. In this study, an efficient and effective damage detection algorithm is proposed using transmissibility along with Mahalanobis distance and Hotelling T-square. A numerically simulated beam and an experimentally tested laboratory structure are used to validate the proposed algorithm. Results demonstrate good performance of the proposed technique in damage detection.

Journal ArticleDOI
TL;DR: In this article, a review of principal component analysis (PCA) and reconstruction-based contribution (RBC) are two commonly used techniques for fault detection and fault diagnosis problems, respectively.

Journal ArticleDOI
TL;DR: This paper describes robust estimation procedures (M-estimators of location and scale) more suitable for non-Gaussian environment and shows that using them as plug-in estimators in anomaly detectors leads to some great improvement in the detection process.
Abstract: Anomaly detection methods are devoted to target detection schemes in which no a priori information about the spectra of the targets of interest is available. This paper reviews classical anomaly detection schemes such as the widely spread Reed–Xiaoli detector and some of its variations. Moreover, the Mahalanobis distance-based detector, rigorously derived from a Kelly’s test-based approach, is analyzed and its exact distribution is derived when both mean vector and covariance matrix are unknown and have to be estimated. Although, most of these techniques are based on Gaussian distribution, we also propose here ways to extend them to non-Gaussian framework. For this purpose, elliptical distributions are considered for background statistical characterization. Through this assumption, this paper describes robust estimation procedures (M-estimators of location and scale) more suitable for non-Gaussian environment. We show that using them as plug-in estimators in anomaly detectors leads to some great improvement in the detection process. Finally, the theoretical contribution is validated through simulations and on real hyperspectral scenes.

Journal ArticleDOI
TL;DR: This method very successfully combines the well-known direct least squares method and the RANSAC algorithm with a realistic statistical model of multiple ellipses in the plane with the potential to solve real time applications.

Journal ArticleDOI
TL;DR: This paper attempts to imitate the way of physical examination of palpebral conjunctiva to detect anemia, so that computers can identify anemia patients automatically in a consolidated manner for a screening process and proves the feasibility of the attempt.

Journal ArticleDOI
TL;DR: In this paper, a simple proof of the Chebyshev's inequality for random vectors is given, which provides a lower bound for the percentage of the population of an arbitrary random vector X with finite mean μ = E(X), and a positive definite covariance matrix V = Cov(X) whose Mahalanobis distance with respect to V to the mean μ is less than a fixed value.
Abstract: In this short note, a very simple proof of the Chebyshev's inequality for random vectors is given. This inequality provides a lower bound for the percentage of the population of an arbitrary random vector X with finite mean μ = E(X) and a positive definite covariance matrix V = Cov(X) whose Mahalanobis distance with respect to V to the mean μ is less than a fixed value. The main advantage of the proof is that it is a simple exercise for a first year probability course. An alternative proof based on principal components is also provided. This proof can be used to study the case of a singular covariance matrix V.

Journal ArticleDOI
TL;DR: A fast least squares version of TMSVM is formulated which solves two modified primal problems instead of two dual problems, and a new multiclass classification algorithm, named DAG-LSTMSVM for multi-class classification, is proposed by combining least squares T MSVM and directed acyclic graph (DAG).
Abstract: Although TWSVM always achieves good performance for data classification, it does not take full advantage of the statistical information of the training data. Recently proposed twin mahalanobis distance-based support vector machine (TMSVM) modifies the standard TWSVM by constructing a pair of Mahalanobis distance-based kernels according to the covariance matrices of two classes of training data, which improves the generalization ability. However, TMSVW solves two dual quadratic programming problems. Moreover, it is proposed to deal with binary classification problems, while most of pattern recognition problems are problems of multi-class classification. In order to enhance the performance of TMSVM, in this paper, we formulate a fast least squares version of TMSVM which solves two modified primal problems instead of two dual problems. The solution of two modified primal problems can easily be obtained by solving a set of linear equations in the primal space. Then we propose a new multiclass classification algorithm, named DAG-LSTMSVM for multi-class classification, by combining least squares TMSVM and directed acyclic graph (DAG). A mahalanobis distance-based distance measure is designed as the class separability criterion to construct the optimal DAG structure. A modified shuffled frog leaping algorithm-based model selection for DAG-LSTMSVM is suggested for parameter selection. The experimental results on artificial dataset and UCI datasets show that the proposed algorithm obtains high classification accuracy and good generalization ability.

Journal ArticleDOI
TL;DR: The results show that the prediction error of the Reynolds stress anisotropy is positively correlated with Mahalanobis distance and KDE distance, demonstrating that both extrapolation metrics can be used to estimate the prediction confidence a priori.
Abstract: Although Reynolds-Averaged Navier-Stokes (RANS) equations are still the dominant tool for engineering design and analysis applications involving turbulent flows, standard RANS models are known to be unreliable in many flows of engineering relevance, including flows with separation, strong pressure gradients or mean flow curvature. With increasing amounts of 3-dimensional experimental data and high fidelity simulation data from Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS), data-driven turbulence modeling has become a promising approach to increase the predictive capability of RANS simulations. Recently, a data-driven turbulence modeling approach via machine learning has been proposed to predict the Reynolds stress anisotropy of a given flow based on high fidelity data from closely related flows. In this work, the closeness of different flows is investigated to assess the prediction confidence a priori. Specifically, the Mahalanobis distance and the kernel density estimation (KDE) technique are used as metrics to quantify the distance between flow data sets in feature space. The flow over periodic hills at Re=10595 is used as the test set and seven flows with different configurations are individually used as training set. The results show that the prediction error of the Reynolds stress anisotropy is positively correlated with Mahalanobis distance and KDE distance, demonstrating that both extrapolation metrics can be used to estimate the prediction confidence a priori. A quantitative comparison using correlation coefficients shows that the Mahalanobis distance is less accurate in estimating the prediction confidence than KDE distance. The extrapolation metrics introduced in this work and the corresponding analysis provide an approach to aid in the choice of the data source and to assess the prediction confidence for data-driven turbulence modeling.

Proceedings ArticleDOI
13 Aug 2016
TL;DR: A novel metric learning model using the capped trace norm based regularization, which uses a singular value threshold to constraint the metric matrix M as low-rank explicitly such that the rank of matrix M is stable when the large singular values vary, is introduced.
Abstract: Metric learning aims at automatically learning a metric from pair or triplet based constraints in data, and it can be potentially beneficial whenever the notion of metric between instances plays a nontrivial role. In Mahalanobis distance metric learning, distance matrix M is in symmetric positive semi-definite cone, and in order to avoid overfitting and to learn a better Mahalanobis distance from weakly supervised constraints, the low-rank regularization has been often imposed on matrix M to learn the correlations between features and samples. As the approximations of the rank minimization function, the trace norm and Fantope have been utilized to regularize the metric learning objectives and achieve good performance. However, these low-rank regularization models are either not tight enough to approximate rank minimization or time-consuming to tune an optimal rank. In this paper, we introduce a novel metric learning model using the capped trace norm based regularization, which uses a singular value threshold to constraint the metric matrix M as low-rank explicitly such that the rank of matrix M is stable when the large singular values vary. The capped trace norm regularization can also be viewed as the adaptive Fantope regularization. We minimize singular values which are less than threshold value and the rank of M is not necessary to be k, thus our method is more stable and applicable in practice when we do not know the optimal rank of matrix M. We derive an efficient optimization algorithm to solve the proposed new model and the algorithm convergence proof is also provided in this paper. We evaluate our method on a variety of challenging benchmarks, such as LFW and Pubfig datasets. Face verification experiments are performed and results show that our method consistently outperforms the state-of-the-art metric learning algorithms.

Journal ArticleDOI
TL;DR: In this article, it is shown that the sum of squares of the standardised scores of all non-zero principal components (PCs) equals the squared Mahalanobis distance.
Abstract: It is shown that the sum of squares of the standardised scores of all non-zero principal components (PCs) equals the squared Mahalanobis distance. A new distance measure, the reduced Mahalanobis distance, is explored in which the number of PCs retained is less than the full rank model. It is illustrated by both one-class and two-class classifiers. Linear discriminant analysis can be employed as a soft model, and principal component analysis using the pooled variance-covariance matrix is introduced as an intermediate view between conjoint and disjoint models allowing linear discriminant analysis to be used on these reduced rank models. By choosing the most discriminatory PCs, it can be shown that the reduced Mahalanobis distance has superior performance over the full rank model for discriminating via soft models. Copyright © 2016 John Wiley & Sons, Ltd.

Posted Content
TL;DR: Zhang et al. as discussed by the authors proposed an end-to-end learning framework called DARI, which integrates the distance metric and representation integration by factorizing the Mahalanobis distance matrix as one top fully-connected layer that is seamlessly integrated with other bottom layers representing the image feature.
Abstract: The past decade has witnessed the rapid development of feature representation learning and distance metric learning, whereas the two steps are often discussed separately. To explore their interaction, this work proposes an end-to-end learning framework called DARI, i.e. Distance metric And Representation Integration, and validates the effectiveness of DARI in the challenging task of person verification. Given the training images annotated with the labels, we first produce a large number of triplet units, and each one contains three images, i.e. one person and the matched/mismatch references. For each triplet unit, the distance disparity between the matched pair and the mismatched pair tends to be maximized. We solve this objective by building a deep architecture of convolutional neural networks. In particular, the Mahalanobis distance matrix is naturally factorized as one top fully-connected layer that is seamlessly integrated with other bottom layers representing the image feature. The image feature and the distance metric can be thus simultaneously optimized via the one-shot backward propagation. On several public datasets, DARI shows very promising performance on re-identifying individuals cross cameras against various challenges, and outperforms other state-of-the-art approaches.

Journal ArticleDOI
TL;DR: Wang et al. as mentioned in this paper proposed a new algorithm for damage detection in structures using an energy-based method to capture linear and nonlinear effects of damage on structural response for more accurate detection, the proposed algorithm combines multiple damage sensitive features through a distancebased method by using Mahalanobis distance Hypothesis testing is employed as the statistical data analysis technique for uncertainty quantification associated with damage detection.
Abstract: Summary This study proposes a new algorithm for damage detection in structures The algorithm employs an energy-based method to capture linear and nonlinear effects of damage on structural response For more accurate detection, the proposed algorithm combines multiple damage sensitive features through a distance-based method by using Mahalanobis distance Hypothesis testing is employed as the statistical data analysis technique for uncertainty quantification associated with damage detection Both the distance-based and the data analysis methods have been chosen to deal with small size data sets Finally, the efficacy and robustness of the algorithm are experimentally validated by testing a steel laboratory prototype, and the results show that the proposed method can effectively detect and localize the defects Copyright © 2015 John Wiley & Sons, Ltd