Mahalanobis distance

About: Mahalanobis distance is a research topic. Over the lifetime, 4616 publications have been published within this topic receiving 95294 citations.

Multi-Scale Mahalanobis Kernel-Based Support Vector Machine for Classification of High-Resolution Remote Sensing Images

Abstract: Support vector machine (SVM) is a powerful cognitive and learning algorithm in the domain of pattern recognition and image classification. However, the generalization ability of SVM is limited when processing classification of high-resolution remote sensing images. One chief reason for this is that the Euclidean distance-based distance matrix in traditional SVM treats different samples equally and overlooks the global distribution of samples. To construct a more effective SVM-based classification method, this paper proposes a multi-scale Mahalanobis kernel-based SVM classifier. In this new method, we first introduce a Mahalanobis distance kernel to improve the global cognitive learning ability of SVM. Then, the Mahalanobis distance kernel is embedded to the multi-scale kernel learning (MSKL) to construct a novel multi-scale Mahalanobis kernel, in which the parameters are optimized by a bio-inspired algorithm, named differential evolution. Finally, the new method is extended to the classification of high-resolution remote sensing images based on the spatial-spectral features. The comparison experiments of five public UCI datasets and two high-resolution remote sensing images verify that the Mahalanobis distance-based method can obtain more accurate classification results than that of the Euclidean distance-based method. In addition, the proposed method produced the best classification results in all the experiments. The global cognitive learning ability of Mahalanobis distance-based method is stronger than that of the Euclidean distance-based method. In addition, this study indicates that the optimized MSKL are potential for the interpretation and understanding of complicated high-resolution remote sensing scene.

Vision aided 3D laser scanner based registration

Abstract: This paper describes a vision and 3D laser based registration approach which utilizes visual features to identify correspondences. Visual features are obtained from the images of a standard color camera and the depth of these features is determined by interpolating between the scanning points of a 3D laser range scanner, taking into consideration the visual information in the neighbourhood of the respective visual feature. The 3D laser scanner is also used to determine a position covariance estimate of the visual feature. To exploit these covariance estimates, an ICP algorithm based on the Mahalanobis distance is applied. Initial experimental results are presented in a real world indoor laboratory environment

Classification complexity in myoelectric pattern recognition.

Abstract: Limb prosthetics, exoskeletons, and neurorehabilitation devices can be intuitively controlled using myoelectric pattern recognition (MPR) to decode the subject’s intended movement. In conventional MPR, descriptive electromyography (EMG) features representing the intended movement are fed into a classification algorithm. The separability of the different movements in the feature space significantly affects the classification complexity. Classification complexity estimating algorithms (CCEAs) were studied in this work in order to improve feature selection, predict MPR performance, and inform on faulty data acquisition. CCEAs such as nearest neighbor separability (NNS), purity, repeatability index (RI), and separability index (SI) were evaluated based on their correlation with classification accuracy, as well as on their suitability to produce highly performing EMG feature sets. SI was evaluated using Mahalanobis distance, Bhattacharyya distance, Hellinger distance, Kullback–Leibler divergence, and a modified version of Mahalanobis distance. Three commonly used classifiers in MPR were used to compute classification accuracy (linear discriminant analysis (LDA), multi-layer perceptron (MLP), and support vector machine (SVM)). The algorithms and analytic graphical user interfaces produced in this work are freely available in BioPatRec. NNS and SI were found to be highly correlated with classification accuracy (correlations up to 0.98 for both algorithms) and capable of yielding highly descriptive feature sets. Additionally, the experiments revealed how the level of correlation between the inputs of the classifiers influences classification accuracy, and emphasizes the classifiers’ sensitivity to such redundancy. This study deepens the understanding of the classification complexity in prediction of motor volition based on myoelectric information. It also provides researchers with tools to analyze myoelectric recordings in order to improve classification performance.

On Classification and Regression Trees for Multiple Responses and Its Application

Abstract: In many application fields, multivariate approaches that simultaneously consider the correlation between responses are needed. The tree method can be extended to multivariate responses, such as repeated measure and longitudinal data, by modifying the split function so as to accommodate multiple responses. Recently, researchers have constructed some decision trees for multiple continuous longitudinal response and multiple binary responses using Mahalanobis distance and a generalized entropy index. However, these methods have limitations according to the type of response, that is, those that are only continuous or binary. In this paper, we will modify the tree for univariate response procedure and suggest a new tree-based method that can analyze any type of multiple responses by using GEE (generalized estimating equations) techniques. To compare the performance of trees, simulation studies on selection probability of true split variable will be shown. Finally, applications using epileptic seizure data and WWW data are introduced.

Scalable Large-Margin Distance Metric Learning Using Stochastic Gradient Descent

Abstract: The key to success of many machine learning and pattern recognition algorithms is the way of computing distances between the input data. In this paper, we propose a large-margin-based approach, called the large-margin distance metric learning (LMDML), for learning a Mahalanobis distance metric. LMDML employs the principle of margin maximization to learn the distance metric with the goal of improving ${k}$ -nearest-neighbor classification. The main challenge of distance metric learning is the positive semidefiniteness constraint on the Mahalanobis matrix. Semidefinite programming is commonly used to enforce this constraint, but it becomes computationally intractable on large-scale data sets. To overcome this limitation, we develop an efficient algorithm based on a stochastic gradient descent. Our algorithm can avoid the computations of the full gradient and ensure that the learned matrix remains within the positive semidefinite cone after each iteration. Extensive experiments show that the proposed algorithm is scalable to large data sets and outperforms other state-of-the-art distance metric learning approaches regarding classification accuracy and training time.