Mahalanobis distance

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

Beyond Mahalanobis metric: Cayley-Klein metric learning

Abstract: Cayley-Klein metric is a kind of non-Euclidean metric suitable for projective space. In this paper, we introduce it into the computer vision community as a powerful metric and an alternative to the widely studied Mahalanobis metric. We show that besides its good characteristic in non-Euclidean space, it is a generalization of Mahalanobis metric in some specific cases. Furthermore, as many Mahalanobis metric learning, we give two kinds of Cayley-Klein metric learning methods: MMC Cayley-Klein metric learning and LMNN Cayley-Klein metric learning. Experiments have shown the superiority of Cayley-Klein metric over Mahalanobis ones and the effectiveness of our Cayley-Klein metric learning methods.

DARI: distance metric and representation integration for person verification

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.

Probabilistic outlier detection for sparse multivariate geotechnical site investigation data using Bayesian learning

Abstract: Various uncertainties arising during acquisition process of geoscience data may result in anomalous data instances (i.e., outliers) that do not conform with the expected pattern of regular data instances. With sparse multivariate data obtained from geotechnical site investigation, it is impossible to identify outliers with certainty due to the distortion of statistics of geotechnical parameters caused by outliers and their associated statistical uncertainty resulted from data sparsity. This paper develops a probabilistic outlier detection method for sparse multivariate data obtained from geotechnical site investigation. The proposed approach quantifies the outlying probability of each data instance based on Mahalanobis distance and determines outliers as those data instances with outlying probabilities greater than 0.5. It tackles the distortion issue of statistics estimated from the dataset with outliers by a re-sampling technique and accounts, rationally, for the statistical uncertainty by Bayesian machine learning. Moreover, the proposed approach also suggests an exclusive method to determine outlying components of each outlier. The proposed approach is illustrated and verified using simulated and real-life dataset. It showed that the proposed approach properly identifies outliers among sparse multivariate data and their corresponding outlying components in a probabilistic manner. It can significantly reduce the masking effect (i.e., missing some actual outliers due to the distortion of statistics by the outliers and statistical uncertainty). It also found that outliers among sparse multivariate data instances affect significantly the construction of multivariate distribution of geotechnical parameters for uncertainty quantification. This emphasizes the necessity of data cleaning process (e.g., outlier detection) for uncertainty quantification based on geoscience data.

Face shape classification from 3D human data by using SVM

Abstract: Face shape is also important information for glasses design companies. In this paper, we proposed a non-contact method to classify the face shape by using Support Vector Machine (SVM) technique. This algorithm consists of three steps: head segmentation, face plane identification, and face shape classification. First, as whole 3D body data is captured and used as input of system, Eigenvector is used to define frontal side. Chin-Neck junction, Ellipsoid Fitting Technique and Mahalanobis distance are combined as a head segmentation algorithm to segment the 3D head. Second, face shape can be observed when projected on a plane. Major axes of ellipsoid are used to define a plane along the head called the face plane. Face shape on the face plane is classified into four classes in third step. To test the performance of the proposed method, ninety subjects are used. SVM is used to classify the face shape into four groups. The four type of the face shape are ellipse shape, long shape, round shape, and square shape. The accuracy rate is 73.68%. The result shows the feasibility of the proposed method. An advantage of this method is that this method is first fully automatic and non-contact face shape classification for whole 3D human body data.