Mahalanobis distance

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

Localized Structural Damage Detection: A Change Point Analysis

Abstract: Many current damage detection techniques rely on the skill and experience of a trained inspector and also require a priori knowledge about the struc- ture's properties. However, this study presents adapta- tion of several change point analysis techniques for their performance in civil engineering damage detection. Lit- erature shows different statistical approaches which are developed for detection of changes in observations for different applications including structural damage detec- tion. However, despite their importance in damage de- tection, control charts and statistical frameworks are not properly utilized in this area. On the other hand, most of the existing change point analysis techniques were originally developed for applications in the stock mar- ket or industrial engineering processes; utilizing them in structural damage detection needs adjustments and ver- ification. Therefore, in this article several change point detection methods are evaluated and adjusted for a dam- age detection scheme. The effectiveness of features from a statistics based local damage detection algorithm called Influenced Coefficient Based Damage Detection Algo- rithm (IDDA) is expanded for a more complex structural system. The statistics used in this study include the uni- variate Cumulative Sum, Exponentially Weighted Mov- ing Average (EWMA), Mean Square Error (MSE), and multivariate Mahalanobis distances, and Fisher Crite- rion. They are used to make control charts that detect and localize the damage by correlating locations of a sen- sor network with the damage features. A Modified MSE statistic, called ModMSE statistic, is introduced to re- move the sensitivity of the MSE statistic to the variance of a data set. The effectiveness of each statistic is analyzed.

Using Posterior-Based Features in Template Matching for Speech Recognition

Abstract: Given the availability of large speech corpora, as well as the increasing of memory and computational resources, the use of template matching approaches for automatic speech recognition (ASR) have recently attracted new attention. In such template-based approaches, speech is typically represented in terms of acoustic vector sequences, using spectral-based features such as MFCC of PLP, and local distances are usually based on Euclidean or Mahalanobis distances. In the present paper, we further investigate template-based ASR and show (on a continuous digit recognition task) that the use of posterior-based features significantly improves the standard template-based approaches, yielding to systems that are very competitive to state-of-the-art HMMs, even when using a very limited number (e.g., 10) of reference templates. Since those posteriors-based features can also be interpreted as a probability distribution, we also show that using Kullback-Leibler (KL) divergence as a local distance further improves the performance of the template-based approach, now beating state-of-the-art of more complex posterior-based HMMs systems (usually referred to as "Tandem").

Approximate Bayesian Computation for Forward Modeling in Cosmology

Abstract: Bayesian inference is often used in cosmology and astrophysics to derive constraints on model parameters from observations. This approach relies on the ability to compute the likelihood of the data given a choice of model parameters. In many practical situations, the likelihood function may however be unavailable or intractable due to non-gaussian errors, non-linear measurements processes, or complex data formats such as catalogs and maps. In these cases, the simulation of mock data sets can often be made through forward modeling. We discuss how Approximate Bayesian Computation (ABC) can be used in these cases to derive an approximation to the posterior constraints using simulated data sets. This technique relies on the sampling of the parameter set, a distance metric to quantify the difference between the observation and the simulations and summary statistics to compress the information in the data. We first review the principles of ABC and discuss its implementation using a Population Monte-Carlo (PMC) algorithm and the Mahalanobis distance metric. We test the performance of the implementation using a Gaussian toy model. We then apply the ABC technique to the practical case of the calibration of image simulations for wide field cosmological surveys. We find that the ABC analysis is able to provide reliable parameter constraints for this problem and is therefore a promising technique for other applications in cosmology and astrophysics. Our implementation of the ABC PMC method is made available via a public code release.

The Mahalanobis distance for functional data with applications to classification

Abstract: This paper presents a general notion of Mahalanobis distance for functional data that extends the classical multivariate concept to situations where the observed data are points belonging to curves generated by a stochastic process. More precisely, a new semi-distance for functional observations that generalize the usual Mahalanobis distance for multivariate datasets is introduced. For that, the development uses a regularized square root inverse operator in Hilbert spaces. Some of the main characteristics of the functional Mahalanobis semi-distance are shown. Afterwards, new versions of several well known functional classification procedures are developed using the Mahalanobis distance for functional data as a measure of proximity between functional observations. The performance of several well known functional classification procedures are compared with those methods used in conjunction with the Mahalanobis distance for functional data, with positive results, through a Monte Carlo study and the analysis of two real data examples.