Mahalanobis distance

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

Comparing Histogram Data Using a Mahalanobis–Wasserstein Distance

Abstract: In this paper, we present a new distance for comparing data described by histograms. The distance is a generalization of the classical Mahalanobis distance for data described by correlated variables. We define a way to extend the classical concept of inertia and codeviance from a set of points to a set of data described by histograms. The same results are also presented for data described by continuous density functions (empiric or estimated). An application to real data is performed to illustrate the effects of the new distance using dynamic clustering.

An adaptive and dynamic dimensionality reduction method for high-dimensional indexing

Abstract: The notorious “dimensionality curse” is a well-known phenomenon for any multi-dimensional indexes attempting to scale up to high dimensions. One well-known approach to overcome degradation in performance with respect to increasing dimensions is to reduce the dimensionality of the original dataset before constructing the index. However, identifying the correlation among the dimensions and effectively reducing them are challenging tasks. In this paper, we present an adaptive Multi-level Mahalanobis-based Dimensionality Reduction (MMDR) technique for high-dimensional indexing. Our MMDR technique has four notable features compared to existing methods. First, it discovers elliptical clusters for more effective dimensionality reduction by using only the low-dimensional subspaces. Second, data points in the different axis systems are indexed using a single B+-tree. Third, our technique is highly scalable in terms of data size and dimension. Finally, it is also dynamic and adaptive to insertions. An extensive performance study was conducted using both real and synthetic datasets, and the results show that our technique not only achieves higher precision, but also enables queries to be processed efficiently.

Exact Confidence Intervals for Channelized Hotelling Observer Performance in Image Quality Studies

Abstract: Task-based assessments of image quality constitute a rigorous, principled approach to the evaluation of imaging system performance. To conduct such assessments, it has been recognized that mathematical model observers are very useful, particularly for purposes of imaging system development and optimization. One type of model observer that has been widely applied in the medical imaging community is the channelized Hotelling observer (CHO), which is well-suited to known-location discrimination tasks. In the present work, we address the need for reliable confidence interval estimators of CHO performance. Specifically, we show that the bias associated with point estimates of CHO performance can be overcome by using confidence intervals proposed by Reiser for the Mahalanobis distance. In addition, we find that these intervals are well-defined with theoretically-exact coverage probabilities, which is a new result not proved by Reiser. The confidence intervals are tested with Monte Carlo simulation and demonstrated with two examples comparing X-ray CT reconstruction strategies. Moreover, commonly-used training/testing approaches are discussed and compared to the exact confidence intervals. MATLAB software implementing the estimators described in this work is publicly available at http://code.google.com/p/iqmodelo/.