Mahalanobis distance

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

A new intrusion detection method based on discriminant analysis

Abstract: SUMMARY Many methods have been proposed to detect intrusions; for example, the pattern matching method on known intrusion patterns and the statistical approach to detecting deviation from normal activities. We investigated a new method for detecting intrusions based on the number of system calls during a user’s network activity on a host machine. This method attempts to separate intrusions from normal activities by using discriminant analysis, a kind of multivariate analysis. We can detect intrusions by analyzing only 11 system calls occurring on a host machine by discriminant analysis with the Mahalanobis’ distance, and can also tell whether an unknown sample is an intrusion. Our approach is a lightweight intrusion detection method, given that it requires only 11 system calls for analysis. Moreover, our approach does not require user profiles or a user activity database in order to detect intrusions. This paper explains our new method for the separation of intrusions and normal behavior by discriminant analysis, and describes the classification method by which

Improved Automatic Skin Detection in Color Images

Abstract: Mahalanobis distance has already proved its strength in hu- man skin detection using a set of skin values. We present this work that uses automatic skin detection after an initial camera calibration. The calibration is done by human sampling from test individuals. A scaling is performed on the work data, before applying the Mahalanobis distance that ensures better results than previous works. We use the TSL color space also used successfully by others authors, where undesired effects are reduced and the skin distribution fits better in a Gaussian model than in others color spaces. Also, using an initial filter, normally large areas of easily distinct non skin pixels, are eliminated from further processing. Analyzing and grouping the resulting elements from the discriminator, improves the ratio of correct detection and reduce the small non skin ar- eas present in a common complex image background, including Asiatic, Caucasian, African and interracial descent persons. Also this method is not restricted to orientation, size or grouping candidates. The present work is a first step in a approach for human face detection in color images, but not limited in any way to this goal.

Analytic Study of Performance of Error Estimators for Linear Discriminant Analysis

Abstract: We derive double asymptotic analytical expressions for the first moments, second moments, and cross-moments with the actual error for the resubstitution and leave-one-out error estimators in the case of linear discriminant analysis in the multivariate Gaussian model under the assumption of a common known covariance matrix and a fixed Mahalanobis distance as dimensionality approaches infinity. Sample sizes for the two classes need not be the same; they are only assumed to reach a fixed, but arbitrary, asymptotic ratio with the dimensionality. From the asymptotic moment representations, we directly obtain double asymptotic expressions for the bias, variance, and RMS of the error estimators. The asymptotic expressions presented here generally provide good small sample approximations, as demonstrated via numerical experiments. The applicability of the theoretical results is illustrated by finding the minimum sample size to bound the RMS in gene-expression classification.

On the distribution of cross-validated Mahalanobis distances

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.

An Evaluation of Mahalanobis-Taguchi System and Neural Network for Multivariate Pattern Recognition

Abstract: The Mahalanobis-Taguchi System is a diagnosis and predictive method for analyzing patterns in multivariate cases. The goal of this study is to compare the ability of the Mahalanobis- Taguchi System and a neural-network to discriminate using small data sets. We examine the discriminant ability as a function of data set size using an application area where reliable data is publicly available. The study uses the Wisconsin Breast Cancer study with nine attributes and one class.