A Test to Determine the Multivariate Normality of a Data Set

Authors:
S. P. Smith;A. K. Jain
Affiliations:
Automation Sciences Laboratory, Palos Verdes Penninsula, CA;Michigan State Univ., East Lansing
Venue:
IEEE Transactions on Pattern Analysis and Machine Intelligence
Year:
1988

Citing 2
Cited 7

A Test of the Gaussian-ness of a Data Set Using Clustering

IEEE Transactions on Pattern Analysis and Machine Intelligence
Structure of multidimensional patterns

Structure of multidimensional patterns

Complexity Measures of Supervised Classification Problems

IEEE Transactions on Pattern Analysis and Machine Intelligence
A Novel Approach to Generate Multiple Shape Models for Tracking Applications

AMDO '02 Proceedings of the Second International Workshop on Articulated Motion and Deformable Objects
Unsupervised Parameterisation of Gaussian Mixture Models

CCIA '02 Proceedings of the 5th Catalonian Conference on AI: Topics in Artificial Intelligence
Texture-based objects recognition for vehicle environment perception using a multiband camera

ISVC'07 Proceedings of the 3rd international conference on Advances in visual computing - Volume Part II
An approach to interval programming problems with left-hand-side stochastic coefficients: An application to environmental decisions analysis

Expert Systems with Applications: An International Journal
Predicting noise filtering efficacy with data complexity measures for nearest neighbor classification

Pattern Recognition
Analysis of data complexity measures for classification

Expert Systems with Applications: An International Journal

Quantified Score

Hi-index	0.16

Visualization

Abstract

A test is described for multivariate normality that is useful in pattern recognition. The test is based on the Friedman-Rafsky (1979) multivariate extension of the Wald-Wolfowitz runs test. The test data are combined with a multivariate swarm of points following the normal distribution generated with mean vector and covariance matrix estimated from the test data. The minimal spanning tree of this resultant ensemble of points is computed and the count of the interpopulation edges in the minimal spanning tree is used as a test statistic. The simulation studied both the null case of the test and one simple deviation from normality. Two conclusions are made from this study. First, the test can be conservatively applied by using the asymptotic normality of the test statistic, even for small sample sizes. Second, the power of the test appears reasonable, especially in high dimensions. Monte Carlo experiments were performed to determine if the test is reliable in high dimensions with moderate sample size. The method is compared to other such tests available in the literature.