Abstract
We introduce a test for detecting multimodality in distributions based on minimal constrained spanning trees. We define a Minimal Ascending Path Spanning Tree (MAPST) on a set of points as a spanning tree that has the minimal possible sum of lengths of links with the constraint that starting from any link, the lengths of the links are non-increasing towards a root node. We define similarly MAPSTs with more than one root. We present some algorithms for finding such trees. Based on these trees, we devise a test for multimodality, called the MAP Test (for Minimal Ascending Path). Using simulations, we estimate percentage points of the MAP statistic and assess the power of the test. Finally, we illustrate the use of MAPSTs for determining the number of modes in a distribution of positions of galaxies on photographic plates from a rich galaxy cluster.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
DRESSLER, A. (1980), “A Catalog of Morphological Types in 55 Rich Clusters of Galaxies,”Astrophysical Journal Supplement Series, 42, 565–609.
GIACOMELLI, F., WIENER, J., KRUSKAL, J. B., POMERANZ, J. W., and LOUD, A. V. (1971), “Subpopulations of Blood Lymphocytes as Demonstrated by Quantitative Cytochemistry,”Journal of Histochemistry and Cytochemistry, 19, 426–433.
HARTIGAN, J. A., and HARTIGAN, P. M. (1985), “The Dip Test of Unimodality,”Annals of Statistics, 13, 70–84.
HARTIGAN, J. A. (1988), “The Span Test for Unimodality,” inClassification and Related Methods of Data Analysis, Ed. H. H. Bock, Amsterdam: North-Holland, 229–236.
HARTIGAN, J.A. and MOHANTY, S. (1992), “The RUNT Test for Multimodality,”Journal of Classification, 9, 63–70.
PRIM, R. C. (1957), “Shortest Connection Networks and some Generalizations,”Bell System Technical Journal, 36, 1389–1401.
SILVERMAN, B. W. (1981), “Using Kernel Density Estimates to Investigate Multimodality,”Journal of the Royal Statistical Society, Series B, 43, 97–99.
SILVERMAN, B. W. (1986),Density Estimation for Statistics and Data Analysis, New York: Chapman and Hall.
ZZAHN, C. T. (1971), “Graph-Theoretical Methods for Detecting and Describing Gestalt Clusters,”IEEE Transactions on Computers, C-20, 68–86.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rozál, G.P.M., Hartigan, J.A. The MAP test for multimodality. Journal of Classification 11, 5–36 (1994). https://doi.org/10.1007/BF01201021
Issue Date:
DOI: https://doi.org/10.1007/BF01201021