The MAP test for multimodality

@article{Rozl1994TheMT,
  title={The MAP test for multimodality},
  author={G. P. Roz{\'a}l and J. Hartigan},
  journal={Journal of Classification},
  year={1994},
  volume={11},
  pages={5-36}
}
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… Expand
Recombining partitions via unimodality tests
In this article we propose a recombination procedure for previously split data. It is basedon the study of modes in the density of the data, since departing from unimodality canbe a sign of theExpand
The UU-test for Statistical Modeling of Unimodal Data
TLDR
A technique called UU-test (Unimodal Uniform test), which attempts to build a piecewise linear approximation of the ecdf that is unimodal and models the data sufficiently in the sense that the data corresponding to each linear segment follows the uniform distribution. Expand
Local Sparse Bump Hunting
  • J. Dazard, J. S. Rao
  • Computer Science, Medicine
  • Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
  • 2010
TLDR
This work introduces a novel supervised and multivariate bump hunting strategy for exploring modes or classes of a target function of many continuous variables, which outperforms a naive PRIM as well as competitive nonparametric supervised and unsupervised methods in the problem of class discovery. Expand
Nonparametric testing of the existence of modes
Given a set of data drawn from an unknown density, it is frequently desirable to estimate the number and location of modes of the density. A test is proposed for the weight of evidence of individualExpand
Are your data gathered? The Folding Test of Unimodality
TLDR
The folding test of unimodality is proposed as a simple statistical description that allows to detect whether data are gathered or not (unimodal or multimodal), and is believed to be the first multivariate and purely statistical unimodal test. Expand
Estimating the Cluster Tree of a Density by Analyzing the Minimal Spanning Tree of a Sample
  • W. Stuetzle
  • Mathematics, Computer Science
  • J. Classif.
  • 2003
TLDR
In this work,unt pruning, a new clustering method that attempts to find modes of a density by analyzing the minimal spanning tree of a sample by exploiting the connection between the minimal spans tree and nearest neighbor density is introduced. Expand
Probabilistic models in cluster analysis
Abstract This paper discusses cluster analysis in a probabilistic and inferential framework as opposed to more exploratory, heuristic or algorithmic approaches. It presents a broad survey onExpand
Computational Aspects of Trimmed Single-Link Clustering
The main drawback of the single-link method is the chaining effect. A few observations between clusters can create a chain, i.e. a path of short edges joining the real clusters and thus making theirExpand
A New Robust Multivariate Mode Estimator for Eye-tracking Calibration
TLDR
A new algorithm to identify the first mode of multivariate distributions, named BRIL, which rely on recursive depth-based filtering and compared to existing methods (conventional depth medians, robust estimators of location and scatter, and clustering-based approaches). Expand
Analysis of large-scale scalar data using hixels
TLDR
A new data representation for scalar data, called hixels, that stores a histogram of values for each sample point of a domain is introduced that proposes new feature detection algorithms using a combination of topological and statistical methods. Expand
...
1
2
...

References

SHOWING 1-9 OF 9 REFERENCES
The runt test for multimodality
Single linkage clusters on a set of points are the maximal connected sets in a graph constructed by connecting all points closer than a given threshold distance. The complete set of single linkageExpand
Graph-Theoretical Methods for Detecting and Describing Gestalt Clusters
  • C. T. Zahn
  • Mathematics, Computer Science
  • IEEE Transactions on Computers
  • 1971
A family of graph-theoretical algorithms based on the minimal spanning tree are capable of detecting several kinds of cluster structure in arbitrary point sets; description of the detected clustersExpand
The Dip Test of Unimodality
On determine la distribution de la statistique de test, asymptotiquement et empiriquement, pour un echantillonnage a partir de la distribution uniforme
Shortest connection networks and some generalizations
The basic problem considered is that of interconnecting a given set of terminals with a shortest possible network of direct links. Simple and practical procedures are given for solving this problemExpand
SUBPOPULATIONS OF BLOOD LYMPHOCYTES DEMONSTRATED BY QUANTITATIVE CYTOCHEMISTRY
TLDR
The results of this analysis demonstrate the existence of at least two distinct populations of blood lymphocytes, indistinguishable by other morphologic criteria. Expand
Density estimation for statistics and data analysis
Introduction. Survey of Existing Methods. The Kernel Method for Univariate Data. The Kernel Method for Multivariate Data. Three Important Methods. Density Estimation in Action.