Cluster Inference by using Transitivity Indices in Empirical Graphs

Abstract A random graph model is introduced for similarities observed between the objects sampled from an unknown cluster structure. We investigate this model and show how some common transitivity indices in empirical graphs can be used for making statistical inferences about cluster structures.

[1]  Frank Harary,et al.  A graph theoretic approach to similarity relations , 1964 .

[2]  Frank Harary,et al.  Graph Theory , 2016 .

[3]  L. Hubert.  Some extensions of Johnson's hierarchical clustering algorithms , 1972 .

[4]  R. F. Ling.  A Probability Theory of Cluster Analysis , 1973 .

[5]  L. Hubert.  Monotone invariant clustering procedures , 1973 .

[6]  D. Mcneil.  Estimating an Author's Vocabulary , 1973 .

[7]  L. Hubert.  Some applications of graph theory to clustering , 1974 .

[8]  F. Baker.  Stability of Two Hierarchical Grouping Techniques Case I: Sensitivity to Data Errors , 1974 .

[9]  John A. Hartigan,et al.  Clustering Algorithms , 1975 .

[10]  R. F. Ling,et al.  Probability Tables for Cluster Analysis Based on a Theory of Random Graphs , 1976 .

[11]  P. Holland,et al.  Local Structure in Social Networks , 1976 .

[12]  L. Hubert,et al.  An Empirical Comparison of Baseline Models for Goodness-of-Fit in r-Diameter Hierarchical Clustering , 1977 .

[13]  J. Hartigan.  Distribution Problems in Clustering , 1977 .

[14]  P. Holland,et al.  TRANSITIVITY IN STRUCTURAL MODELS OF SMALL GROUPS , 1977 .

[15]  R. Kempton,et al.  Stochastic Abundance Models , 1980 .

[16]  S. Engen,et al.  Stochastic abundance models. , 1978 .

[17]  Ove Frank,et al.  Estimation of the Number of Connected Components in a Graph by Using a Sampled Subgraph , 1978 .

[18]  Robin Wilson,et al.  Applications of graph theory , 1979 .

[19]  Ove Frank,et al.  Estimating a graph from triad counts , 1979 .

[20]  L. A. Goodman,et al.  Measures of association for cross classifications , 1979 .

[21]  Frank Harary,et al.  Matrix measures for transitivity and balance , 1979 .

[22]  Ove Frank,et al.  Transitivity in stochastic graphs and digraphs , 1980 .

[23]  O. Frank.  A Survey of Statistical Methods for Graph Analysis , 1981 .