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Barthelemy J.-P., Guenoche A. — Trees and proximity representations |
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Предметный указатель |
Separation index, 2-relation associated with 147—149
Separation index, specification of 56
Separation, acquisition of an array of 48—49
Similarity 47
Similarity analysis 32
Single linkage method 101 123 124 221
Son (or successor) 6
Spherical completion 91 92
Spherical distances 90 91 117 126
Spherical tree distance 92 127
Splits 173 177 179—181 192
Stability 213
Star 5 90
Steiner trees 14—15
Stirling 2-associated numbers of the second kind 33
Stirling numbers of the second kind 33
Sub-dominant ultrametric 98 99 124
Sub-graph 3 9
Sub-trees 25 29
Super-modularity condition 160
Supplementary hypotheses 81
Support tree 221
Support tree, quadratic approximation on 62—66
Systematic biology 14 33
Taxonomy 79
template 218
Ternary trees 5
TEXTSIZE 24
Threshold calculation 106
Threshold graphs 103 106 124
Threshold graphs, connected components of 99—101
Topological distance 79
Tractable problems 127
Tree analysis, algorithms 200—205
Tree analysis, binary variables 200
Tree decomposition 196—200
Tree distance 39—85 87 118—119 126 128 158
Tree distance and Euclidean distance 194
Tree distance as sum of ultrametric and centroid quasi-distance 114
Tree distance, approximation by 60—66
Tree distance, approximation using (r,k)-decomposition 119—121
Tree distance, coding of 56—60
Tree distance, combinatorial characterisation 193
Tree distance, decomposition 126—127
Tree distance, decomposition into sum of centroid distance and ultrametric 112—116
Tree distance, integral 128
Tree distance, reduction of dissimilarity to 67—70
Tree distance, reinterpretation of 192—193
Tree drawing 23—31
Tree file 7
tree nodes 81
Tree relations 218
Tree representations 50 123 193 229
Tree separations 50—52 78 133 193 195—196 213—216
tree structures 80
Trees 1—37
Trees, coding and representation 6—9
Trees, definition 4
Trees, random selection 34
Trees, reconstructing 143—147
Triple reduction method 111—112
Typicality 34
Ultrametric adjustment 125
Ultrametric approximation on fixed tree 111—112
Ultrametric distance 110 111 121
Ultrametric distance, dissimilarity reduction to 112
| Ultrametric geometry 124
Ultrametric inequality 92 93 103 110
Ultrametric reduction algorithm 121
Ultrametrics 80 87 90—112 123—124 126 218
Ultrametrics and Euclidean distances 96—97
Ultrametrics and minimal spanning trees 97—99
Ultrametrics for mean connection 109
Ultrametrics, algorithms for constructing 101—104
Ultrametrics, approximation by 125
Ultrametrics, approximation of distance index by 109—111
Ultrametrics, associated with valued trees 97
Ultrametrics, characterisation of 91—93
Ultrametrics, definition 91—93
Ultrametrics, dendrogram representation of 95—96
Ultrametrics, sub-dominant 102 103
Uniqueness problem 54—56
Uniqueness theorem 138
Unitary distance 49 78
Universale problem 81
Updating 47
Valued Buneman family 193
Valued family 192
Valued graph 3 9—10 15
Valued tree 49 50 58 77 118—119 156 222 231
Valued tree, automatic drawing of 23
Valued tree, ultrametrics associated with 97
Valued X-tree see “X-trees”
Vertices 1 12
Weak neighbour concept 149
Well-formed triple 58
X-tree models 46
X-trees 33—34 54—56 81—82 116
X-trees and Buneman family 181—183
X-trees, combinatorial description 171—220
X-trees, compatibility 194—196
X-trees, concept of 12—31
X-trees, constrained 79
X-trees, definition 15—16 193
X-trees, enumeration 16—18
X-trees, equivalence of 138—139 213
X-trees, free, separated 17 19 58 78 137—138 162 166 167 211
X-trees, free, separated, ternary 18
X-trees, free, separated, valued 45
X-trees, free, ternary 18
X-trees, fundamental relation 134—139 166—167
X-trees, global description 171—192
X-trees, hierarchical 22 23
X-trees, isomorphism of 16 183
X-trees, labelling 15
X-trees, local study of 205—206
X-trees, non-valued 50
X-trees, number of 18
X-trees, ordering of 194—196
X-trees, random selection 19—21
X-trees, relation of compatibility of 195
X-trees, remarks on 34
X-trees, rooted 22
X-trees, separated 20
X-trees, specification 56
X-trees, ternary 18
X-trees, ternary, separated 18
X-trees, topology of 133—169
X-trees, unique 167
X-trees, unique valued 56
X-trees, valued 23 34 54 78 91 193
“Psycho-maitres” 78 79
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