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| Ïîèñê ïî óêàçàòåëÿì |
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| Barthelemy J.-P., Guenoche A. — Trees and proximity representations |
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| Ïðåäìåòíûé óêàçàòåëü |
26-relation associated with separation index 147—149
Additive constant problem 123
Additive separation 54
Additive tree distances 33 34 49 53 54 58 60 75 78—80 82 90
Additive trees 14
ADDTREE algorithm 149—151 167
Adjustment problem 98
Affine transformations 41 219
Algorithm comparison 221—226
Algorithm comparison, criteria 222—224
Analysis of 0/1 variable 217—218
Analysis of information 14
Approximation by centroid distances 89—90
Approximation by tree analysis 60—66
Approximation by tree distance 60—66
Approximation by ultrametrics 125
Approximation criterion 45
Approximation of dissimilarity of centroid distances 90
Approximation of distance index by ultrametrics 109—111
Approximation problem 45
Arbitrary distance index 98
Arbitrary separation index 147
Arboreal index 200
Archaeological data 187—188 204
Aristotelian classification 34
Arrays, acquistion of 0/1 185—187
Articulation point 58
Ascending hierarchical classification 121
Ascending hierarchical classification, algorithms 124—125
Ascending hierarchical classification, program for 104—109
Associated 2-relation 148
Asymmetric proximities 229—230
Automatic classification 13
Automatic drawing of valued trees 23
Average linkage method 104 109 120 121 123 221
Average linkage ultrametric 121
Axial drawing 25 28—31 121
Bi-directed trees 82 230
Bi-tree proximity 230
binary variables 183—187
Binary variables, tree analysis of set of 196—205
Bipartition 183
Boolean analysis 217—218
Boolean functions 185
Brothers 6
Buneman construction 78 217
Buneman construction, applications of 192—196
Buneman construction, definition 183
Buneman family 179—181 192—194 196 200 206
Buneman family and X-trees 181—183
Buneman family, definition 180
Buneman family, local characterisation 210—211
Buneman family, recognition of 196—200
Buneman graph, algorithm for 202
Buneman graph, construction of 202—205
Buneman graph, maximal cliques of 201—205
Buneman theory 171—192 216—217
Buneman theory, consequences of 217
Bunemanian 197 200 201 204
Burt array 218
Burt table 188
Centroid component 123
Centroid distances 87—90 119 121 123 126
Centroid distances, approximation by 89—90
Centroid distances, approximation of dissimilarity of 90
Centroid distances, characterisations of 88—89
Centroid distances, definition 88
Centroid distances, properties of 89
Centroid quasi-distance 114—115
Chain effect 103 123
Characteristic function 194
Chasles relation 163
Cladistic distance 79
class 22 42
Class, concept of 34
Classification theory 32
Classification tree 119—121
CLIQUE 3
Clusters 81—82
Coarse partition 94
Coding and decoding 78
Cognitive psychology 80
Combinatorial mathematics 18 31
Common ancestor 126 127
Compatibility concept 194—196
Complemented family, 2-relation associated with 208—209
Complemented family, graph associated with 173—176
Complemented form 218
Complete graph 3 98
Complete linkage algorithm 104 123
Connected components 3
Connected components of threshold graphs 99—101
Connected graph 2 3 9 10
Contrast model 80 81
Cophenetic value 123
Cubical proximities 230—231
CYCLE 2
Data acquisition 46—49
Data analysis 10
Decision problems 128
Decomposition method 120—121 221
Decomposition of  at point r 115
Decomposition of tree distance 126—127
Degrees of freedom 56—60
Dendrograms 23 25 33 34 77 92—95 105 113 116 121 123 125—127 212 221 228
Dendrograms, ultrametric represented by 95—96
Denucleation 54
Diagonal code 57 70 82—83
Diagonal order 58—60
Diameter of a tree 28—29
Direct form 218
Disconnected graph 2
Discrete partition 94
Dissimilarity 41 48 66 70 73
Dissimilarity, approximation by centroid distance 90
Dissimilarity, reduction to tree distance 67—70
Dissimilarity, reduction to ultrametric distance 112
Distance index 41 78 87 89 92 98 99 102 103
Distance index, approximation by ultrametrics 109—111
E-representation 43—45
Edge-lengths 49 62 63 70 71 105 119 120 222
Edge-lengths, calculation of 64—66
Edges 1
End-points 1 2
Equivalence classes 110
Euclidean distance 46 89 96—97 126
Euclidean distance and tree distance 194
Euclidean representations 44 76—77 81—82 123 137
Euclidean separation 194
Euclidean spaces 43
Evolutionary hypothesis 13 14
Experimental data 45—46
Factor analysis method 123
Factorial methods 187
familiarity 34
Father (or predecessor) 6
Filing 47
Flat method 124
Forbidden split 206
Forest decomposition 158 160 161
Form invariance 137
Four-leaf configuation 60
Four-point condition 52—54 60 62 66 78 83 89 91 92 113 114 147 166 211
Four-point configurations 205—211
Fundamental relation 133
Fundamental relation, X-tree 134—139 166—167
Gauss — Seidel method 63
Generalised trees 231
Generator 218
Graph 1—3 31—33
| Graph of localisations 188—192 218
Graph theory 31
Graph theory, introduction to 32
Graph theory, terminology 1—12
Graph, associated with complemented family 173—176
Greedy algorithms 10 32
groupings 140—142 151
Groupings and pregroupings relative to 2-relation 140—141
Groupings in restructuring a tree 143—147
Groupings, concept of 167—168
Groupings, method of 140—142 151—156
Groupings, properties of 141
Hamiltonian cycle of a graph 128
Helly’s property 175
Heuristic methods 66—76 119—121 133 149
hierarchical classification 77 79 93—95 117 127
Hierarchical drawing 24 28 96
Hierarchical representations 123
hierarchical trees 22—23 33—34 93 94
Hierarchy index function 125
Indexed hierarchy 93 94 102
INDTREES method 80
Induction hypothesis 4—5 56 60 138 175
Information processing 78
Input data 128
Integer valued distance index 128
Integral tree distance 128
Interior vertices 4
Intermediary vertices 12
Invariance 124 213
Isometry 41 43
Isomorphism 183
Isotonic function 81
Keyboard input 47
Labelling, concept of 175
Labelling, function of 158
Lagrange multipliers 62
Latent vertices 12 15 174
Leaf 4
Least squares approximation 90 110
Least squares approximation on support tree 111
Least squares method 39 45 60 119 125
Length of edge see “Edge-length”
Length of path 2
Linear transformations 41
Localisations 172—177 180 181
Localisations, enumeration of 188—189
Localisations, graph of 188—192 218
Mathematical programming methods 60—62
Mathematical psychology 14 76 78 82
Maximal cliques of Buneman graph 201—205
Meaningfulness 81 117 218—219
Meaningfulness, theory 41
Measurement theory 41 76
Median of three tree vertices 57—58
Metaphor 44
Method of closest predecessors 70—73 75 221
Method of decomposition 120—121 221
Method of dispersion 73—75 75 221
Method of groupings 151—156 221
Method of reduction 75 221
Metric criteria 222
Metric spaces 42 50
Minimal chain 32
Minimal spanning trees 9—10 32 90 97 98 100—101 124
Minimal spanning trees and ultrametrics 97—99
Minimal spanning trees, construction of 10—12
Model 44 60
Monomial 218
Monotone transformation 41 212—216 218
Monotone transformation, definition 212
Monte-Carlo methods 34
MoveTo 24
Multidimensional Scaling (MDS) 77 80
Neighbour relation 157
Neighbourhood 1 149
Neighbourhood relations 133
nodes 4
Non-metric algorithms 218—219
Non-metric criteria 222—223
Non-spatial distance models 80
Non-symmetric proximity 230
NP-complete problems 33 127
NP-completeness 127—129
NP-difficult problems 127—129
Opening 99
Operational research 10 14 79
Optimal clique covering 198
Optimal diagonal code 58—60
Order relation 6
Ordered reading 22
Oriented trees 79
Partial graph 3 9
Partial minimal spanning trees 11
Partial sub-tree 15
Partial trees 10
Path 2
Path, length of 2
Penalisation function 110
Penalisation method 110 125
Penalty function 62
Phylogenetic trees 13—14 33 78 79 82 126
Phylogenetic trees, topology 166
Planar diagonal order 59 60
Planar drawings 23
Point by point order relation 98
Prelocalisation 173
Premetric space 41 43 60 61
Premetric space, linear representation 43
Present-day-ancestor method 127
Priifer code 19
Proof of convergence 111
Proximity 77
Proximity, measures of 39—41 76—77
Proximity, representation of 39
Prtifer word 20
Pruning 54
Psychometry 79
Pyramids 125
Quadratic approximation on support tree 62—66
Quadruple reduction method (Roux) 66—70
Qualitative invariance 211—216
r,k-decomposition 117—121
r,k-decomposition of 115
Radial drawing 24—27 30 109
Random values 47
RANDOMIZE 20
Real vertices 12 14 15 174
Rectangular array data 227—229
Rectangular tree separations 228
Reduction method 75 221
Regrouping algorithms 142 149
Representation of proximity 39
Representation space 42
Representation, concept of 42
Rooted trees 5 6
Rooted X-trees 22—23
Scaling 80 82
Schroder’s fourth problem 33
Score matrix 150
Scores in restructuring a tree 143—147
Scores theorem 157—160 164—166 168
Scores, calculation of 143 161
Scores, concept of 142—143
Scores, definition 142
Scores, generalised 161
Scores, reinterpretation of concept of 157
Semantic memory 79
Separation 42 50 51
Separation index 41—43 50 52 96 113 128 133 148 149 157 162 165 192 193
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