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Barthelemy J.-P., Guenoche A. — Trees and proximity representations
Barthelemy J.-P., Guenoche A. — Trees and proximity representations



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Название: Trees and proximity representations

Авторы: Barthelemy J.-P., Guenoche A.

Аннотация:

Barthelemy and Guenoche's book is concerned precisely with the study of classification models, using discrete mathematics and combinatorics to represent, interpret and reveal the structure of the relations existing deep within families of objects; it therefore seems to lie at the heart of the problem area which has just been mentioned. We do not hesitate to insist on this point: for all those who are concerned with current developments in the domain of artificial intelligence and who wish to approach this domain scientifically, this book is connected directly or indirectly with their interests, even though they will not find here any explicit reference to Artificial Intelligence. Perhaps the authors have thereby deprived themselves of an easy publicity bandwagon.


Язык: en

Рубрика: Computer science/Дискретная математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 238

Добавлена в каталог: 10.11.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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