Barthelemy J.-P., Guenoche A. — Trees and proximity representations :: Электронная библиотека попечительского совета мехмата МГУ

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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:

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

Предметный указатель

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 $\delta$ 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 $\delta$       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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