Classification and dissimilarity analysis:
Gespeichert in:
| Weitere Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1994
|
| Schriftenreihe: | Lecture notes in statistics
93 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 238 S. graph. Darst. |
| ISBN: | 0387944001 |
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| 245 | 1 | 0 | |a Classification and dissimilarity analysis |c Bernard Van Cutsem (editor) |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1994 | |
| 300 | |a XIII, 238 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in statistics |v 93 | |
| 650 | 4 | |a Analyse discriminante | |
| 650 | 7 | |a Analyse discriminante |2 ram | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Statistik | |
| 650 | 4 | |a Classification | |
| 650 | 4 | |a Discriminant analysis | |
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Statistics | |
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Datensatz im Suchindex
| _version_ | 1805067158947889152 |
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| adam_text |
CONTENTS
PREFACE
.
V
LIST
OF
CONTRIBUTORS
.
XIII
CHAPTER
1
INTRODUCTION
.
1
BERNARD
VAN
CUTSEM
1.1
CLASSIFICATION
IN
THE
HISTORY
OF
SCIENCE
.
1
1.2
DISSIMILARITY
ANALYSIS
.
2
1.3
ORGANISATION
OF
THIS
PUBLICATION
.
3
1.4
REFERENCES
.
4
CHAPTER
2
THE
PARTIAL
ORDER
BY
INCLUSION
OF
THE
PRINCIPAL
CLASSES
OF
DISSIMILARITY
ON
A
FINITE
SET,
AND
SOME
OF
THEIR
BASIC
PROPERTIES
.
5
FRANK
CRITCHLEY
AND
BERNARD
FICHET
2.1
INTRODUCTION
.
5
2.1.1
WHAT
IS
DISSIMILARITY
ANALYSIS?
.
5
2.1.2
WHAT
'
S
IN
THIS
CHAPTER?
.
8
2.2
PRELIMINARIES
.
9
2.2.1
THE
VECTOR
SPACE
T
GENERATED
BY
THE
DISSIMILARITIES
.
9
2.2.2
SOME
ELEMENTARY
DISSIMILARITIES
.
11
2.2.3
SOME
GENERAL
TYPES
OF
DISSIMILARITIES
.
12
2.2.4
STABILITY
UNDER
INCREASING
TRANSFORMATIONS
.
13
2.2.5
THE
QUOTIENT
SPACE
OF
AN
EVEN
DISSIMILARITY
.
14
2.2.6
EMBEDDABILITY
IN
A
METRIC
SPACE
.
15
2.2.7
THE
SET
OF
ALL
SEMI-DISTANCES
.
16
2.2.8
STABILITY
UNDER
REPLICATION
.
17
VIII
B.
VAN
CUTSEM,
ED.
2.3
THE
GENERAL
STRUCTURES
OF
DISSIMILARITY
DATA
ANALYSIS
AND
THEIR
GEOMETRICAL
AND
TOPOLOGICAL
NATURE
.
18
2.3.1
EUCLIDEAN
SEMI-DISTANCES
.
18
2.3.2
SEMI-DISTANCES
OF
LI-TYPE
.
21
2.3.3
HYPERMETRIC
SEMI-DISTANCES
.
23
2.3.4
QUASI-HYPERMETRIC
DISSIMILARITIES
.
25
2.3.5
ULTRAMETRIC
SEMI-DISTANCES
.
26
2.3.6
TREE
SEMI-DISTANCES
.
28
2.3.7
STAR
SEMI-DISTANCES
.
33
2.3.8
ROBINSONIAN
DISSIMILARITIES
.
34
2.3.9
STRONGLY-ROBINSONIAN
DISSIMILARITIES
.
38
2.4
INCLUSIONS
.
39
2.4.1
SOME
IMMEDIATE
INCLUSIONS
.
39
2.4.2
OTHER
INCLUSIONS
.
41
2.5
THE
CONVEX
HULLS
.
46
2.6
WHEN
ARE
THE
INCLUSIONS
STRICT?
.
48
2.7
THE
INCLUSIONS
SHOWN
ARE
EXHAUSTIVE
.
52
2.8
DISCUSSION
.
53
2.8.1
FURTHER
MATHEMATICAL
STUDY
.
54
2.8.2
EXTENSIONS
TO
OTHER
TYPES
OF
DATA
.
56
2.8.3
CONNECTIONS
WITH
NEIGHBOURING
DISCIPLINES
.
57
2.8.4
THE
FUTURE
OF
DISSIMILARITY
ANALYSIS
.
57
ACKNOWLEDGEMENTS
.
58
REFERENCES
.
58
CHAPTER
3
SIMILARITY
FUNCTIONS
.
67
SERGE
JOLY
AND
GEORGES
LE
CALVE
3.1
INTRODUCTION
.
67
3.2
DEFINITIONS.
EXAMPLES
.
68
3.2.1
DEFINITIONS
.
68
3.2.2
EXAMPLES
.
69
3.2.2.1
LINEAR
FUNCTION
.
69
3.2.2.2
HOMOGRAPHIC
FUNCTION
.
69
3.2.2.3
QUADRATIC
FUNCTION
.
70
CLASSIFICATION
AND
DISSIMILARITY
ANALYSIS
IX
3.2.2.4
EXPONENTIAL
FUNCTION
.
70
3.2.2.5
CIRCULAR
FUNCTION
.
70
3.2.2.6
GRAPHICAL
REPRESENTATIONS
.
71
3.3
THE
W
M
(D?)
FORMS
.
72
3.3.1
DEFINITIONS
AND
PROPERTIES
.
72
3.3.2
THE
W
M
(D
2
)
FORM
.
74
TORGERSON
FORM
.
75
3.3.3
TYANSFORMATIONS
OF
D
.
77
D
A
AND
THE
EUCLIDEAN
DISTANCES
.
78
3.4
THE
W
M
(D)
FORM
.
79
3.4.1
GEOMETRICAL
INTERPRETATIONS
AND
PROPERTIES
.
79
3.4.2
ABOUT
METRIC
PROJECTION
.
81
3.4.3
W
M
(D)
AND
"
A4
1
-TYPE
"
DISTANCE
.
82
APPENDIX:
SOME
INDICES
OF
DISSIMILARITY
FOR
CATEGORICAL
VARIABLES
.
84
REFERENCES
.
86
CHAPTER
4
AN
ORDER-THEORETIC
UNIFICATION
AND
GENERALISATION
OF
CERTAIN
FUNDAMENTAL
BIJECTIONS
IN
MATHEMATICAL
CLASSIFICATION.
I
.
87
FRANK
CRITCHLEY
AND
BERNARD
VAN
CUTSEM
4.1
INTRODUCTION
AND
OVERVIEW
.
87
4.2
A
FEW
NOTES
ON
ORDERED
SETS
.
89
4.2.1
INTRODUCTION
.
89
4.2.2
DUALITY
AND
ORDER-ISOMORPHISMS
.
90
4.2.3
SEMI-LATTICES
AND
LATTICES
.
91
4.2.4
RESIDUAL
AND
RESIDUATED
MAPPINGS
.
92
4.3
PREDISSIMILARITIES
.
93
4.4
BIJECTIONS
.
95
4.4.0
OVERVIEW
.
95
4.4.1
INDEXED
HIERARCHIES
(S
FINITE,
L
=
R+)
.
95
4.4.2
DENDROGRAMS
(S
FINITE,
L
=
R
+
)
.
97
4.4.3
NUMERICALLY
STRATIFIED
CLUSTERINGS
(S
FINITE,
L
=
R-|_)
.
98
4.4.4
INDEXED
REGULAR
GENERALISED
HIERARCHIES
(S
ARBITRARY,
L
=
R+)
.
.
98
4.4.5
GENERALISED
DENDROGRAMS
(S
ARBITRARY,
L
=
R+)
.
99
4.4.6
PREFILTERS
(S
ARBITRARY,
L
=
R+)
.
100
X
B.
VAN
CUTSEM,
ED.
4.4.6
RESIDUAL
MAPS
(S
FINITE,
L
OBEYS
LMIN
AND
JSL)
.
101
4.5
THE
UNIFYING
AND
GENERALISING
RESULT
.
102
4.6
FURTHER
PROPERTIES
OF
AN
ORDERED
SET
.
104
4.7
STRATIFICATIONS
AND
GENERALISED
STRATIFICATIONS
.
105
4.8
RESIDUAL
MAPS
.
108
4.9
ON
THE
ASSOCIATED
RESIDUATED
MAPS
.
110
4.10
SOME
APPLICATIONS
TO
MATHEMATICAL
CLASSIFICATION
.
ILL
ACKNOWLEDGEMENTS
.
113
APPENDIX
A
:
PROOFS
.
114
REFERENCES
.
118
CHAPTER
5
AN
ORDER-THEORETIC
UNIFICATION
AND
GENERALISATION
OF
CERTAIN
FUNDAMENTAL
BIJECTIONS
IN
MATHEMATICAL
CLASSIFICATION.
II
.
121
FRANK
CRITCHLEY
AND
BERNARD
VAN
CUTSEM
5.1
INTRODUCTION
AND
OVERVIEW
.
121
5.2
THE
CASE
E
=
A
X
B
OF
THEOREM
4.5.1
.
122
5.3
OTHER
ASPECTS
OF
THE
CASE
E
=
AXB
.
124
5.3.1
DUALITY
.
124
5.3.2
MULTIWAY
DATA
.
126
5.3.3
RESIDUAL
MAPS
.
126
5.4
PREFILTERS
.
127
5.5
ULTRAMETRICS
AND
REFLEXIVE
LEVEL
FOLIATIONS
.
127
5.5.1
THE
MAIN
RESULT
.
127
5.5.2
REMARKS
ON
THEOREM
5.5.1
.
128
5.5.3
VARIANTS
OF
THEOREM
5.5.1
.
130
5.6
ON
GENERALISATIONS
OF
INDEXED
HIERARCHIES
.
131
5.6.1
INTRODUCTION
.
131
5.6.2
BENZECRI
STRUCTURES
.
131
5.6.3
SPECIAL
CASES
OF
BENZECRI
STRUCTURES
.
134
5.6.4
THE
CONDITION
LSU
.
135
5.7
BENZECRI
STRUCTURES
.
136
5.8
SUBDOMINANTS
.
138
ACKNOWLEDGEMENTS
.
139
APPENDIX
B:
PROOFS
.
140
CLASSIFICATION
AND
DISSIMILARITY
ANALYSIS
XI
REFERENCES
.
147
CHAPTER
6
THE
RESIDUATION
MODEL
FOR
THE
ORDINAL
CONSTRUCTION
OF
DISSIMILARITIES
AND
OTHER
VALUED
OBJECTS
.
149
BRUNO
LECLERC
6.1
INTRODUCTION
.
149
6.2
RESIDUATED
MAPPINGS
AND
CLOSURE
OPERATORS
.
151
6.2.1
RESIDUATED
AND
RESIDUAL
MAPPINGS
.
151
6.2.2
CLOSURE
AND
ANTICLOSURE
OPERATORS
.
153
6.3
LATTICES
OF
OBJECTS
AND
LATTICES
OF
VALUES
.
154
6.3.1
LATTICES
.
154
6.3.2
DISTRIBUTIVITY
.
154
6.3.3
LATTICES
OF
OBJECTS:
TEN
EXAMPLES
.
155
6.3.4
LATTICES
OF
VALUES
.
158
6.4
VALUED
OBJECTS
.
159
6.4.1
CONSEQUENCES
OF
THE
LATTICE
STRUCTURES
HYPOTHESIS
.
159
6.4.2
VALUED
OBJECTS:
DEFINITIONS
AND
EXAMPLES
.
160
6.5
LATTICES
OF
VALUED
OBJECTS
.
164
6.6
NOTES
AND
CONCLUSIONS
.
167
ACKNOWLEDGEMENTS
.
169
REFERENCES
.
169
CHAPTER
7
ON
EXCHANGEABILITY-BASED
EQUIVALENCE
RELATIONS
INDUCED
BY
STRONGLY
ROBINSON
AND,
IN
PARTICULAR,
BY
QUADRIPOLAR
ROBINSON
DISSIMILARITY
MATRICES
.
173
FRANK
CRITCHLEY
7.1
OVERVIEW
.
173
7.1.1
PREAMBLE
.
173
7.1.2
QUADRIPOLAR,
ROBINSON
AND
STRONGLY
ROBINSON
MATRICES
.
174
7.1.3
PLAN
AND
PRINCIPAL
RESULTS
.
176
7.2
PRELIMINARIES
.
177
7.3
QUADRIPOLAR
ROBINSON
MATRICES
OF
ORDER
FOUR
.
179
7.4
EQUIVALENCE
RELATIONS
INDUCED
BY
STRONGLY
ROBINSON
MATRICES
.
181
7.4.1
EXCHANGEABILITY
AND
CONNECTEDNESS
.
181
XII
B.
VAN
CUTSEM,
ED.
7.4.2
INTERNAL
EVENNESS
.
184
7.4.3
LOGICAL
RELATIONSHIPS
.
185
7.5
REDUCED
FORMS
.
187
7.5.1
EXTERNAL
EVENNESS
.
187
7.5.2
PROPERTIES
OF
REDUCED
FORMS
.
189
7.6
LIMITING
R-FORMS
OF
STRONGLY
ROBINSON
MATRICES
.
191
7.7
LIMITING
R-FORMS
OF
QUADRIPOLAR
ROBINSON
MATRICES
.
193
REFERENCES
.
197
CHAPTER
8
DIMENSIONALITY
PROBLEMS
IN
LI-NORM
REPRESENTATIONS
.
201
BERNARD
FICHET
8.1
INTRODUCTION
.
201
8.2
PRELIMINARIES
AND
NOTATIONS
.
202
8.2.1
DISSIMILARITIES
.
202
8.2.2
SOME
NOTATIONS
.
202
8.2.3
SOME
CHARACTERIZATIONS
.
203
8.3
DIMENSIONALITY
FOR
SEMI-DISTANCES
OF
LP-TYPE
.
204
8.4
DIMENSIONALITY
FOR
SEMI-DISTANCES
OF
LJ-TYPE
.
207
8.5
NUMERICAL
CHARACTERIZATIONS
OF
SEMI-DISTANCES
OF
LI-TYPE
.
209
8.5.1
SOLVING
THE
GENERAL
PROBLEM
.
210
8.5.2
REDUCING
THE
PROBLEM
.
211
8.5.3
APPROXIMATIONS
.
212
8.5.3.1
LEAST
ABSOLUTE
DEVIATIONS
APPROXIMATIONS
.
212
8.5.3.2
LEAST
SQUARES
APPROXIMATION
.
213
8.5.3.3
THE
ADDITIVE
CONSTANTS
.
213
8.6
APPENDICES
.
215
8.6.1
APPENDIX
1
.
215
8.6.2
APPENDIX
2
.
216
8.6.3
APPENDIX
3
.
216
8.6.4
APPENDIX
4
.
218
REFERENCES
.
222
UNIFIED
REFERENCE
LIST
.
225 |
| any_adam_object | 1 |
| author2 | VanCutsem, Bernard 1932- |
| author2_role | edt |
| author2_variant | b v bv |
| author_GND | (DE-588)172035651 |
| author_facet | VanCutsem, Bernard 1932- |
| building | Verbundindex |
| bvnumber | BV009961689 |
| callnumber-first | Q - Science |
| callnumber-label | QA278 |
| callnumber-raw | QA278.65 |
| callnumber-search | QA278.65 |
| callnumber-sort | QA 3278.65 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 230 SI 856 |
| ctrlnum | (OCoLC)31172170 (DE-599)BVBBV009961689 |
| dewey-full | 001/.01/2 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 001 - Knowledge |
| dewey-raw | 001/.01/2 |
| dewey-search | 001/.01/2 |
| dewey-sort | 11 11 12 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Allgemeines Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV009961689 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T03:29:46Z |
| institution | BVB |
| isbn | 0387944001 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006601799 |
| oclc_num | 31172170 |
| open_access_boolean | |
| owner | DE-739 DE-384 DE-19 DE-BY-UBM DE-12 DE-824 DE-473 DE-BY-UBG DE-20 DE-83 DE-188 DE-706 |
| owner_facet | DE-739 DE-384 DE-19 DE-BY-UBM DE-12 DE-824 DE-473 DE-BY-UBG DE-20 DE-83 DE-188 DE-706 |
| physical | XIII, 238 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in statistics |
| series2 | Lecture notes in statistics |
| spelling | Classification and dissimilarity analysis Bernard Van Cutsem (editor) New York [u.a.] Springer 1994 XIII, 238 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in statistics 93 Analyse discriminante Analyse discriminante ram Mathematik Statistik Classification Discriminant analysis Mathematics Statistics Abstand (DE-588)4228463-6 gnd rswk-swf Automatische Klassifikation (DE-588)4120957-6 gnd rswk-swf Ähnlichkeitstheorie (DE-588)4000567-7 gnd rswk-swf Automatische Klassifikation (DE-588)4120957-6 s DE-604 Abstand (DE-588)4228463-6 s Ähnlichkeitstheorie (DE-588)4000567-7 s VanCutsem, Bernard 1932- (DE-588)172035651 edt Lecture notes in statistics 93 (DE-604)BV002447846 93 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006601799&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Classification and dissimilarity analysis Lecture notes in statistics Analyse discriminante Analyse discriminante ram Mathematik Statistik Classification Discriminant analysis Mathematics Statistics Abstand (DE-588)4228463-6 gnd Automatische Klassifikation (DE-588)4120957-6 gnd Ähnlichkeitstheorie (DE-588)4000567-7 gnd |
| subject_GND | (DE-588)4228463-6 (DE-588)4120957-6 (DE-588)4000567-7 |
| title | Classification and dissimilarity analysis |
| title_auth | Classification and dissimilarity analysis |
| title_exact_search | Classification and dissimilarity analysis |
| title_full | Classification and dissimilarity analysis Bernard Van Cutsem (editor) |
| title_fullStr | Classification and dissimilarity analysis Bernard Van Cutsem (editor) |
| title_full_unstemmed | Classification and dissimilarity analysis Bernard Van Cutsem (editor) |
| title_short | Classification and dissimilarity analysis |
| title_sort | classification and dissimilarity analysis |
| topic | Analyse discriminante Analyse discriminante ram Mathematik Statistik Classification Discriminant analysis Mathematics Statistics Abstand (DE-588)4228463-6 gnd Automatische Klassifikation (DE-588)4120957-6 gnd Ähnlichkeitstheorie (DE-588)4000567-7 gnd |
| topic_facet | Analyse discriminante Mathematik Statistik Classification Discriminant analysis Mathematics Statistics Abstand Automatische Klassifikation Ähnlichkeitstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006601799&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002447846 |
| work_keys_str_mv | AT vancutsembernard classificationanddissimilarityanalysis |