Modern algorithms of cluster analysis:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cham
Springer
[2018]
|
| Schriftenreihe: | Studies in Big Data
volume 34 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030275068&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Literaturverzeichnis Seite 391-416 |
| Umfang: | xx, 421 Seiten Illustrationen, Diagramme |
| ISBN: | 9783319693071 |
| ISSN: | 2197-6503 |
Internformat
MARC
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| 264 | 1 | |a Cham |b Springer |c [2018] | |
| 264 | 4 | |c © 2018 | |
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| 490 | 1 | |a Studies in Big Data |v volume 34 |x 2197-6503 | |
| 500 | |a Literaturverzeichnis Seite 391-416 | ||
| 650 | 4 | |a Engineering | |
| 650 | 4 | |a Big data | |
| 650 | 4 | |a Applied mathematics | |
| 650 | 4 | |a Engineering mathematics | |
| 650 | 4 | |a Computational intelligence | |
| 650 | 4 | |a Engineering | |
| 650 | 4 | |a Computational Intelligence | |
| 650 | 4 | |a Big Data | |
| 650 | 4 | |a Applications of Mathematics | |
| 650 | 4 | |a Big Data/Analytics | |
| 700 | 1 | |a Kłopotek, Mieczysław |d 1960- |e Verfasser |0 (DE-588)121988570 |4 aut | |
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Datensatz im Suchindex
| _version_ | 1819362764402982912 |
|---|---|
| adam_text | Contents
1 Introduction............................................................ 1
2 Cluster Analysis........................................................ 9
2.1 Formalising the Problem........................................... 13
2.2 Measures of Similarity/Dissimilarity............................. 16
2.2.1 Comparing the Objects Having Quantitative
Features.................................................. 18
2.2.2 Comparing the Objects Having Qualitative Features .... 26
2.3 Hierarchical Methods of Cluster Analysis.......................... 29
2.4 Partitional Clustering............................................ 34
2.4.1 Criteria of Grouping Based on Dissimilarity............... 35
2.4.2 The Task of Cluster Analysis in Euclidean Space......... 36
2.4.3 Grouping According to Cluster Volume...................... 45
2.4.4 Generalisations of the Task of Grouping................... 46
2.4.5 Relationship Between Partitional and Hierarchical
Clustering ............................................... 47
2.5 Other Methods of Cluster Analysis................................. 48
2.5.1 Relational Methods........................................ 48
2.5.2 Graph and Spectral Methods................................ 49
2.5.3 Relationship Between Clustering for Embedded
and Relational Data Representations....................... 50
2.5.4 Density-Based Methods..................................... 51
2.5.5 Grid-Based Clustering Algorithms.......................... 55
2.5.6 Model-Based Clustering.................................... 56
2.5.7 Potential (Kernel) Function Methods....................... 56
2.5.8 Cluster Ensembles......................................... 59
2.6 Whether and When Grouping Is Difficult?........................... 64
v
vi Contents
3 Algorithms of Combinatorial Cluster Analysis........................ 67
3.1 ¿-means Algorithm................................................ 68
3.1.1 The Batch Variant of the ¿-means Algorithm............... 72
3.1.2 The Incremental Variant of the ¿-means Algorithm .... 72
3.1.3 Initialisation Methods for the ¿-means Algorithm...... 73
3.1.4 Enhancing the Efficiency of the ¿-means Algorithm .... 79
3.1.5 Variants of the ¿-means Algorithm........................ 81
3.2 EM Algorithm..................................................... 96
3.3 FCM: Fuzzy c-means Algorithm.................................... 100
3.3.1 Basic Formulation....................................... 100
3.3.2 Basic FCM Algorithm..................................... 103
3.3.3 Measures of Quality of Fuzzy Partition.................. 106
3.3.4 An Alternative Formulation.............................. 110
3.3.5 Modifications of the FCM Algorithm...................... Ill
3.4 Affinity Propagation............................................ 128
3.5 Higher Dimensional Cluster “Centres” for ¿-means................ 130
3.6 Clustering in Subspaces via ¿-means............................. 132
3.7 Clustering of Subsets—¿-Bregman Bubble Clustering............... 135
3.8 Projective Clustering with ¿-means.............................. 136
3.9 Random Projection............................................... 137
3.10 Subsampling..................................................... 140
3.11 Clustering Evolving Over Time................................... 142
3.11.1 Evolutionary Clustering................................ 142
3.11.2 Streaming Clustering.................................... 143
3.11.3 Incremental Clustering.................................. 145
3.12 Co-clustering................................................... 145
3.13 Tensor Clustering............................................... 147
3.14 Manifold Clustering............................................. 149
3.15 Semisupervised Clustering....................................... 151
3.15.1 Similarity-Adapting Methods............................. 152
3.15.2 Search-Adapting Methods................................. 153
3.15.3 Target Variable Driven Methods.......................... 155
3.15.4 Weakened Classification Methods......................... 156
3.15.5 Information Spreading Algorithms........................ 157
3.15.6 Further Considerations.................................. 159
3.15.7 Evolutionary Clustering................................. 161
4 Cluster Quality Versus Choice of Parameters......................... 163
4.1 Preparing the Data.............................................. 163
4.2 Setting the Number of Clusters.................................. 165
4.2.1 Simple Heuristics....................................... 167
4.2.2 Methods Consisting in the Use of Information
Criteria............................................... 168
Contents
vii
4.2.3 Clustergrams............................................ 168
4.2.4 Minimal Spanning Trees.................................. 169
4.3 Partition Quality Indexes....................................... 170
4.4 Comparing Partitions............................................ 173
4.4.1 Simple Methods of Comparing Partitions................ 175
4.4.2 Methods Measuring Common Parts of Partitions.......... 176
4.4.3 Methods Using Mutual Information........................ 177
4.5 Cover Quality Measures.......................................... 179
5 Spectral Clustering................................................. 181
5.1 Introduction.................................................... 181
5.2 Basic Notions................................................... 184
5.2.1 Similarity Graphs....................................... 185
5.2.2 Graph Laplacian......................................... 187
5.2.3 Eigenvalues and Eigenvectors of Graph Laplacian....... 195
5.2.4 Variational Characterization of Eigenvalues............. 198
5.2.5 Random Walk on Graphs................................... 203
5.3 Spectral Partitioning........................................... 209
5.3.1 Graph Bi-Partitioning................................... 210
5.3.2 k-way Partitioning...................................... 214
5.3.3 Isoperimetric Inequalities.............................. 224
5.3.4 Clustering Using Random Walk............................ 225
5.3.5 Total Variation Methods................................. 229
5.3.6 Out of Sample Spectral Clustering ...................... 233
5.3.7 Incremental Spectral Clustering......................... 238
5.3.8 Nodal Sets and Nodal Domains............................ 239
5.4 Local Methods................................................... 241
5.4.1 The Nibble Algorithm.................................... 242
5.4.2 The PageRank-Nibble Algorithm........................... 244
5.5 Large Datasets.................................................. 247
5.5.1 Using a Sampling Technique.............................. 248
5.5.2 Landmark-Based Spectral Clustering...................... 250
5.5.3 Randomized SVD.......................................... 253
5.5.4 Incomplete Cholesky Decomposition....................... 254
5.5.5 Compressive Spectral Clustering......................... 256
6 Community Discovery and Identification in Empirical Graphs.......... 261
6.1 The Concept of the Community.................................... 263
6.1.1 Local Definitions....................................... 264
6.1.2 Global Definitions...................................... 265
6.1.3 Node Similarity Based Definitions....................... 265
6.1.4 Probabilistic Labelling Based Definitions............... 265
6.2 Structure-based Similarity in Complex Networks.................. 266
6.2.1 Local Measures.......................................... 266
viii Contents
6.2.2 Global Measures...................................... 268
6.2.3 Quasi-Local Indices.................................. 270
6.3 Modularity—A Quality Measure of Division into
Communities.................................................. 270
6.3.1 Generalisations of the Concept of Modularity......... 274
6.3.2 Organised Modularity................................. 275
6.3.3 Scaled Modularity.................................... 276
6.3.4 Community Score...................................... 276
6.4 Community Discovery in Undirected Graphs..................... 277
6.4.1 Clique Based Communities............................. 277
6.4.2 Optimisation of Modularity........................... 277
6.4.3 Greedy Algorithms Computing Modularity............... 278
6.4.4 Hierarchical Clustering.............................. 280
6.4.5 Spectral Methods..................................... 282
6.4.6 Bayesian Methods..................................... 295
6.5 Discovering Communities in Oriented Graphs................... 296
6.5.1 Newman Spectral Method............................... 297
6.5.2 Zhou/Huang/ Schôlkopf Method......................... 297
6.5.3 Other Random Walk Approaches......................... 298
6.6 Communities in Large Empirical Graphs........................ 299
6.7 Heuristics and Metaheuristics Applied for Optimization
of Modularity................................................ 300
6.8 Overlapping Communities...................................... 304
6.8.1 Detecting Overlapping Communities via Edge
Clustering........................................... 306
6.9 Quality of Communities Detection Algorithms.................. 307
6.10 Communities in Multi-Layered Graphs.......................... 311
6.11 Software and Data............................................ 313
7 Data Sets........................................................... 315
Appendix A: Justification of the FCM Algorithm......................... 319
Appendix B: Matrix Calculus............................................ 321
Appendix C: Personalized PageRank Vector............................... 339
Appendix D: Axiomatic Systems for Clustering........................... 347
Appendix E: Justification for the fc-means++ Algorithm................. 381
References............................................................ 391
Index.................................................................. 417
|
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| author | Wierzchoń, Sławomir T. 1949- Kłopotek, Mieczysław 1960- |
| author_GND | (DE-588)121988554 (DE-588)121988570 |
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| author_role | aut aut |
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| dewey-full | 006.3 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 006 - Special computer methods |
| dewey-raw | 006.3 |
| dewey-search | 006.3 |
| dewey-sort | 16.3 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV044880844 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T18:13:09Z |
| institution | BVB |
| isbn | 9783319693071 |
| issn | 2197-6503 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030275068 |
| oclc_num | 1031434828 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-29T DE-739 |
| owner_facet | DE-355 DE-BY-UBR DE-29T DE-739 |
| physical | xx, 421 Seiten Illustrationen, Diagramme |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | Springer |
| record_format | marc |
| series | Studies in Big Data |
| series2 | Studies in Big Data |
| spellingShingle | Wierzchoń, Sławomir T. 1949- Kłopotek, Mieczysław 1960- Modern algorithms of cluster analysis Studies in Big Data Engineering Big data Applied mathematics Engineering mathematics Computational intelligence Computational Intelligence Big Data Applications of Mathematics Big Data/Analytics |
| title | Modern algorithms of cluster analysis |
| title_auth | Modern algorithms of cluster analysis |
| title_exact_search | Modern algorithms of cluster analysis |
| title_full | Modern algorithms of cluster analysis Sławomir T. Wierzchoń, Mieczysław A. Kłopotek |
| title_fullStr | Modern algorithms of cluster analysis Sławomir T. Wierzchoń, Mieczysław A. Kłopotek |
| title_full_unstemmed | Modern algorithms of cluster analysis Sławomir T. Wierzchoń, Mieczysław A. Kłopotek |
| title_short | Modern algorithms of cluster analysis |
| title_sort | modern algorithms of cluster analysis |
| topic | Engineering Big data Applied mathematics Engineering mathematics Computational intelligence Computational Intelligence Big Data Applications of Mathematics Big Data/Analytics |
| topic_facet | Engineering Big data Applied mathematics Engineering mathematics Computational intelligence Computational Intelligence Big Data Applications of Mathematics Big Data/Analytics |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030275068&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV041647338 |
| work_keys_str_mv | AT wierzchonsławomirt modernalgorithmsofclusteranalysis AT kłopotekmieczysław modernalgorithmsofclusteranalysis |