Clustering by using a simplex structure:
Abstract: "In this paper we interpret clustering as a mapping of data into a simplex. If the data itself has simplex structure this mapping becomes linear. Spectral analysis is an often used tool for clustering data. We will show that corresponding singular vectors or eigenvectors comprise simp...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Konrad-Zuse-Zentrum für Informationszentrum
2004
|
| Schriftenreihe: | ZIB-Report
2004,03 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | Abstract: "In this paper we interpret clustering as a mapping of data into a simplex. If the data itself has simplex structure this mapping becomes linear. Spectral analysis is an often used tool for clustering data. We will show that corresponding singular vectors or eigenvectors comprise simplex structure. Therefore they lead to a cluster algorithm, which consists of a simple linear mapping. An example for this kind of algorithms is the Perron cluster analysis (PCCA). We have applied it in practice to identify metastable sets of molecular dynamical systems. In contrast to other algorithms, this approach provides an a priori criterion to determine the number of clusters. In this paper we extend the ideas to more general problems like clustering of bipartite graphs." |
| Beschreibung: | 22 S. |
Internformat
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| 520 | 3 | |a Abstract: "In this paper we interpret clustering as a mapping of data into a simplex. If the data itself has simplex structure this mapping becomes linear. Spectral analysis is an often used tool for clustering data. We will show that corresponding singular vectors or eigenvectors comprise simplex structure. Therefore they lead to a cluster algorithm, which consists of a simple linear mapping. An example for this kind of algorithms is the Perron cluster analysis (PCCA). We have applied it in practice to identify metastable sets of molecular dynamical systems. In contrast to other algorithms, this approach provides an a priori criterion to determine the number of clusters. In this paper we extend the ideas to more general problems like clustering of bipartite graphs." | |
| 650 | 4 | |a Bipartite graphs | |
| 650 | 4 | |a Cluster analysis | |
| 650 | 4 | |a Simplexes (Mathematics) | |
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Datensatz im Suchindex
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| adam_text |
KONRAD-ZUSE-ZENTRUM FUR INFORMATIONSTECHNIK BERLIN TAKUSTRAGE 7 D-14195
BERLIN-DAHLEM GERMANY MARCUS WEBER" CLUSTERING BY USING A SIMPLEX
STRUCTURE SUB GATTINGEN 215 167 597 *SUPPORTED BY DFG RESEARCH CENTER
"MATHEMATICS FOR KEY TECHNOLOGIES" IN BERLIN ZIB-REPORT 04-03 (FEBRUARY
2004) CONTENTS 1 INTRODUCTION - CLUSTERING AS A MAPPING OF DATA INTO A
SIMPLEX 2 2 SPECIAL MATRICES AND SIMPLEX STRUCTURES 4 2.1 STOCHASTIC
TRANSITION MATRIX 4 2.1.1 EIGENVECTORS OF A REDUCIBLE TRANSITION MATRIX
5 2.1.2 SIMPLEX STRUCTURE OF PERTURBED EIGENVECTORS 6 2.1.3 EIGENVALUES
OF T AND THE NUMBER OF CLUSTERS 10 2.2 ADJACENCY MATRIX OF A BIPARTITE
GRAPH 11 2.2.1 REDUCIBLE ADJACENCY MATRIX 11 2.2.2 ADJACENCY MATRIX WITH
OVERLAPPING BI-CLIQUES 11 2.2.3 SINGULAR VALUES OF A AND THE NUMBER OF
CLUSTERS 14 2.3 LESS INPUT VECTORS LEAD TO A WRONG DATA CLASSIFICATION
16 3 CLUSTER ALGORITHMS 17 3.1 SEARCH ROUTINE FOR THE VERTICES OF A
SIMPLEX 17 3.2 ALMOST INVARIANT SETS AND BICLUSTERING 18 3.2.1 ALMOST
INVARIANT SETS 18 3.2.2 CLUSTERING OF BIPARTITE GRAPHS 18 4 CONCLUSION
20 |
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| author | Weber, Marcus 1972- |
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| building | Verbundindex |
| bvnumber | BV019409481 |
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| ctrlnum | (OCoLC)56571533 (DE-599)BVBBV019409481 |
| discipline | Informatik |
| format | Book |
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| id | DE-604.BV019409481 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-10T17:06:53Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012871495 |
| oclc_num | 56571533 |
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| physical | 22 S. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Konrad-Zuse-Zentrum für Informationszentrum |
| record_format | marc |
| series | ZIB-Report |
| series2 | ZIB-Report |
| spelling | Weber, Marcus 1972- Verfasser (DE-588)132289881 aut Clustering by using a simplex structure Marcus Weber Berlin Konrad-Zuse-Zentrum für Informationszentrum 2004 22 S. txt rdacontent n rdamedia nc rdacarrier ZIB-Report 2004,03 Abstract: "In this paper we interpret clustering as a mapping of data into a simplex. If the data itself has simplex structure this mapping becomes linear. Spectral analysis is an often used tool for clustering data. We will show that corresponding singular vectors or eigenvectors comprise simplex structure. Therefore they lead to a cluster algorithm, which consists of a simple linear mapping. An example for this kind of algorithms is the Perron cluster analysis (PCCA). We have applied it in practice to identify metastable sets of molecular dynamical systems. In contrast to other algorithms, this approach provides an a priori criterion to determine the number of clusters. In this paper we extend the ideas to more general problems like clustering of bipartite graphs." Bipartite graphs Cluster analysis Simplexes (Mathematics) ZIB-Report 2004,03 (DE-604)BV013191727 2004,03 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012871495&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Weber, Marcus 1972- Clustering by using a simplex structure ZIB-Report Bipartite graphs Cluster analysis Simplexes (Mathematics) |
| title | Clustering by using a simplex structure |
| title_auth | Clustering by using a simplex structure |
| title_exact_search | Clustering by using a simplex structure |
| title_full | Clustering by using a simplex structure Marcus Weber |
| title_fullStr | Clustering by using a simplex structure Marcus Weber |
| title_full_unstemmed | Clustering by using a simplex structure Marcus Weber |
| title_short | Clustering by using a simplex structure |
| title_sort | clustering by using a simplex structure |
| topic | Bipartite graphs Cluster analysis Simplexes (Mathematics) |
| topic_facet | Bipartite graphs Cluster analysis Simplexes (Mathematics) |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012871495&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013191727 |
| work_keys_str_mv | AT webermarcus clusteringbyusingasimplexstructure |