# Topographic Mapping of Large Dissimilarity Data Sets

Hammer B, Hasenfuss A (2010) *Neural Computation* 22(9): 2229-2284.

Download

**No fulltext has been uploaded. References only!**

*Journal Article*|

*Original Article*|

*Published*|

*English*

No fulltext has been uploaded

Author

Hammer, Barbara

^{UniBi}; Hasenfuss, AlexanderDepartment

Abstract

Topographic maps such as the self-organizing map (SOM) or neural gas (NG) constitute powerful data mining techniques that allow simultaneously clustering data and inferring their topological structure, such that additional features, for example, browsing, become available. Both methods have been introduced for vectorial data sets; they require a classical feature encoding of information. Often data are available in the form of pairwise distances only, such as arise from a kernel matrix, a graph, or some general dissimilarity measure. In such cases, NG and SOM cannot be applied directly. In this article, we introduce relational topographic maps as an extension of relational clustering algorithms, which offer prototype-based representations of dissimilarity data, to incorporate neighborhood structure. These methods are equivalent to the standard (vectorial) techniques if a Euclidean embedding exists, while preventing the need to explicitly compute such an embedding. Extending these techniques for the general case of non-Euclidean dissimilarities makes possible an interpretation of relational clustering as clustering in pseudo-Euclidean space. We compare the methods to well-known clustering methods for proximity data based on deterministic annealing and discuss how far convergence can be guaranteed in the general case. Relational clustering is quadratic in the number of data points, which makes the algorithms infeasible for huge data sets. We propose an approximate patch version of relational clustering that runs in linear time. The effectiveness of the methods is demonstrated in a number of examples.

Publishing Year

ISSN

eISSN

PUB-ID

### Cite this

Hammer B, Hasenfuss A. Topographic Mapping of Large Dissimilarity Data Sets.

*Neural Computation*. 2010;22(9):2229-2284.Hammer, B., & Hasenfuss, A. (2010). Topographic Mapping of Large Dissimilarity Data Sets.

*Neural Computation*,*22*(9), 2229-2284. doi:10.1162/NECO_a_00012Hammer, B., and Hasenfuss, A. (2010). Topographic Mapping of Large Dissimilarity Data Sets.

*Neural Computation*22, 2229-2284.Hammer, B., & Hasenfuss, A., 2010. Topographic Mapping of Large Dissimilarity Data Sets.

*Neural Computation*, 22(9), p 2229-2284. B. Hammer and A. Hasenfuss, “Topographic Mapping of Large Dissimilarity Data Sets”,

*Neural Computation*, vol. 22, 2010, pp. 2229-2284. Hammer, B., Hasenfuss, A.: Topographic Mapping of Large Dissimilarity Data Sets. Neural Computation. 22, 2229-2284 (2010).

Hammer, Barbara, and Hasenfuss, Alexander. “Topographic Mapping of Large Dissimilarity Data Sets”.

*Neural Computation*22.9 (2010): 2229-2284.
This data publication is cited in the following publications:

This publication cites the following data publications:

### 2 Citations in Europe PMC

Data provided by Europe PubMed Central.

Indefinite Proximity Learning: A Review.

Schleif FM, Tino P.,

PMID: 26313601

Schleif FM, Tino P.,

*Neural Comput*27(10), 2015PMID: 26313601

Self-Organizing Hidden Markov Model Map (SOHMMM).

Ferles C, Stafylopatis A.,

PMID: 24001407

Ferles C, Stafylopatis A.,

*Neural Netw*48(), 2013PMID: 24001407

### 68 References

Data provided by Europe PubMed Central.

Computationally Related Problems

Sahni,

Sahni,

*SIAM Journal on Computing*3(4), 1974
Clustering by Compression

Cilibrasi,

Cilibrasi,

*IEEE Transactions on Information Theory*51(4), 2005
Discriminative Clustering of Yeast Stress Response

Kaski, 2005

Kaski, 2005

Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis

Kruskal,

Kruskal,

*Psychometrika*29(1), 1964
A Unified Framework for Model-based Clustering

Zhong,

Zhong,

*Journal of Machine Learning Research*4(6), 2003
Edit distance-based kernel functions for structural pattern classification

NEUHAUS,

NEUHAUS,

*Pattern Recognition*39(10), 2006
On the equivalence between kernel self-organising maps and self-organising mixture density networks.

Yin H.,

PMID: 16759835

Yin H.,

*Neural Netw*19(6-7), 2006PMID: 16759835

Batch and median neural gas.

Cottrell M, Hammer B, Hasenfuss A, Villmann T.,

PMID: 16782307

Cottrell M, Hammer B, Hasenfuss A, Villmann T.,

*Neural Netw*19(6-7), 2006PMID: 16782307

On the information and representation of non-Euclidean pairwise data

LAUB,

LAUB,

*Pattern Recognition*39(10), 2006
Fuzzy classification by fuzzy labeled neural gas.

Villmann T, Hammer B, Schleif F, Geweniger T, Herrmann W.,

PMID: 16815673

Villmann T, Hammer B, Schleif F, Geweniger T, Herrmann W.,

*Neural Netw*19(6-7), 2006PMID: 16815673

Supervised Batch Neural Gas

Hammer, 2006

Hammer, 2006

Clustering by passing messages between data points.

Frey BJ, Dueck D.,

PMID: 17218491

Frey BJ, Dueck D.,

*Science*315(5814), 2007PMID: 17218491

Quantifying the local reliability of a sequence alignment.

Mevissen HT, Vingron M.,

PMID: 9005433

Mevissen HT, Vingron M.,

*Protein Eng.*9(2), 1996PMID: 9005433

Scalability for clustering algorithms revisited

Farnstrom,

Farnstrom,

*ACM SIGKDD Explorations Newsletter*2(1), 2000
A tutorial on spectral clustering

Luxburg,

Luxburg,

*Statistics and Computing*17(4), 2007
The Self-Organizing Maps: Background, Theories, Extensions and Applications

Yin, 2008

Yin, 2008

Patch clustering for massive data sets

Alex,

Alex,

*Neurocomputing*72(7-9), 2009Pekalska, 2005

### Export

0 Marked Publications### Web of Science

View record in Web of Science®### Sources

PMID: 20569180

PubMed | Europe PMC