Local and global mappings of topology representing networks

Agnes Vathy-Fogarassy, J. Abonyi

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

As data analysis tasks often have to deal with complex data structures, the nonlinear dimensionality reduction methods play an important role in exploratory data analysis. In the literature a number of nonlinear dimensionality reduction techniques have been proposed (e.g. Sammon mapping, Locally Linear Embedding). These techniques attempt to preserve either the local or the global geometry of the original data, and they perform metric or non-metric dimensionality reduction. Nevertheless, it is difficult to apply most of them to large data sets. There is a need for new algorithms that are able to combine vector quantisation and mapping methods in order to visualise the data structure in a low-dimensional vector space. In this paper we define a new class of algorithms to quantify and disclose the data structure, that are based on the topology representing networks and apply different mapping methods to the low-dimensional visualisation. Not only existing methods are combined for that purpose but also a novel group of mapping methods (Topology Representing Network Map) are introduced as a part of this class. Topology Representing Network Maps utilise the main benefits of the topology representing networks and of the multidimensional scaling methods to disclose the real structure of the data set under study. To determine the main properties of the topology representing network based mapping methods, a detailed analysis of classical benchmark examples (Wine and Optical Recognition of Handwritten Digits data set) is presented.

Original languageEnglish
Pages (from-to)3791-3803
Number of pages13
JournalInformation Sciences
Volume179
Issue number21
DOIs
Publication statusPublished - Oct 18 2009

Fingerprint

Topology
Data structures
Dimensionality Reduction
Data Structures
Wine
Vector quantization
Vector spaces
Locally Linear Embedding
Exploratory Data Analysis
Vector Quantization
Visualization
Network topology
Reduction Method
Digit
Complex Structure
Large Data Sets
Vector space
Data analysis
Geometry
Quantify

Keywords

  • Data visualisation
  • Dimensionality reduction
  • GNLP-NG
  • Mapping quality
  • OVI-NG
  • Topology representing networks
  • TRNMap

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Theoretical Computer Science
  • Computer Science Applications
  • Information Systems and Management

Cite this

Local and global mappings of topology representing networks. / Vathy-Fogarassy, Agnes; Abonyi, J.

In: Information Sciences, Vol. 179, No. 21, 18.10.2009, p. 3791-3803.

Research output: Contribution to journalArticle

Vathy-Fogarassy, Agnes ; Abonyi, J. / Local and global mappings of topology representing networks. In: Information Sciences. 2009 ; Vol. 179, No. 21. pp. 3791-3803.
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