Visualization of fuzzy clusters by fuzzy Sammon mapping projection: Application to the analysis of phase space trajectories

Balazs Feil, Balazs Balasko, J. Abonyi

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

Since in practical data mining problems high-dimensional data are clustered, the resulting clusters are high-dimensional geometrical objects, which are difficult to analyze and interpret. Cluster validity measures try to solve this problem by providing a single numerical value. As a low dimensional graphical representation of the clusters could be much more informative than such a single value, this paper proposes a new tool for the visualization of fuzzy clustering results. By using the basic properties of fuzzy clustering algorithms, this new tool maps the cluster centers and the data such that the distances between the clusters and the data-points are preserved. During the iterative mapping process, the algorithm uses the membership values of the data and minimizes an objective function similar to the original clustering algorithm. Comparing to the original Sammon mapping not only reliable cluster shapes are obtained but the numerical complexity of the algorithm is also drastically reduced. The developed tool has been applied for visualization of reconstructed phase space trajectories of chaotic systems. The case study demonstrates that proposed FUZZSAMM algorithm is a useful tool in user-guided clustering.

Original languageEnglish
Pages (from-to)479-488
Number of pages10
JournalSoft Computing
Volume11
Issue number5
DOIs
Publication statusPublished - Mar 2007

Fingerprint

Fuzzy Mapping
Phase Space
Visualization
Trajectories
Projection
Trajectory
Fuzzy clustering
Clustering algorithms
Fuzzy Clustering
Clustering Algorithm
Chaotic systems
Cluster Validity
Fuzzy Algorithm
Graphical Representation
Data mining
High-dimensional Data
Chaotic System
Data Mining
High-dimensional
Objective function

ASJC Scopus subject areas

  • Computational Mechanics

Cite this

Visualization of fuzzy clusters by fuzzy Sammon mapping projection : Application to the analysis of phase space trajectories. / Feil, Balazs; Balasko, Balazs; Abonyi, J.

In: Soft Computing, Vol. 11, No. 5, 03.2007, p. 479-488.

Research output: Contribution to journalArticle

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