Browsing by Author "Tasdemir, Kadim"

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Citation - WoS: 135
Citation - Scopus: 162
Exploiting Data Topology in Visualization and Clustering Self-Organizing Maps
(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2009) Kadim Tasdemir; Erzsebet Merenyi; Tasdemir, Kadim; Merenyi, Erzsebet
The self-organizing map (SOM) is a powerful method for visualization cluster extraction and data mining. It has been used successfully for data of high dimensionality and complexity where traditional methods may often be insufficient. In order to analyze data structure and capture cluster boundaries from the SOM one common approach is to represent the SOM's knowledge by visualization methods. Different aspects of the information learned by the SOM are presented by existing methods but data topology which is present in the SOM's knowledge is greatly underutilized. We show in this paper that data topology can be integrated into the visualization of the SOM and thereby provide a more elaborate view of the cluster structure than existing schemes. We achieve this by introducing a weighted Delaunay triangulation (a connectivity matrix) and draping it over the SOM. This new visualization CONNvis also shows both forward and backward topology violations along with the severity of forward ones which indicate the quality of the SOM learning and the data complexity. CONNvis greatly assists in detailed identification of cluster boundaries. We demonstrate the capabilities on synthetic data sets and on a real 8-D remote sensing spectral image.
Citation - WoS: 5
Citation - Scopus: 5
Exploring topology preservation of SOMs with a graph based visualization
(Springer Verlag, 2008) Kadim TaÅŸdemir; Tasdemir, Kadim
The Self-Organizing Map (SOM) which projects a (high-dimensional) data manifold onto a lower-dimensional (usually 2-d) rigid lattice is a commonly used manifold learning algorithm. However a postprocessing - that is often done by interactive visualization schemes - is necessary to reveal the knowledge of the SOM. Thanks to the SOM property of producing (ideally) a topology preserving mapping existing visualization schemes are often designed to show the similarities local to the lattice without considering the data topology. This can produce inadequate tools to investigate the detailed data structure and to what extent the topology is preserved during the SOM learning. A recent graph based SOM visualization CONNvis [1] which exploits the underutilized knowledge of data topology can be a suitable tool for such investigation. This paper discusses that CONNvis can represent the data topology on the SOM lattice despite the rigid grid structure and hence can show the topology preservation of the SOM and the extent of topology violations. © 2008 Springer Berlin Heidelberg. © 2021 Elsevier B.V. All rights reserved.
Citation - WoS: 23
Citation - Scopus: 24
Graph Based Representations of Density Distribution and Distances for Self-Organizing Maps
(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2010) Kadim Tasdemir; Tasdemir, Kadim
The self-organizing map (SOM) is a powerful method for manifold learning because of producing a 2-D spatially ordered quantization of a higher dimensional data space on a rigid lattice and adaptively determining optimal approximation of the (unknown) density distribution of the data. However a postprocessing visualization scheme is often required to capture the data manifold. A recent visualization scheme CONNvis which is shown effective for clustering uses a topology representing graph that shows detailed local data distribution within receptive fields. This brief proposes that this graph representation can be adapted to show local distances. The proposed graphs of local density and local distances provide tools to analyze the correlation between these two information and to merge them in various ways to achieve an advanced visualization. The brief also gives comparisons for several synthetic data sets.