Topology Representing Networks for the Visualization of Manifolds

In practical data mining tasks, high-dimensional data has to be analyzed. In most of the cases it is very informative to map and visualize the hidden structure of a complex data set in a low-dimensional space. In this paper a new class of mapping algorithms is defined. These algorithms combine topology representing networks and different nonlinear mapping algorithms. While the former methods aim to quantify the data and disclose the real structure of the objects, the nonlinear mapping algorithms are able to visualize the quantized data in the low-dimensional vector space. In this paper, techniques based on these methods are gathered and the results of a detailed analysis performed on them are shown. The primary aim of this analysis is to examine the preservation of distances and neighborhood relations of the objects. Preservation of neighborhood relations was analyzed both in local and global environments. To evaluate the main properties of the examined methods we show the outcome of the analysis based both on synthetic and real benchmark examples.

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