ViSOM - a novel method for multivariate data projection and structure visualization

Abstract

Abstract-When used for visualization of high-dimensional data, the self-organizing map (SOM) requires a coloring scheme such as the U-matrix to mark the distances between neurons. Even so, the structures of the data clusters may not be apparent and their shapes are often distorted. In this paper, a visualization-induced SOM (ViSOM) is proposed to overcome these shortcomings. The algorithm constrains and regularizes the inter-neuron distance with a parameter that controls the resolution of the map. The mapping preserves the inter-point distances of the input data on the map as well as the topology. It produces a graded mesh in the data space such that the distances between mapped data points on the map resemble those in the original space, like in the Sammon mapping. However, unlike the Sammon mapping, the ViSOM can accommodate both training data and new arrivals and is much simpler in computational complexity. Several experimental results and comparisons with other methods are presented.

Cooperation-Controlled Learning for Explicit Class Structure in Self-Organizing Maps

“…However, it is difficult to visualize class boundaries in self-organizing maps. As discussed in Section 1 , there have been many attempts to visualize connection weights [ 3 , 6 , 8 , 14 , 16 , 17 , 26 – 28 ]. One of the main problems lies in the focus upon cooperation between neurons in the conventional self-organizing maps; neighboring neurons must behave as similarly as possible.…”

“…While the above techniques are applied to SOM results, there are several methods where connection weights are actively modified so as to improve class structure. For example, the visualization induced self-organizing map (ViSOM) [ 14 ] was introduced to preserve data structure and topology as faithfully as possible by regularizing the distances of interneurons. Along the same line, the probabilistic regularized self-organizing map (PRSOM) [ 15 ] was also proposed to regularize interneuron distances by introducing the MDS type metric to preserve pair-wise distances between neurons in the input and output space.…”

Cluster Visualization and Nonlinear Projection Techniques for Biological Sequences

“…Similarly, in [16] the inter-point distances in the feature space between the SOM neurons are used for presenting graphically the underlying structure of the data. A further refinement of these approaches is the visualization-induced SOM [29] an algorithm that regularizes and scales the inter-neuron distances so as to control the resolution of the mappings.…”

Unsupervised Spatiotemporal Analysis of FMRI Data Using Graph-Based Visualizations of Self-Organizing Maps

“…These include sizes of the receptive fields, local density distribution or distance (or similarity) across node prototypes. These components have been exploited for visualization of data clusters via several visualization schemes such as U-matrix [27] or its variants [28], [29], visualization-induced SOM [30], or double SOM [31]. A more comprehensive review on various visualization schemes of the SOM can be found in [26], [32], and [33].…”