A Modified SOM Algorithm Using Learning by Epoch and Higher Order Statistics

Abstract

The Self-organizing Map (SOM) is a specialized artificial neural network (ANN) that facilitates data visualization, aiding in the understanding of high-dimensional data and representing clustering mechanisms by grouping similar data together. However, the conventional SOM demonstrates limitations when handling non-Gaussian data distributions, often resulting in suboptimal initial placements, slower convergence, and less effective clustering. To address these challenges, we propose a novel approach to enhance SOM performance by integrating a learning-by-epoch strategy. This strategy introduces a step in the SOM algorithm that checks the kurtosis and skewness of input vectors. If significant deviations are detected, normalization is applied to ensure that the input data falls within an appropriate range. In our experiments using the Iris dataset, the conventional SOM achieved an error rate of 0.0889 after converging in 2100 iterations. The modified SOM reported in previous studies and k-means algorithm yielded error rates of 0.0444 and 0.0476, respectively, with convergence in 1950 iterations. Notably, our proposed SOM outperformed both, achieving an excellent error rate of 0.022 and converging in just 1630 iterations. Additionally, when applied to satellite images, the basic SOM exhibited under-segmentation issues, failing to accurately delineate distinct land cover regions. In contrast, the segmentation results from our modified SOM demonstrated superior performance, yielding a more accurate and finely segmented image. The proposed method achieved the highest Normalized Mutual Information (NMI) across all tested satellite images. Table 1 summarizes these comparative results among different SOM algorithms, highlighting that our proposed modified SOM consistently outperformed other methods in terms of cluster error rate and convergence iterations.