Abstract: The self-organizing map (SOM) model is a well-known neural network model with wide spread of applications. The main characteristics of SOM are two-fold, namely dimension reduction and topology preservation. Using SOM, a high-dimensional data space will be mapped to some low-dimensional space. Meanwhile, the topological relations among data will be preserved. With such characteristics, the SOM was usually applied on data clustering and visualization tasks. However, the SOM has main disadvantage of the need to know the number and structure of neurons prior to training, which are difficult to be determined. Several schemes have been proposed to tackle such deficiency. Examples are growing/expandable SOM, hierarchical SOM, and growing hierarchical SOM. These schemes could dynamically expand the map, even generate hierarchical maps, during training. Encouraging results were reported. Basically, these schemes adapt the size and structure of the map according to the distribution of training data. That is, they are data-driven or dataoriented SOM schemes. In this work, a topic-oriented SOM scheme which is suitable for document clustering and organization will be developed. The proposed SOM will automatically adapt the number as well as the structure of the map according to identified topics. Unlike other data-oriented SOMs, our approach expands the map and generates the hierarchies both according to the topics and their characteristics of the neurons. The preliminary experiments give promising result and demonstrate the plausibility of the method.
Abstract: The SOM has several beneficial features which make
it a useful method for data mining. One of the most important
features is the ability to preserve the topology in the projection.
There are several measures that can be used to quantify the goodness
of the map in order to obtain the optimal projection, including the
average quantization error and many topological errors. Many
researches have studied how the topology preservation should be
measured. One option consists of using the topographic error which
considers the ratio of data vectors for which the first and second best
BMUs are not adjacent. In this work we present a study of the
behaviour of the topographic error in different kinds of maps. We
have found that this error devaluates the rectangular maps and we
have studied the reasons why this happens. Finally, we suggest a new
topological error to improve the deficiency of the topographic error.