Self-organizing map : visualization and data handling

Abstract

Data visualization, which is the graphical presentation of data information, has been widely applied in industrial areas, e.g. signal compression, pattern recognition, image processing, etc. Self-Organizing Map (SOM), a widely used visualization method proposed by Kohonen, is an unsupervised learning network to visualize high-dimensional data in a low-dimensional map. SOM is able to present the data topology by assigning each datum to a neuron with the highest similarity, so that the data with similar features are mapped onto adjacent neurons. The traditional SOM uses the uniform grid map. Thus, some input data are projected onto the same neuron. Apparently, it is not an effective way for preserving the data relationship between clusters or within one cluster. And pre-defining the map size is another disadvantage of SOM. In this thesis, a new algorithm named Polar Self-Organizing Map (PolSOM) is proposed. PolSOM is constructed on a 2-D polar map with two variables, radius and angle, which represent data weight and feature respectively. Compared with the traditional algorithms which project data on a Cartesian map by using Euclidian distance as the only variable, PolSOM can manifest the precise data topology, and obtain the intra cluster density and inter cluster density by a new clustering criterion, synthetical cluster density (SCD). In PolSOM, not only similar data are grouped together, data characteristics are reflected by their positions on the map. PolSOM, in fact, adopts the conventional hard assignment for the training process. In this thesis, a new variant of PolSOM algorithm, named Probabilistic Polar Self-Organizing Map (PPoSOM), is proposed. Instead of using the hard assignment, PPoSOM employs the soft assignment that the assignment of a datum to a neuron is based on a probabilistic function. It is developed to enhance the visualization performance. It is worth noting that the obtained principled weight-updating rule of PPoSOM makes the visualization performance, measured by synthetical cluster density (SCD), greatly improve. SOM usually considers the whole data set in one go, whereas the representative data are not well utilized. The learning process is found to be rigid and time-consuming when one is dealing with large data sets. In this thesis, we propose to apply density based data reduction method as pre-processing, which means that the proposed method extracts representative data preliminarily for the SOM training. This method is found to be particularly useful in terms of reducing the overall computational time. Finally, an interesting application on World University Rankings is included in this thesis. A new perspective on studying the nature of different universities is introduced. SOM is employed to provide estimates for the missing scores of some universities. Principal component analysis (PCA) is used to analyze the underlying nature of each university. The results and analyses show that we can effectively determine the underlying characteristics of a university by studying how its ranking varies with the change of weights on different features. Our study shows that the proposed approach is more effective than simply relying on a linear weighted sum ranking system.