The study of self-organizing maps on optimization, visualization, clustering and complex networks

Abstract

This thesis focuses on the study of Self-Organizing Maps in terms of optimization, visualization, clustering, and complex networks. Self-organizing map (SOM), an unsupervised neural network technique, visualizes high-dimensional data on a low-dimensional map. In SOM, the data topology is preserved through assigning the data with similar features to adjacent neurons. Based on the network structure of SOM, a novel optimization algorithm named self-organizing potential field network (SOPFN) is developed. In the proposed technique, the neuron with the best weight is considered as the target with the attractive force, while the neuron with the worst weight is considered as the obstacle with the repulsive force. The competitive and cooperative behaviors of SOPFN provide a remarkable ability to escape from the local optimum. Simulations are performed, compared, and analyzed on eight benchmark functions. The results presented illustrate that the SOPFN algorithm achieves a significant performance improvement on multimodal problems. Since SOM cannot exhibit the inter-neuron distance due to its uniform neuron distribution, polar self-organizing map (PolSOM), a new visualization algorithm, is proposed. PolSOM is constructed on a 2-D polar map with two variables, radius and angle, which represent data weight and feature, respectively. The separation between two clusters and the closeness within one cluster are both presented in PolSOM. As a result, PolSOM not only preserves the data topology and the inter-neuron distance, it also visualizes the characteristic of clusters. The simulations and comparisons with Sammon's mapping, SOM and ViSOM are provided based on four data sets. The results illustrate the effectiveness of the PolSOM algorithm for multidimensional data visualization. The SOM-based clustering methods suffer from the constraints such as the shapes of clusters and large-scale data sets. To address these problems, the PolSOM-based clustering algorithm is devised to identify arbitrary shaped convex clusters. The data density and distance are both considered into the merging criteria, which can filter out the noise and outliers. The density index, taking into account the internal homogeneity and external separation, improves the clustering accuracy. Intensive experimental study on highly demanding synthetic and real data sets are conducted and the results signify that the proposed algorithm is able to handle the complicated clustering with no a priori knowledge. Attributed to the property of PolSOM, it is worth noting that the proposed clustering algorithm can manifest the trait of clusters. In a large-scale complex network with the fixed topology, how to balance the routing and congestion is the critical question. Based on the learning mechanism of SOM, it is applied to the traffic flow of complex networks. The introduced routing strategy adapts the optimal path to the change in the traffic condition of a network based on the estimated waiting time which on the neighboring nodes of the delivered packet is considered as part of the routing cost. Since the proposed algorithm decreases the traffic load on the nodes that are susceptible to congestion with the large betweenness centrality, the optimized network can handle a greater number of generated packets. The simulation results compared with the shortest-path routing strategy verify that the traffic capacity is significantly enhanced by the proposed SOM-based routing strategy in ER random network and BA scale-free network.