Unsupervised connectionist algorithms for clustering an environmental data set: A comparison

Abstract

Various unsupervised algorithms for vector quantization can be found in the literature. Being based on different assumptions, they do not all yield exactly the same results on the same problem. To better understand these differences, this article presents an evaluation of some unsupervised neural networks, considered among the most useful for quantization, in the context of a real-world problem: radioelectric wave propagation. Radio wave propagation is highly dependent upon environmental characteristics (e.g. those of the city, country, mountains, etc.). Within the framework of a cell net planning its radiocommunication strategy, we are interested in determining a set of environmental classes, sufficiently homogeneous, to which a specific prediction model of radio electrical field can be applied. Of particular interest are techniques that allow improved analysis of results. Firstly, Mahalanobis’ distance, taking data correlation into account, is used to make assignments. Secondly, studies of class dispersion and homogeneity, using both a data structure mapping representation and statistical analysis, emphasize the importance of the global properties of each algorithm. In conclusion, we discuss the advantages and disadvantages of each method on real problems.

Introduction

Faced with the current explosion of mobile communication systems, cell net planning is a strategic stage for telecommunication operators. Choosing the location and size of the glazed zone of transmitting stations is a key factor in optimizing the development of a radio mobile network. Cell planning depends upon the attenuation of radio electrical waves. Moreover, the laws of wave propagation change with the environment. Currently, there is no global theoretical model to explain this attenuation under all circumstances. Conversely, a statistical model can easily be built (for example, using supervised connectionist techniques), if homogeneous classes of environment can be defined (for example, in the mountain or in a sparse suburb). We thus aim to define a partition of the environment that is homogeneous enough to provide a correct predictive model of the radio electrical wave propagation for each class.

Such a clustering can be obtained with vector quantization algorithms, including unsupervised neural networks. A variety of such models have been presented in the literature, using different approaches, and thus giving different results, for determining classes and the frontiers between them. It is clear that such algorithms cannot be compared on their performances, but only for the subjective quality of their results. This is one reason why it is very interesting to compare unsupervised algorithms on a real data set. As mentioned, this comparison can only be subjective, in terms of the properties of the obtained classes and frontiers. Algorithms used in the vector quantization models are presented in Section 2, whereas Section 3 proposes a set of statistical tools allowing for a better analysis of the behavior of these models. A national geographic database, describing physical geography in France, is used for this comparison. We extract a random corpus of 5000 patterns from four typical regions represented in total by 65,000 patterns. Each pattern has eight attributes: altitude and the percentage presence of seven other parameters (water, wood, field, rock and three grades of construction density) within an area of $\text{400×400}\text{m}{}^2$. Each parameter is standardized according to mean and standard deviation calculated over the 65,000 patterns.