The idea of representation has been used in various fields of study from data analysis to political science. In this paper, we define representativeness and describe a method to isolate data points that can represent the entire data set. Also, we show how the minimum set of representative data points can be generated. We use data from GLOBE (a project to study the effects on Land Change based on a set of parameters that include temperature, forest cover, human population, atmospheric parameters and many other variables) to test & validate the algorithm. Principal Component Analysis (PCA) is used to reduce the dimensions of the multivariate data set, so that the representative points can be generated efficiently and its Representativeness has been compared against Random Sampling of points from the data set.
A new method has been developed to perform environmental assessment at regional scale. This involves a combination of a self-organizing map (SOM) neural network and principal component analysis (PCA). The method is capable of clustering ecosystems in terms of environmental conditions and suggesting relative cumulative environmental impacts of multiple factors across a large region. Using data on land-cover, population, roads, streams, air pollution, and topography of the Mid-Atlantic region, the method was able to indicate areas that are in relatively poor environmental condition or vulnerable to future deterioration. Combining the strengths of SOM with those of PCA, the method offers an easy and useful way to perform a regional environmental assessment. Compared with traditional clustering and ranking approaches, the described method has considerable advantages, such as providing a valuable means for visualizing complex multidimensional environmental data at multiple scales and offering a single assessment or ranking needed for a regional environmental assessment while still facilitating the opportunity for more detailed analyses. The Land Transformation Model (LTM), which couples geographic information systems (GIS) with artificial neural networks (ANNs) to forecast land use changes, is presented here. A variety of social, political, and environmental factors contribute to the model’s predictor variables of land use change. This paper presents a version of the LTMparameterized for Michigan’s Grand Traverse Bay Watershed and explores how factors such as roads, highways, residential streets, rivers, Great Lakes coastlines, recreational facilities, inland lakes, agricultural density, and quality of views can influence urbanization patterns in this coastal watershed. ANNs are used to learn the patterns of development in the region and test the predictive capacity of the model, while GIS is used to develop the spatial, predictor drivers and perform spatial analysis on the results. The predictive ability of the model improved at larger scales when assessed using a moving scalable window metric. Finally, the individual contribution of each predictor variable was examined and shown to vary across spatial scales. At the smallest scales, quality views were the strongest predictor variable. We interpreted the multi-scale influences of land use change, illustrating the relative influences of site (e.g. quality of views, residential streets) and situation (e.g. highways and county roads) variables at different scales. # 2002 Elsevier Science Ltd. All rights reserved. Kohonen's self-organizing map (SOM) is a popular neural network architecture for solving problems in the field of explorative data analysis, clustering, and data visualization. One of the major drawbacks of the SOM algorithm is the difficulty for nonexpert users to interpret the information contained in a trained SOM. In this paper, this problem is addressed by introducing an enhanced version of the Clusot algorithm. This algorithm consists of two main steps: 1) the computation of the Clusot surface utilizing the information contained in a trained SOM and 2) the automatic detection of clusters in this surface. In the Clusot surface, clusters present in the underlying SOM are indicated by the local maxima of the surface. For SOMs with 2-D topology, the Clusot surface can, therefore, be considered as a convenient visualization technique. Yet, the presented approach is not restricted to a certain type of 2-D SOM topology and it is also applicable for SOMs having an n-dimensional grid topology. The problem of dimension reduction is introduced as a way to overcome the curse of the dimensionality when dealing with vector data in high-dimensional spaces and as a modelling tool for such data. It is defined as the search for a low-dimensional manifold that embeds the high-dimensional data. A classification of dimension reduction problems is proposed. A survey of several techniques for dimension reduction is given, including principal component analysis, projection pursuit and projection pursuit regression, principal curves and methods based on topologically continuous maps, such as Kohonen’s maps or the generalised topographic mapping. Neural network implementations for several of these techniques are also reviewed, such as the projection pursuit learning network and the BCM neuron with an objective function. Several appendices complement the mathematical treatment of the main text.