NASA Technical Reports Server (NTRS) 19850013734: Technical support for creating an artificial intelligence system for feature extraction and experimental design

Techniques for classifying objects into groups or classes go under many different names including, most commonly, cluster analysis. Mathematically, the general problem is to find a "best" mapping of objects into an index set consisting of class identifiers. When an a priori grouping of objects exists, the process of deriving the classification rules from samples of classified objects is known as "discrimination". When such rules are applied to objects of unknown class, the process is denoted "classification." For this paper, our problem is to classify into groups a set of objects that are each associated with a series of measurements (ratio, interval, ordinal, or nominal levels of measurement). Each measurement produces one variable in a multidimensional variable space. Thus, objects may be represented as vectors or points in this multidimensional space and the usual multivariate statistical techniques may be used. In some applications each object also may exist in geographical space; i.e., each object is associated with a location on the earth's surface. Although an object's location in geographical space can be represented by a pair of planar or spherical coordinates (and, possibly, by a third coordinate representing height or elevation), problems exist in simply considering location as another measurement. These will be discussed below. A basic methodological philosophy in classification is to consider the distances between objects in the multi-dimensional measurement space. It is expected that similar objects will be represented by points that lie near to one another in this space. In this sense, clustering can be considered the process of defining regions of the measurement space that divide the points (and their associated objects) into optimal classes. New points (and objects) can then be classified by determining which region they lie in. In cluster analysis the objective is to take a set of objects with unknown classification and to group these objects into "natural" classes or clusters (Hand, 1981). The selection of measurements to use in the cluster analysis is of critical importance because the groupings that result are completely determined by the choice of measurements. If these measurements are irrelevant to the objective or application of the grouping (e.g., trying to identify groups of locations with similar remote sensor characteristics), the clustering is likely to produce irrelevant groupings. Once the measurements have been selected, it may be desirable to reduce their number to make computation feasible and/or to eliminate variables that will not add significantly to the analysis. In order to do this a measure of how closely the reduced set of measurements or dimensions corresponds to the original set is needed along with an algorithm to find the subset of variables that optimizes this measure. The most popular approach is the method of principle components which is based on linear transformations of variables and the deletion of variables that account for very little of the total variance. More recently, non-linear methods have been proposed and are based on a wide range of structural criteria (for example, using multidimensional scaling techniques). A wide variety of cluster analysis techniques exist; these can be conveniently divided into two major approaches, hierarchical and optimization. In a hierarchical analysis, the final groupings are formed by iteratively grouping subclusters or by iteratively splitting parent clusters (i.e., agglomerative or divisive approaches).

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