Decision Regions

When performing pattern recognition, a set of patterns can be represented in a pattern space, in which each pattern is represented as a point at a particular set of coordinates; a pattern’s coordinates are defined by the values of its features.  Pattern classification can then proceed by carving the pattern space into areas called decision regions.  A decision region is an area or volume, marked by cuts in the pattern space.  All of the patterns within a usable decision region belong to the same class.  As a result, the location of a pattern – identifying what decision region it lies in – can be used to classify it.  Obviously, the complexity of a pattern recognition problem is determined by the complexity of decision regions required to separate patterns of different classes (Lippmann, 1987, 1989).  Conversely, the computational power of a classifier is determined by the shape and number of cuts it can make into a pattern space.  For instance, perceptrons (Rosenblatt, 1962) are limited to solving linearly separable problems because they can only make a single straight cut that divides a pattern space into two decision regions (Minsky & Papert, 1969).

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