


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).
References:
 Lippmann, R. P. (1987). An introduction to computing with neural nets. IEEE ASSP magazine, April, 422.
 Lippmann, R. P. (1989). Pattern classification using neural networks. IEEE Communications magazine, November, 4764.
 Minsky, M. L., & Papert, S. (1969). Perceptrons: An Introduction To Computational Geometry (1st ed.). Cambridge, Mass.,: MIT Press
 Rosenblatt, F. (1962). Principles Of Neurodynamics. Washington: Spartan Books.
(Added November 2010)



