Clustering and classification are the major subdivisions of pattern recognition techniques. Using these techniques, samples can be classified according to a specific property by measurements indirectly related to the property of interest (such as the type of fuel responsible for an underground spill). An empirical relationship or classification rule can be developed from a set of samples for which the property of interest and the measurements are known. The classification rule can then be used to predict the property in samples that are not part of the original training set.
The set of samples for which the property of interest and measurements is known is called the training set. The set of measurements that describe each sample in the data set is called a pattern. The determination of the property of interest by assigning a sample to its respective category is called recognition, hence the term pattern recognition. For pattern recognition analysis, each sample is represented as a data vector x D (x1, x2, x3, xj, : : : , xn), where component xj is a measurement, e.g. the area a of the jth peak in a chromatogram. Thus, each sample is considered as a point in an n-dimensional measurement space. The dimensionality of the space corresponds to the number of measurements that are available for each sample. A basic assumption is that the distance between pairs of points in this measurement space is inversely related to the degree of similarity between the corresponding samples. Points representing samples from one class will cluster in a limited region of the measurement space distant from the points corresponding to the other class. Pattern recognition (i.e. clustering and classification) is a set of methods for investigating data represented in this manner, in order to assess its overall structure, which is defined as the overall relationship of each sample to every other in the data set.