Clustering and classification are the major subdivisions of pattern recognition. Using these techniques, samples can be classified according to a specific property through measurements indirectly related to a property of interest (e.g. the type of fuel responsible for an underground spill). An empirical relationship or classification rule is 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 the measurements are 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
= (
x
1
,
x
2
,
x
3
,
x
j
, …,
x
p
), where component
x
j
is a measurement, e.g. the area of the
j
th peak in a chromatogram. Each sample is considered as a point in a p‐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 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, to assess its overall structure, which is defined as the overall relation of each sample to every other in the data set.
