Statistical Signal Processing in Engineering

23Classification and Clustering

There are many applications where a set of data should be classified as belonging to a predefined subset, or to discover the structure of the data when those subsets are not known. In signal processing, a signal can contain or not a specific waveform, or an image can be contain or not a feature of interest (e.g., a search for faces in images), or feature extraction can be used to reduce the complexity of the image itself. This chapter covers methods for classification and clustering as part of routine statistical signal processing for signal detection or feature extraction. The topic is broad, and the focus is to discuss the essential concepts collected in Table 23.1.

Table 23.1 Taxonomy of principles and methods for classification and clustering.

Classification (Section 23.2)	Clustering (Section 23.6)
Prior knowledge	is known/estimated	No a‐priori classes and numbers
p(k) is known (Bayesian)
Application	Classify new sample x into k	Grouping of homogeneous data
(structure discovery from data)
Methods	Detection theory (Section 23.2.1)	K‐means and EM clustering
Bayesian classifiers (Section 23.4)
Metric	Classification probability ...