Pattern Recognition, 4th Edition

16.3. Hypothesis Testing in Cluster Validity

In this framework, the null hypothesis H⁰ will be expressed in a slightly different way. This is because our major concern is not to test a parameter against a specific value. In contrast, our concern here is to test whether the data of X possess a “random” structure or not. Thus, in this case, the null hypothesis H⁰ should be a statement of randomness concerning the structure of X. Thus, our goal is now twofold.

• First, we must generate a reference data population under the random hypothesis, that is, a data population that models a random structure.
• Second, we must define an appropriate statistic, whose values are indicative of the structure of a data set, and compare the value that results from ...