Unsupervised learning and the identification of finite mixtures

The first portion of this paper is tutorial. Beginning with a standard definition of an abstract pattern-recognition machine, "learning" is given a mathematical meaning and the distinction is made between supervised and unsupervised learning. The bibliography will help the interested reader retrace the history of learning in pattern recognition. The exposition now focuses attention on unsupervised learning. Carefully, it is explained how problems in this subject can be viewed as problems in the identification of finite mixtures, a statistical theory that has achieved some maturity. From this vantage point, it is demonstrated that identification theory implies unsupervised learning is possible in many important cases. The remaining sections present a general method for achieving unsupervised learning. Other authors have proposed schemes having greater computational convenience, but no method previously published is as inclusive as the one revealed here, which we demonstrate to be effective for all the many cases wherein unsupervised learning is known to be possible.