The N-Tuple Subspace Classifier: Extensions and Survey

This article is written in recognition of W. Bledsoe, who with Browning, introduced the N-tuple subspace classifier in 1959. This 1959 article was the first article to introduce subspace classifiers and the sum rule to combine the outputs of the classifiers. A mathematical notation is given to easily express in a precise and unambiguous way everything going on in the N-tuple subspace classifier. Extensions of the N-tuple method are discussed using a generalized product expression and we relate the generalization to graphical models. We discuss the sum rule, the product rule, and the plurality voting rule for combining the scores of the subspace classifiers. We selected a representative sample of papers that the 1959 N-tuple subspace classifier inspired. Some of the papers introduced specialized improvements. Many of the papers showed the value of the N-tuple subspace classifier in all kinds of applications and compared the results of one or more varieties of the N-tuple subspace classifier with other state-of-the-art classifiers. Their experiments showed that the N-tuple subspace classifier was competitive with the state-of-the-art classifiers and often had a higher accuracy. Finally, we highlight some papers that describe experiments of the N-tuple subspace classifier executing in a quantum computer.