Projector operators in clustering

In a recent paper, the notion of quantum perceptron has been introduced in connection with projection operators. Here, we extend this idea, using these kind of operators to produce a clustering machine, that is, a framework that generates different clusters from a set of input data. Also, we consider what happens when the orthonormal bases first used in the definition of the projectors are replaced by frames and how these can be useful when trying to connect some noised signal to a given cluster.