Projector operators in clustering

TL;DR

This paper extends the concept of quantum perceptrons using projection operators to develop a clustering framework, exploring the use of frames for handling noisy signals and enhancing cluster detection.

Contribution

It introduces a clustering machine based on projection operators and investigates the use of frames to improve noise robustness in cluster identification.

Findings

Development of a projection operator-based clustering framework

Analysis of frames as an alternative to orthonormal bases for noise handling

Potential improvements in clustering robustness with frames

Abstract

In a recent paper the notion of {\em quantum perceptron} has been introduced in connection with projection operators. Here we extend this idea, using these kind of operators to produce a {\em clustering machine}, i.e. a framework which 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.