A proposal of quantum data representation to improve the discrimination power

Abstract

This work proposes a quantum representation for improvement of data discrimination power, transforming a non linearly separable problem into a linearly separable problem. This methodology proposed here can be naturally employed as data preprocessing for classification task. A classical real world system will be viewed as a composition of quantum systems, where any observable measurement process of the real world data are created from an expected value measure of a quantum system state. In this projection measure a quantum phase information is naturally lost, making the inverse mapping from the classical space into quantum space impossible. However, it is possible find an arbitrate quantum state that represents the same classical information originally measured. A genetic algorithm is employed for search this arbitrate quantum state, going back from classical world to quantum world representation. The genetic algorithm searches for a compatible quantum state with the real world data, where the lost quantum phase is adjusted with the constraints to minimize the classes’ variance and to maximize the distance between the classes’ centroids. Computational simulations shown that the proposed methodology was able to transform a non linearly separable problem in classical representation space into a linearly separable problem in the quantum representation space, demonstrating an enhancement of data discrimination power.