Quantum Low Entropy based Associative Reasoning or QLEAR Learning

In this paper, we propose the classification method based on a learning paradigm we are going to call Quantum Low Entropy based Associative Reasoning or QLEAR learning. The approach is based on the idea that classification can be understood as supervised clustering, where a quantum entropy in the context of the quantum probabilistic model, will be used as a "capturer" (measure, or external index), of the "natural structure" of the data. By using quantum entropy we do not make any assumption about linear separability of the data that are going to be classified. The basic idea is to find close neighbors to a query sample and then use relative change in the quantum entropy as a measure of similarity of the newly arrived sample with the representatives of interest. In other words, method is based on calculation of quantum entropy of the referent system and its relative change with the addition of the newly arrived sample. Referent system consists of vectors that represent individual classes and that are the most similar, in Euclidean distance sense, to the vector that is analyzed. Here, we analyze the classification problem in the context of measuring similarities to prototype examples of categories. While nearest neighbor classifiers are natural in this setting, they suffer from the problem of high variance (in bias-variance decomposition) in the case of limited sampling. Alternatively, one could use machine learning techniques (like support vector machines) but they involve time-consuming optimization. Here we propose a hybrid of nearest neighbor and machine learning technique which deals naturally with the multi-class setting, has reasonable computational complexity both in training and at run time, and yields excellent results in practice.