A hybrid quantum feature selection algorithm using a quantum inspired graph theoretic approach

Abstract

Quantum machine learning bridges the gap between abstract developments in quantum computing and the applied research on machine learning. It generally exposes the synthesis of important machine learning algorithms in a quantum framework. Dimensionality reduction of a dataset with a suitable feature selection strategy is one of the most important tasks in knowledge discovery and data mining. The efficient feature selection strategy helps to improve the overall accuracy of a large dataset in terms of machine learning operations. In this paper, a quantum feature selection algorithm using a graph-theoretic approach has been proposed. The proposed algorithm has used the concept of correlation coefficient based graph-theoretic classical approach initially and then applied the quantum Oracle with CNOT operation to verify whether the dataset is suitable for dimensionality reduction or not. If it is suitable, then our algorithm can efficiently estimate their high correlation values by using quantum parallel amplitude estimation and amplitude amplification techniques. This paper also shows that our proposed algorithm substantially outperforms than some popular classical feature selection algorithms for supervised classification in terms of query complexity of $O(\frac {k\sqrt {N_{c}^{(k)}N_{f}^{(k)}}}{\epsilon })$, where N is the size of the feature vectors whose values are ⩾ THmin(minimum threshold), k is the number of iterations and where 𝜖 is the error for estimating those feature vectors. Compared with the classical counterpart, i.e. the performance of our quantum algorithm quadratically improves than others.