An Approach of Feature Subset Selection Using Simulated Quantum Annealing

Abstract

Feature selection is one of the important preprocessing steps in machine learning and data mining domain. However, finding the best feature subsets for large datasets is computationally expensive task. Meanwhile, quantum computing has emerged as a new computational model that is able to speed up many classical computationally expensive problems. Annealing-based quantum model, for example, finds the lowest energy state of an Ising model Hamiltonian, which is the formalism for Quadratic Unconstrained Binary Optimization (QUBO). Due to its capabilities in producing quality solution to the hard combinatorial optimization problems with less computational effort, quantum annealing has the potentiality in feature subset selection. Although several hard optimization problems are solved, using quantum annealing, not sufficient work has been done on quantum annealing based feature subset selection. Though the reported approaches have good theoretical foundation, they usually lack required empirical rigor. In this paper, we attempt to reduce classical benchmark feature evaluation functions like mRMR, JMI, and FCBF to QUBO formulation, enabling the use of quantum annealing based optimization to feature selection. We then apply QUBO of ten datasets using both Simulated Annealing (SA) and Simulated Quantum Annealing (SQA) and compared the result. Our empirical results confirm that, for seven in ten datasets, SQA is able to produce at most equal or less number of features in all selected subset compared to SA does. SQA also results in stable feature subsets for all datasets.