Quantum-Based Feature Selection for Multi-classification Problem in Complex Systems with Edge Computing

TL;DR

This work introduces QReliefF, a quantum-enhanced feature selection method for multi-classification in complex systems with edge computing. By encoding samples as quantum states and transforming nearest-neighbor search into quantum similarity computations via amplitude estimation and the Grover-Long search, it achieves theoretical complexity reductions in both similarity calculations and neighbor finding, while reducing resource demands. A Rigetti-based simulation demonstrates feasibility, showing that the final weight vector accurately identifies relevant features and aligns with classical ReliefF results. The approach offers potential for real-time, low-resource feature selection on edge devices, though privacy considerations are identified as a direction for future work. Overall, QReliefF advances quantum-assisted feature selection with concrete complexity and implementation details, contributing to scalable machine learning on distributed edge infrastructures.

Abstract

The complex systems with edge computing require a huge amount of multi-feature data to extract appropriate insights for their decision making, so it is important to find a feasible feature selection method to improve the computational efficiency and save the resource consumption. In this paper, a quantum-based feature selection algorithm for the multi-classification problem, namely, QReliefF, is proposed, which can effectively reduce the complexity of algorithm and improve its computational efficiency. First, all features of each sample are encoded into a quantum state by performing operations CMP and R_y, and then the amplitude estimation is applied to calculate the similarity between any two quantum states (i.e., two samples). According to the similarities, the Grover-Long method is utilized to find the nearest k neighbor samples, and then the weight vector is updated. After a certain number of iterations through the above process, the desired features can be selected with regards to the final weight vector and the threshold τ. Compared with the classical ReliefF algorithm, our algorithm reduces the complexity of similarity calculation from O(MN) to O(M), the complexity of finding the nearest neighbor from O(M) to O(sqrt(M)), and resource consumption from O(MN) to O(MlogN). Meanwhile, compared with the quantum Relief algorithm, our algorithm is superior in finding the nearest neighbor, reducing the complexity from O(M) to O(sqrt(M)). Finally, in order to verify the feasibility of our algorithm, a simulation experiment based on Rigetti with a simple example is performed.

Figures (11)

• Figure 1: Quantum circuit of getting ${{\rm{1}} \over {\sqrt N }}\sum\limits_{i = 0}^{N-1} {\left| i \right\rangle }$, and H is the Hadamard operation, $\circ$ represents the control qubit conditional being set to zero.
• Figure 2: Quantum circuit of CMP operation, and $\bullet$ represents the control qubit conditional being set to one.
• Figure 3: Quantum circuit of swap test operation, and the symbol of two crosses connected by a line represents the swap operation.
• Figure 4: Quantum circuit of amplitude estimation operation, ${G^J}$ represents $J$ iterations of Grover-Long method Long2001Grover and $F_M^{ - 1}$ represents the inverse Fourier transform Zhou2017Quantum.
• Figure 5: Quantum circuit with one iteration in Grover-Long method Long2001Grover, and $q\left[ 0 \right]$ denotes the highest qubit, $q\left[ n-1 \right]$ denotes the lowest qubit.