Quantum-Based Feature Selection for Multi-classification Problem in
  Complex Systems with Edge Computing
Wenjie Liu Junxiu Chen Yuxiang Wang Peipei Gao Zhibin Lei Xu Ma
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 {\tau}. 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.