Intertwine: Nonlinear Quantum Feature Selection With Multikernel Circuits

Abstract

Feature selection accelerates training, enhances interpretability, and reduces data dimensionality by identifying the most relevant and important features, thereby improving machine learning performance. However, current quantum feature selection (QFS) methods are still in their early stages and predominantly focus on linear relationships within the data. This limitation overlooks potential nonlinear relationships, preventing the selection of the most representative feature subset. Consequently, this shortcoming can degrade the performance of subsequent learning tasks, especially on nonlinear datasets. To address this challenge, we propose Intertwine, a nonlinear quantum feature selection method with multikernel circuits. Specifically, we design a quantum multikernel circuit that independently maps each feature, enabling the extraction of multiple kernel matrices. This process maps all features into the quantum kernel space, where the original nonlinear relationships become linearly separable, effectively capturing the inherent nonlinear structure in the data. We then construct a nonlinear feature selection objective function by incorporating class labels, kernel matrices, and orthogonality constraints to guide the selection process. Finally, we validate the effectiveness of Intertwine on both synthetic and public datasets. Experimental results demonstrate that Intertwine outperforms state-of-the-art QFS methods, achieving an average improvement of 4.60% in classification accuracy. The source code for the proposed Intertwine method is publicly available at https://github.com/xhchangsha/quantum-feature-selection