High-dimensional data has long been a notoriously challenging issue. Existing quantum dimension reduction technology primarily focuses on quantum principal component analysis. However, there are only a few studies on quantum feature selection (QFS) algorithms, and these algorithms are often not robust. Additionally, there are limited quantum circuits specifically designed for feature selection, and they still cannot address the objective function based on sparse learning. To address these issues, this paper proposes a robust QFS algorithm by designing a novel sparse optimization circuit. Specifically, we first apply sparse regularization and least squares loss to construct the proposed objective function. Then, six types of quantum registers and their initial states are prepared. Furthermore, quantum techniques such as quantum phase estimation and controlled rotation are employed to construct a sparse optimization circuit, which is used to obtain the final quantum state of the feature selection variable.Finally, a series of experiments are conducted to verify the accuracy of the feature selection and the robustness of the proposed algorithm.
High-dimensional data has long been a notoriously challenging issue. Existing quantum dimension reduction technology primarily focuses on quantum principal component analysis. However, there are only a few studies on quantum feature selection (QFS) algorithms, and these algorithms are often not robust. Additionally, there are limited quantum circuits specifically designed for feature selection, and they still cannot address the objective function based on sparse learning. To address these issues, this paper proposes a robust QFS algorithm by designing a novel sparse optimization circuit. Specifically, we first apply sparse regularization and least squares loss to construct the proposed objective function. Then, six types of quantum registers and their initial states are prepared. Furthermore, quantum techniques such as quantum phase estimation and controlled rotation are employed to construct a sparse optimization circuit, which is used to obtain the final quantum state of the feature selection variable.Finally, a series of experiments are conducted to verify the accuracy of the feature selection and the robustness of the proposed algorithm.
High dimensional data has been a notoriously challenging issue. Existing quantum dimension reduction technology mainly focuses on quantum principal component analysis. There are only a few works on the direction of quantum feature selection algorithm which they are not robust. Also, there are few quantum circuits designed for feature selection, in which some steps are not quantized yet. For example, existing quantum circuits cannot solve the objective function based on sparse learning. To deal with these issues, this paper proposes a robust quantum feature selection by designing a new quantum circuit. Specifically, the sparse regularization term and least squares loss are first applied to construct the proposed objective function. And then, six kinds of quantum registers and their initial states are prepared. In addition, quantum techniques, such as quantum phase estimation and controlled rotation, are employed to construct an alternating iterative quantum circuit to obtain the final quantum state of the feature selection variable. Finally, a series of experiments are conducted to verify that the proposed algorithm can accurately select important features and has good robustness.
High dimensional data has been a notoriously challenging issue. Existing quantum dimension reduction technology mainly focuses on quantum principal component analysis. There are only a few works on the direction of quantum feature selection algorithm which they are not robust. Also, there are few quantum circuits designed for feature selection, in which some steps are not quantized yet. For example, existing quantum circuits cannot solve the objective function based on sparse learning. To deal with these issues, this paper proposes a robust quantum feature selection by designing a new quantum circuit. Specifically, the sparse regularization term and least squares loss are first applied to construct the proposed objective function. And then, six kinds of quantum registers and their initial states are prepared. In addition, quantum techniques, such as quantum phase estimation and controlled rotation, are employed to construct an alternating iterative quantum circuit to obtain the final quantum state of the feature selection variable. Finally, a series of experiments are conducted to verify that the proposed algorithm can accurately select important features and has good robustness.
The KNN (K-nearest neighbors) algorithm is one of Top-10 data mining algorithms and is widely used in various fields of artificial intelligence. This leads to that quantum KNN algorithms have developed and achieved certain speed improvements, denoted as Q-KNN. However, these Q-KNN methods must face two key problems as follows. The first one is that they are mainly focused on neighbor selection without paying attention to the influence of K value on the algorithm. The second is that only the neighbor selection process is quantized, and the selection of K value is not quantized. To solve these problems, this paper designs a novel quantum circuit for KNN classification, so as to simultaneously quantumize the neighbor selection and K value selection process. Specifically, the least squares loss and sparse regularization term are first used to construct the objective function of the proposed quantum KNN, so that it can simultaneously obtain the optimal K value and K nearest neighbors of the testing data. And then, a new quantum circuit is proposed to quantumize the process through quantum phase estimation, controlled rotation, and inverse phase estimation techniques. Finally, experiments are conducted with qiskit and matlab to output the quantum and classical results of the algorithm, verifying that the proposed algorithm can output the optimal K value and K nearest neighbors for each testing data.
This paper explores the application of quantum computing to the critical tasks of feature selection and dimensionality reduction within machine learning. Traditional methods often struggle with high-dimensional data, leading to computational bottlenecks and potentially reduced model accuracy. We propose a novel approach leveraging the principles of quantum error correction and quantum entanglement to construct an algorithm capable of efficiently identifying and reducing the most relevant features. The core mechanism utilizes quantum machine learning techniques, specifically quantum feature mapping and feature extraction, to transform data into a quantum state that inherently captures feature relationships. This allows for a more effective selection process based on quantum interference and the exploration of complex correlations. We demonstrate, theoretically, the potential advantages of this approach over classical methods, highlighting improvements in both efficiency and predictive accuracy. The algorithm's design incorporates error correction to mitigate the effects of noise inherent in quantum systems, further enhancing its robustness. The research contributes to the growing field of quantum machine learning, offering a new paradigm for tackling complex data challenges.
The curse of dimensionality in high-dimensional optimization: It is inherently seen that the dimensionality of feature space presents a fundamental challenge to high-dimensional optimization: as dimensionality increases, feature space becomes computationally inefficient, overfitted and model interpretability declines, thus requiring highly robust sparsity-based solutions. To find a solution to these problems, a new quantum-inspired framework of sparse optimization is proposed in this study, which combines probabilistic Q-bit representation and L1-regularized optimization to efficiently consider large solution spaces but with a sparsity constraint. The suggested method builds on quantum-inspired search algorithms such as initiation by superposition and rotation gate updates to the search to improved exploration and exploitation ratio, leading to a better convergence process. Experimental analyses show that the framework produces better optimization accuracy, indicated by much lower Mean Squared Error (MSE) and convergence rates than classical and met heuristic baselines, with the framework also having a higher level of sparsity in the solution space. These results highlight the effectiveness of the proposed method in handling high-dimensional problems, making it particularly suitable for applications in signal processing, machine learning-based feature selection, and large-scale scientific computing tasks.
Quantum-enhanced feature selection is a promising approach to address the challenges posed by high-dimensional data in machine learning. Traditional feature selection methods often struggle to effectively identify the most informative features, leading to suboptimal model performance and increased computational cost. This paper proposes a novel quantum algorithm designed to accelerate and enhance feature selection, offering a significant improvement over existing techniques. We explore the potential of quantum algorithms, specifically focusing on Grover's search algorithm and quantum-enhanced k-means clustering, to achieve efficient identification of relevant features. The core mechanism involves exploiting quantum phenomena like superposition and entanglement to enhance the search space and improve the selection process. We demonstrate the effectiveness of our approach through theoretical analysis and preliminary experiments on benchmark datasets, showcasing its potential to reduce computational cost and improve accuracy in high-dimensional feature selection scenarios.