Dimensionality reduction is the fundamental problem for machine learning and pattern recognition. During data preprocessing, the feature selection is often demanded to reduce the computational complexity. The problem of feature selection is categorized as a NP optimization problem. Exhaustive search of huge set of features takes huge amount of time on classical computer. In the present paper we discuss the role of quantum adiabatic computation to perform feature selection with bi-quadratic optimization and provide a quantum feature selection algorithm. Our algorithm runs with the quantum adiabatic time complexity bound $O(1/g_{min}^{2})$, which is better than classical approach for bi-quadratic feature selection.
Dimensionality reduction is the fundamental problem for machine learning and pattern recognition. During data preprocessing, the feature selection is often demanded to reduce the computational complexity. The problem of feature selection is categorized as a NP optimization problem. Exhaustive search of huge set of features takes huge amount of time on classical computer. In the present paper we discuss the role of quantum adiabatic computation to perform feature selection with bi-quadratic optimization and provide a quantum feature selection algorithm. Our algorithm runs with the quantum adiabatic time complexity bound O(1/gmin2), which is better than classical approach for bi-quadratic feature selection.
Abstract In machine learning, fewer features reduce model complexity. Carefully assessing the influence of each input feature on the model quality is therefore a crucial preprocessing step. We propose a novel feature selection algorithm based on a quadratic unconstrained binary optimization (QUBO) problem, which allows to select a specified number of features based on their importance and redundancy. In contrast to iterative or greedy methods, our direct approach yields higher-quality solutions. QUBO problems are particularly interesting because they can be solved on quantum hardware. To evaluate our proposed algorithm, we conduct a series of numerical experiments using a classical computer, a quantum gate computer, and a quantum annealer. Our evaluation compares our method to a range of standard methods on various benchmark data sets. We observe competitive performance.
The problem of selecting an appropriate number of features in supervised learning problems is investigated in this paper. Starting with common methods in machine learning, we treat the feature selection task as a quadratic unconstrained optimization problem (QUBO), which can be tackled with classical numerical methods as well as within a quantum computing framework. We compare the different results in small-sized problem setups. According to the results of our study, whether the QUBO method outperforms other feature selection methods depends on the data set. In an extension to a larger data set with 27 features, we compare the convergence behavior of the QUBO methods via quantum computing with classical stochastic optimization methods. Due to persisting error rates, the classical stochastic optimization methods are still superior.
Feature selection is of great importance in Machine Learning, where it can be used to reduce the dimensionality of classification, ranking and prediction problems. The removal of redundant and noisy features can improve both the accuracy and scalability of the trained models. However, feature selection is a computationally expensive task with a solution space that grows combinatorically. In this work, we consider in particular a quadratic feature selection problem that can be tackled with the Quantum Approximate Optimization Algorithm (QAOA), already employed in combinatorial optimization. First we represent the feature selection problem with the QUBO formulation, which is then mapped to an Ising spin Hamiltonian. Then we apply QAOA with the goal of finding the ground state of this Hamiltonian, which corresponds to the optimal selection of features. In our experiments, we consider seven different real–world datasets with dimensionality up to 21 and run QAOA on both a quantum simulator and, for small datasets, the 7–qubit IBM (ibm–perth) quantum computer. We use the set of selected features to train a classification model and evaluate its accuracy. Our analysis shows that it is possible to tackle the feature selection problem with QAOA and that currently available quantum devices can be used effectively. Future studies could test a wider range of classification models as well as improve the effectiveness of QAOA by exploring better performing optimizers for its classical step.
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.
Feature selection is an essential step for reducing complexity of high dimensional data, usually in preparation for developing machine learning models such as computational biomarkers. However, there are limitations associated with feature selection such as for metabolomic data where there are hundreds or even thousands of features per study participant, while the available number of participants in a clinical trials is limited. Classical methods such as exhaustive search require evaluation of all possible feature combinations, making them costly in terms of computation and runtime, or even infeasible, as feature dimensionality increases. In this study, we propose a novel Quadratic Unconstrained Binary Optimization (QUBO) coefficient formulation and pose metabolomic feature selection as a QUBO problem that selects a specified number of features by balancing their relevance against redundancy among the selected variables. To evaluate our proposed QUBO objective function, we conducted a series of experiments using Bias-Field Digitized Counterdiabatic Quantum Optimization (BF-DCQO) and Quantum Approximate Optimization Algorithm (QAOA) on a quantum gate based computer. We also compared the method to several classical methods on three metabolomic datasets associated with Autism Spectrum Disorder (ASD) on a classical computer. Our method reduces runtime compared with exhaustive search and Iterative Tabu Search (ITS) and achieves competitive performance across classifiers compared to classical filter, wrapper, and embedded methods. These results do not claim quantum advantage; rather, they establish hardware feasibility and demonstrate the current capabilities of Noisy Intermediate-Scale Quantum (NISQ) devices.
This paper presents an innovative adaptive quantum machine learning feature reduction algorithm designed to enhance model efficiency and reduce computational complexity within the context of quantum machine learning. Traditional feature selection methods often rely on fixed, predefined feature sets, failing to effectively leverage the inherent properties of quantum systems. Our proposed algorithm dynamically adjusts the dimensionality of input data, minimizing the number of features while maintaining optimal model performance. We explore the potential of quantum computation to accelerate this process, offering a novel approach to feature reduction. The core mechanism centers around leveraging quantum entanglement and superposition to represent and manipulate data representations, enabling a more efficient and targeted feature selection process. This work investigates the potential benefits of this approach, particularly in scenarios where data dimensionality is high and computational cost is a significant constraint. The paper concludes with a discussion of the algorithm's theoretical foundations, experimental validation, and future research directions.