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 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 multi-kernel circuits. Specifically, we design a quantum multi-kernel 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 quantum feature selection 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.

The assignment of a fixed weight value to an attribute (or variable) is not always considered reasonable, as it may not effectively preserve user similarity, potentially resulting in a decline in the performance of collaborative filtering recommendation algorithms. In this article, we introduce a piecewise weighting method that incorporates hyper-class representation to enhance collaborative filtering recommendations. Our approach begins with applying a kernel function to map the original data into a kernel space, facilitating the learning of attribute weights. Subsequently, we construct a hyper-class representation of the data to derive weights for segmented attribute values (hyper-classes) within each attribute, creating a piecewise weighting function. This piecewise weighting function is then utilized to compute user similarities for collaborative filtering recommendations. Finally, we conduct a series of experiments to assess the performance of the collaborative filtering recommendation algorithm. The results demonstrate that the proposed algorithm, employing the piecewise weighting function, outperforms the compared algorithm that uses fixed weight values, as assessed by RMSE, Mean Absolute Error (MAE), and Precision. The source code for the proposed algorithm is available at https://github.com/Lijy207/HCPW .

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.

Noisy data is ubiquitous in quantum computer, greatly affecting the performance of various algorithms. However, existing quantum support vector machine models are not equipped with anti-noise ability, and often deliver low performance when learning accurate hyperplane normal vectors from noisy data. To attack this issue, an anti-noise quantum support vector machine algorithm is developed in this paper. Specifically, a weight factor is first embedded into the hinge loss, so as to construct the objective function of anti-noise support vector machine. And then, an alternative iterative optimization strategy and a quantum circuit are designed for solving the objective function, aiming to obtain the normal vector and intercept of the hyperplane that finally divides the data. Finally, the classification and anti-noise effect of the algorithm are verified on artificial dataset and public dataset. Experimental results show that the proposed algorithm is efficient, yet maintains stable accuracy in noisy data.

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.

Recommendation has become especially crucial during the COVID-19 pandemic as a significant number of people rely on online shopping from home. Existing recommendation algorithms, designed to address issues like cold start and data sparsity, often overlook the time constraints of users. Specifically, users expect to receive recommendations for products of interest in the shortest possible time. To address this challenge, we propose a novel collaborative filtering recommendation algorithm that leverages the advantages of quantum computing circuits based on data reconstruction. This approach allows for the rapid identification of users similar to the target user, thereby improving recommendation speed. In our method, we utilize the information of known users to linearly reconstruct that of the target users, forming a relational matrix. Subsequently, we employ \(l_{2,1}-\) norm and \(l_{1}-\) norm to sparsely constrain the relationship matrix, deducing the weight of each known user. The final step involves providing similar recommendations to target users based on these weights. Furthermore, we implement the proposed algorithm using a quantum circuit, enabling exponential acceleration. The final weight matrix is derived from the quantum state outputted by the circuit. The speed of this process is theoretically demonstrated in detail. Experimental results indicate that our algorithm outperforms state-of-the-art methods in terms of root mean squared error (RMSE), mean absolute error (MAE) and normalized discounted cumulative gain (NDCG). Compared to state-of-the-art comparison algorithms, the proposed algorithm achieves the fastest recommendation speed across eight public datasets.

The challenge of the dimensional disaster in multi-view data is an ongoing and formidable issue. Current multi-view feature selection algorithms aim to reduce dimensions by learning a feature subset that effectively captures the overall information of the data, integrating the characteristics from multiple views. However, they often overlook the detrimental impact of noise in the data, which compromises the performance of multi-view feature selection and yields inefficient feature subsets. To address this problem, this paper proposes an anti-noise multi-view feature selection algorithm. In particular, we begin by combining least squares loss and regularization techniques to learn the relationship between the data and labels. Subsequently, we introduce sample constraints, including view weight and sample weight, as well as feature weight factors, into the objective function. This incorporation reduces the significance of noisy samples, thereby enhancing the algorithm’s ability to resist noise interference. In comparative evaluations with state-of-the-art algorithms, the proposed algorithm exhibits an average improvement of 4.42% in classification accuracy when applied to publicly available datasets with added noise1

Data collected from nature is usually unlabeled, and it is difficult to be used directly. This issue is well addressed by crowdsourcing, which provides a reasonable way for effectively using these unlabeled data. Generally, workers in crowdsourcing tasks are not professionals, so it is hard to obtain high-quality labels. To address this issue, a robust sparse weighted classification algorithm is proposed, which try to adjust the samples that are not correctly classified in the original lables as much as possible. Specifically, we evalute the ability of different workers(indicator weight matrix) to accurately label different samples by fitting the real data matrix to its weighted reconstruction matrix. And then,$ l_{2,1}$-norm and worker labeling ability similarity matrix are added, and negative effects of some bad workers are eliminated through the row sparsity property of$ l_{2,1}$-norm. Finally, the optimal indicator weight matrix is obtained by optimizing the two matrices in the objective function simultaneously. Therefore, the obtained optimal indicator weight matrix takes the similarity of worker labeling ability into consideration, and infers all the predicted labels. The results on synthetic and real data sets demonstrate that our algorithm is superior to other state-of-the-art methods.

KNN classification is an improvisational learning mode, in which they are carried out only when a test data is predicted that set a suitable K value and search the K nearest neighbors from the whole training sample space, referred them to the lazy part of KNN classification. This lazy part has been the bottleneck problem of applying KNN classification due to the complete search of K nearest neighbors. In this paper, a one-step computation is proposed to replace the lazy part of KNN classification. The one-step computation actually transforms the lazy part to a matrix computation as follows. Given a test data, training samples are first applied to fit the test data with the least squares loss function. And then, a relationship matrix is generated by weighting all training samples according to their influence on the test data. Finally, a group lasso is employed to perform sparse learning of the relationship matrix. In this way, setting K value and searching K nearest neighbors are both integrated to a unified computation. In addition, a new classification rule is proposed for improving the performance of one-step KNN classification. The proposed approach is experimentally evaluated, and demonstrated that the one-step KNN classification is efficient and promising.

Distance function is a main metrics of measuring the affinity between two data points in machine learning. Extant distance functions often provide unreachable distance values in real applications. This can lead to incorrect measure of the affinity between data points. This paper proposes a reachable distance function for KNN classification. The reachable distance function is not a geometric direct-line distance between two data points. It gives a consideration to the class attribute of a training dataset when measuring the affinity between data points. Concretely speaking, the reachable distance between data points includes their class center distance and real distance. Its shape looks like “Z,” and we also call it a Z distance function. In this way, the affinity between data points in the same class is always stronger than that in different classes. Or, the intraclass data points are always closer than those interclass data points. We evaluated the reachable distance with experiments, and demonstrated that the proposed distance function achieved better performance in KNN classification.

Data representation is usually a natural form with their attribute values. On this basis, data processing is an attribute-centered calculation. However, there are three limitations in the attribute-centered calculation, saying, inflexible calculation, preference computation, and unsatisfactory output. To attempt the issues, a new data representation, named as hyper-classes representation, is proposed for improving recommendation. First, the cross entropy, KL divergence and JS divergence of features in data are defined. And then, the hyper-classes in data can be discovered with these three parameters. Finally, a kind of recommendation algorithm is used to evaluate the proposed hyper-class representation of data, and shows that the hyper-class representation is able to provide truly useful reference information for recommendation systems and makes recommendations much better than existing algorithms, i.e., this approach is efficient and promising.