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.