It is not always reasonable to set a fixed weight value to an attribute (or a variable) because this cannot accurately maintain the similarity between users and leads to decrease the performance of collaborative filtering recommendation algorithms. In this paper, a piecewise weighting method is proposed with the hyper-class representation for improving the collaborative filtering recommendation. Specifically, a kernel function is first applied to map the original data into the kernel space, and to learn the weight of each attribute. And then, the hyper-class representation of the data is constructed to learn the weight of the segmented attribute value (hyper-class) for each attribute, so as to construct a piecewise weighting function. In addition, the piecewise weighting function is applied to calculate the similarity between users for a collaborative filtering recommendation. Finally, experiments are conducted to examine the collaborative filtering recommendation algorithm, and show that the proposed algorithm with piecewise weighting functions is more efficient than the compared algorithm with fixed weight values, in terms of Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and Precision.

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.