Quantum algorithm for soft margin support vector machine with hinge loss function

Soft margin support vector machine(SVM)with hinge loss function is an important classification algorithm,which has been widely used in image recognition,text classification and so on.However,solving soft margin SVM with hinge loss function generally entails the sub-gradient projection algorithm,which is very time-consuming when processing big training data set.To achieve it,an efficient quantum algorithm is proposed.Specifically,this algorithm implements the key task of the sub-gradient projection algorithm to obtain the classical sub-gradients in each iteration,which is mainly based on quantum amplitude estimation and amplification algorithm and the controlled rotation operator.Compared with its classical counterpart,this algorithm has a quadratic speedup on the number of training data points.It is worth emphasizing that the optimal model parameters obtained by this algorithm are in the classical form rather than in the quantum state form.This enables the algorithm to classify new data at little cost when the optimal model parameters are determined.

基于改进支持向量机的药品包装纸盒快速鉴别研究

目的为实现在司法鉴定中对药品包装纸盒类检材的简单快速无损检验。方法利用X射线荧光光谱法,以Rh做阳极靶,在电压为50 kV、电流为30μA、功率为1.5 kW的条件下,对40组不同产地、不同厂家的药品包装纸盒样本进行检验。依据药品包装纸盒的化学元素组成对样本设置标签,建立蒙特卡洛算法(Monte Carlo Algorithm,MC)优化下的支持向量机(Support Vector Machine,SVM)分类模型,对惩罚因子进行仿真寻优,同时结合分治算法实现折半查找,使迭代过程具有自我学习能力,最终基于K-fold交叉验证,得到兼具拟合性和衍生性的惩罚因子组。结果计算机模拟结果表明,当3组支持向量机惩罚因子设置为933、280、732时,MC-SVM模型可实现对100%的训练集的拟合以及90%的预测集的分类,Hinge Loss函数最低损失值为0.0938。结论此方法可为药品包装纸盒类物证的检验以及支持向量机的参数优化提供新思路。