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摘要:
针对标签分布不平衡的轨道角动量(OAM)识别问题，提出了一种基于全局代价SMOTE的深度极限学习机(DELM)的衍生模型。与典型的机器学习方法不同，本文所提方法能够获得映射模型解析表达，避免了反复的参数优化过程，使模型适用于工程应用。在数据生成阶段，利用协方差的逆矩阵去除量纲的影响，有效度量了同一类样本的差异性。在模型选择阶段，考虑了光信号在大气湍流中的传输特性，采用DELM表征光斑样本和标签之间的映射关系，并用FISTA算法计算模型的解析表达。在不同强度的大气湍流数据集上进行实验，对比了WELM、k近邻等代表性的方法。实验结果表明，在不同的湍流强度下，所提方法均方根误差达到
0.2049 和0.0894 ，各项评价指标均优于对比方法。证明了所提方法能够充分挖掘了OAM光斑集合的特征，具有更好的识别效果。Abstract:To identify orbital angular momentum (OAM) with imbalanced label, a derived model based on global cost SMOTE and deep extreme learning machine (DELM) has been proposed. Different from typical machine learning methods, the proposed model can obtain the analytical expression of the mapping model. It will avoid the repeated parameter optimization process, thus building a suitable model for time-varying engineering applications. In the data generation stage, the inverse matrix of covariance is used to remove the dimension influence, and the differences of the same sample set are measured effectively. In the model selection stage, considering the transmission characteristics of light signal in atmosphere turbulence, the DELM is adopted to quantify the mapping relationship between light spots and labels. Then the FISTA algorithm helps to calculate the analytical expression of the model. Experiments are carried out on different intensity atmospheric turbulence data sets. The representative comparative methods include WELM and K-nearest neighbor. Experimental results show that the root mean square error(RMSE) of the proposed method achieve
0.2049 and0.0894 , which are superior to the comparison method under different turbulence intensities. It is proved that the proposed method can fully explore the characteristics of OAM spot collection and has better recognition effect. -
图 3 所提方法和对比方法的RMSE对比图
Figure 3. Comparison chart of RMSE between the proposed method and other methods
图 4 所提方法和对比方法的G-mean对比图
Figure 4. Comparison chart of G-mean between the proposed method and other methods
图 5 所提方法和对比方法的ROC曲线对比图
Figure 5. Comparison chart of ROC curve between the proposed method and other methods
表 1 所提方法伪代码
Table 1. The pseudocode of proposed method
（1）数据生成阶段，根据式（11）进行重采样；
（2）if(样本数目<平均样本数目)；
（3） 根据式（12）计算马氏距离；
添加新样本到样本集合中sample=[sample s]；
（4）end；
（5）利用多层ELM网络构建特征向量与OAM标签关系；
（6）初始化目标函数并根据式（15）制定最优准则；
（7）计算Lipschitz条件的近似函数；
（8）利用FISTA迭代求解每一层输出权重；
（9）利用式（19）计算综合权重；
（10）返回输出层权重的解析解$ {{\boldsymbol{\beta }}_j} $和OAM模态估计值。
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表 3 消融实验
Table 3. The ablation experiment
深度ELM SMOTE-DELM $ C_n^2 = {10^{ - 14}} $ 0.2552 0.2049 $ C_n^2 = {10^{ - 15}} $ 0.0924 0.0894
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