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摘要:
针对标签分布不平衡的涡旋光束轨道角动量(OAM)识别问题，提出了一种基于全局代价的合成少数类过采样技术（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，并用快速迭代收缩阈值FISTA算法计算模型的解析表达式。在不同强度的大气湍流数据集上进行实验，对比了WELM、k近邻等代表性方法性能。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 the vortex beams orbital angular momentum (OAM) with imbalanced labels, this paper proposes a derived model based on global cost SMOTE and deep extreme learning machine (DELM). Unlike typical machine learning methods, the proposed model can obtain the analytical expression of the mapping model. It avoids repeated parameter optimization, thus building a suitable model for time-varying engineering applications. In the data generation stage, the inverse matrix of covariance was used to remove the influence of dimensions, and the differences among samples within the same category were effectively measured. In the model selection stage, considering the transmission characteristics of light signals in atmospheric turbulence, the DELM was adopted to quantify the mapping relationship between light spots and labels. Then the FISTA algorithm was used to calculate the model’s analytical expression. Experiments were carried out on different intensity atmospheric turbulence data sets. The representative comparative methods include WELM and k-nearest neighbor. Experimental results show that the proposed method’s root mean square error (RMSE) achieves
0.2049 and0.0894 , which are superior to the comparison methods under different turbulence intensities. This proves that the proposed method can fully explore the characteristics of OAM spot collection and has a better recognition effect. -
图 3 所提方法和对比方法的RMSE对比图
Figure 3. Comparison of the RMSE of 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 of the G-mean of 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 of the ROC curves of the proposed method and other methods
表 1 所提方法伪代码
Table 1. 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 2 混淆矩阵
Table 2. Confusion matrix
真实结果 预测结果 正例 反例 正例 TP （真正例） FN （假反例） 反例 FP （假正例） TN （真反例）
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表 3 消融实验
Table 3. 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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