A Kind of Deep Belief Networks Based on Nonlinear Features Extraction with Application to PM2.5 Concentration Prediction and Diagnosis
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摘要: 传统的深度置信网络（Deep brief networks，DBN）在建立高维数据分类模型时，往往存在网络负荷大，运算复杂度高等问题.本文首先基于非线性PCA（NPCA）对高维样本数据进行降维，然后以提取到的非线性特征作为DBN的网络输入，构建了一类含非线性特征提取预处理机制的DBN分类器.并从信息熵理论的角度出发，证明了所提改进DBN分类器在网络结构和算法复杂度方面的优势.通过一个PM2.5浓度预测与影响因素诊断实例，验证了所提改进DBN在一类分类和影响因素诊断问题中的应用，并与传统的分类器进行对比，显示了所提方法在建模精度及收敛速度上的优势.Abstract: To build a classifier model of high dimensional data, the traditional deep brief networks (DBN) modeling method suffers from large network load and high algorithm complexity. In this work, the data dimension is reduced based on the nonlinear PCA (NPCA), then a new DBN classifier with nonlinear feature extraction pre-processing mechanism is proposed where the nonlinear feature is extracted as the network input to the DBN. With the entropy theory, the advantage of the improved DBN is proved in terms of network structure and algorithm complexity. A PM2.5 concentration prediction and diagnosis problem is employed to exemplify applications of the proposed methods. Compared with the traditional classifier, it shows the advantage of the proposed method in modeling accuracy and convergence speed.
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Key words:
- Deep brief networks (DBN) /
- nonlinear-PCA (NPCA) /
- PM2.5 /
- entropy
1) 本文责任编委 刘艳军 -
图 4 PM2.5预测诊断流程图
Fig. 4 The flow chart of PM2.5 concentration$'$s prediction and diagnosis
图 6 华电二区的预测效果对比图
Fig. 6 The comparison in the second area of Huadian with different structures
图 8 华电二区超限数据贡献图
Fig. 8 The contribution chart of the overrun data in the second area of Huadian
表 1 网络结构对比
Table 1 The comparison of the network structure
模型 结构 隐含层节点数 总节点数 算法总空间复杂度 NPCA-DBN (6-10-10) + (6-10-6-6-1) 32 55 $6\times 10\times 10+6\times 10\times 6\times 6\times 1$ DBN 10-12-10-10-1 32 43 $10\times 12\times 10\times 10$ 
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表 2 建模精度与收敛速度对比
Table 2 The comparison of the network structure
监测点 指标 NPCA-DBN NPCA-ANN NPCA-SVM NPCA-PLS DBN ANN SVM PLS 地表 MRE ($\times10^{-2}$) 13.32 22.21 13.14 26.82 17.92 23.40 12.19 24.54 水厂 训练时间(s) 44 16 180 46 89 33 349 94 华电 MRE ($\times10^{-2}$) 14.57 25.15 13.04 29.48 17.01 24.16 10.22 27.16 二区 训练时间(s) 37 12 211 49 90 38 401 103 胶片 MRE ($\times10^{-2}$) 10.51 26.49 11.09 33.16 12.77 23.32 12.73 30.06 厂 训练时间(s) 42 16 198 57 108 42 399 108
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表 3 PM2.5浓度级别
Table 3 The PM2.5 concentration level
浓度范围(${\rm \mu g/m^3}$) 级别 优良级别 0$\, \sim\, $50 1级 优 50$\, \sim\, $100 2级 良 101$\, \sim\, $150 3级 轻度污染 151$\, \sim\, $200 4级 中度污染 201$\, \sim\, $ 5级 重度污染
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