基于互信息自编码和变分路由的胶囊网络结构优化

鲍静益; 徐宁; 尚蕴浩; 楚昕

doi:10.11999/JEIT201094

基于互信息自编码和变分路由的胶囊网络结构优化

doi: 10.11999/JEIT201094

鲍静益¹,
徐宁^2, ,,
尚蕴浩²,
楚昕²

1.
常州工学院常州 213032
2.
河海大学常州校区常州 213022

基金项目: 国家自然科学基金(61872199)，中央高校基本业务费(B210202083)

详细信息

作者简介:
鲍静益：女，1984年生，讲师，研究方向为模式识别与现代信号处理

徐宁：男，1981年生，副教授，研究方向为模式识别与现代信号处理

尚蕴浩：男，1997年生，硕士生，研究方向为图像处理和深度学习

楚昕：女，1995年生，硕士生，研究方向为图像处理和深度学习

通讯作者:
徐宁　20101832@hhu.edu.cn

中图分类号: TP181; TN911.73
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- 被引次数: 0
出版历程
- 收稿日期: 2020-12-30
- 修回日期: 2021-07-01
- 网络出版日期: 2021-07-08
- 刊出日期: 2021-11-23

Optimization in Capsule Network Based on Mutual Information Autoencoder and Variational Routing

1.
Changzhou Institute of Technology, Changzhou 213032, China
2.
Hohai University Changzhou Campus, Changzhou 213022, China

Funds: The National Natural Science Foundation of China (61872199), The Fundamental Research Funds for the Central Universities (B210202083)

摘要

摘要: 胶囊网络是一类有别于卷积神经网络的新型网络模型。该文尝试提高其泛化性和精准性：首先，利用变分路由来缓解经典路由对先验信息依赖性强、易导致模型过拟合的问题。通过使用高斯混合模型(GMM)来拟合低级矩阵胶囊，并利用变分法求取近似分布，避免了参数最大似然点估计的误差，用置信度评估来获得泛化性能的提高；其次，考虑到实际数据大多无标签或者标注困难，构建互信息评价标准的胶囊自编码器，实现特征参数的有效筛选。即通过引入局部编码器，只保留胶囊中对原始输入识别最有效的特征，在减轻网络负担的同时提高了其分类识别的精准性。该文的方法在MNIST, FashionMNIST, CIFAR-10和CIFAR-100等数据集上进行了对比测试，实验结果表明：该文方法对比经典胶囊网络，其性能得到显著改善。
- 胶囊网络 /
- 变分路由 /
- 基于互信息评价的胶囊自编码器
Abstract: Capsule network is a new type of network model which is different from convolutional neural network. This paper attempts to improve its generalization and accuracy. Firstly, variational routing is used to alleviate the problem of classic routing that is highly dependent on prior information and can easily lead to model overfitting. By using the Gaussian Mixture Model (GMM) to fit the low-level matrix capsule and using the variational method to fit the approximation distribution, the error of the maximum likelihood point estimation is avoided, and the confidence calculation is used to improve the generalization performance; Secondly, considering that the actual data is mostly untagged or difficult to label, a capsule autoencoder with mutual information evaluation criterion is constructed to achieve effective selection of feature parameters. That is, by introducing a local encoder, only the most effective features in the capsule for identifying and classifying the original input are retained, which reduces the computational burden of the network while improving the accuracy of classification and recognition at the same time. The method in this paper is compared and tested on datasets such as MNIST, FashionMNIST, CIFAR-10, and CIFAR-100. The experimental results show that the performance of the proposed method is significantly improved compared with the classic capsule network.
- Capsule network /
- Variational routing /
- Capsule autoencoder based on mutual information

HTML全文

图 1 基于变分路由的胶囊网络模型示意图

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图 2 胶囊自编码器结构示意图

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图 3 基于互信息的胶囊自编码器评估模型

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图 4 变分路由胶囊网络分类准确性

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图 5 情况1下的最邻近样本示意图

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图 6 情况2下的最邻近样本示意图

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图 7 情况3下的最邻近样本示意图

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表 1 变分路由算法伪代码

输入：投票矩阵$ {\boldsymbol{\nu }}_{n} $，激活值$ a $，迭代次数T
(1) 初始化：令${\alpha }_{0}=0.001,{ {\boldsymbol{m} } }_{0}={{{\textit{0}}} },{r}_{nk}=1/k,{ {\boldsymbol{W} } }_{0}$为单位矩　　阵，$ {\beta }_{0},{\nu }_{0} $为常数。
(2) VBM 步:
(3) 更新 ${r}_{nk}\leftarrow {r}_{nk}\cdot a$
(4) 更新 ${N}_{k},{\tilde {{\boldsymbol{\nu}} } }_{k},{{\boldsymbol{S}}}_{k}$(通过式(12)—式(14))
(5) 更新 $ {\alpha }_{k} $ (通过式(16))
(6) 更新 ${{\boldsymbol{m}}}_{k},{\beta }_{k},{{\boldsymbol{W}}}_{k}^{-1},{{\boldsymbol{\nu}} }_{k},{{\boldsymbol{W}}}_{k}$(通过式(18)—式(22))
(7) T=T–1
(8) VBE 步：
(9) 更新 $ \mathrm{l}\mathrm{n}{\rho }_{nk} $(通过式(9))
(10) 　　其中 $\ln{\tilde {\pi } }_{k}=\varphi \left({\alpha }_{k}\right)\varphi \left(\displaystyle\sum\nolimits_{i=1}^{k}{\alpha }_{k}\right)$
(11) 　　　$\ln\tilde {\varLambda }=\displaystyle\sum\nolimits_{i=1}^{D}\varphi \left(\frac{ {{\boldsymbol{\nu}} }_{k}+1-i}{2}\right)+D\ln 2+\ln\left\|{\boldsymbol{W}}\right\|$
(12) 　　$\begin{array}{l}{E}_{Mk,{\varLambda }_{K} }\left[{\left({ {\boldsymbol{\nu} } }_{n}-{ {\boldsymbol{\mu} } }_{k}\right)}^{\mathrm{T} }\varLambda \left({ {\boldsymbol{\nu} } }_{n}-{ {\boldsymbol{\mu} } }_{k}\right)\right]\\ =D{\beta }_{k}^{-1}+{{\boldsymbol{\nu}} }_{k}{\left({{\boldsymbol{\nu}}}_{n}-{{\boldsymbol{m}}}_{k}\right)}^{\mathrm{T} }{{\boldsymbol{W}}}_{k}\left({{\boldsymbol{\nu}} }_{n}-{{\boldsymbol{m}}}_{k}\right)\end{array}$
(13) ${{\boldsymbol{M}}}_{k} = \mathrm{s}\mathrm{q}\mathrm{u}\mathrm{e}\mathrm{e}\mathrm{z}\mathrm{e}\left({{\boldsymbol{m}}}_{k}\right)$($ \mathrm{s}\mathrm{q}\mathrm{u}\mathrm{e}\mathrm{e}\mathrm{z}\mathrm{e} $为维度转换函数)
(14) $ a = \mathrm{s}\mathrm{q}\mathrm{u}\mathrm{e}\mathrm{e}\mathrm{z}\mathrm{e}\left({N}_{k}\right) $
(15) 输出：${{\boldsymbol{M}}}_{k} ,a$
首先完成(1)～(2)中输入和初始化步骤，然后开始迭代(4)～(8)的　VBM步和(10)～(13)的VBE步，直到T为0时停止更新，然后计算　(13)～(14)的${{\boldsymbol{M}}}_{k}$和$ a $，并完成(15)。

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表 2 基于编码胶囊的路由伪代码

输入$ x $，t=3，初始化$ b=0 $
步骤1　计算$ c $，$ c\leftarrow \mathrm{S}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{m}\mathrm{a}\mathrm{x}\left(b\right) $
计算$ h $，$ h\leftarrow H\left(x\right) $
计算$ g $，$ g\leftarrow G\left(h\right) $
计算$ u $，$ u=w\cdot \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{c}\mathrm{a}\mathrm{t}\left(g,h\right) $
更新$ s,s\leftarrow \sum \left(c\cdot u\right) $
更新$ v,v\leftarrow \mathrm{S}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{s}\mathrm{h}\left(\mathrm{s}\right) $
更新$ t,t\leftarrow t-1 $
步骤2　更新$ b,b\leftarrow b+\left(g+h\right)\cdot v $
步骤3　输出$ v $
完成步骤1，当$ t $不为0时，完成步骤2更新$ b $，并将$ b $代入　步骤1计算$ v $和$ t $；当$ t $为0时，结束迭代计算，完成步骤3。

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表 3 分类准确率对比(%)

模型	MNIST 准确率	FashionMNIST 准确率
CNN	98.00	90.30
ResNet	99.27	94.90
Inception-V3	99.29	94.97
CN	99.30	92.50
VBCN	99.50	93.50

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表 4 泛化性对比(%)

模型	Two_MNIST 准确率	Two_FashionMNIST 准确率
CNN	45.30	41.40
ResNet	89.09	59.60
Inception-V3	77.35	68.45
CN	93.15	82.60
VBCN	95.65	86.20

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表 5 CIFAR-10测试准确率对比

标签	类别名称	经典CN准确率	改进CN准确率
0	飞机	0.73	0.81
1	汽车	0.76	0.87
2	鸟	0.71	0.74
3	猫	0.45	0.54
4	鹿	0.66	0.76
5	狗	0.55	0.60
6	青蛙	0.58	0.64
7	马	0.77	0.80
8	船	0.59	0.67
9	卡车	0.71	0.77
均值	---	0.65	0.72

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表 6 CIFAR-100测试准确率对比(%)

模型	CIFAR-100准确率
经典CN	46.98
改进CN	52.33

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