子空间结构保持的多层极限学习机自编码器

陈晓云; 陈媛

doi:10.16383/j.aas.c200684

子空间结构保持的多层极限学习机自编码器

doi: 10.16383/j.aas.c200684

陈晓云^1,,
陈媛^1,

1.
福州大学数学与计算机科学学院福州 350116

基金项目: 国家自然科学基金(11571074)资助

详细信息

作者简介:
陈晓云：福州大学数学与计算机科学学院教授. 主要研究方向为数据挖掘，机器学习和模式识别. 本文通信作者. E-mail: c_xiaoyun@fzu.edu.cn

陈媛：福州大学数学与计算机科学学院硕士研究生. 主要研究方向为数据挖掘和模式识别. E-mail: cy_inohurry@163.com

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出版历程
- 收稿日期: 2020-08-26
- 录用日期: 2021-01-26
- 网络出版日期: 2021-03-17
- 刊出日期: 2022-04-13

Multi-layer Extreme Learning Machine Autoencoder With Subspace Structure Preserving

CHEN Xiao-Yun^1
,,
CHEN Yuan^1
,

1.
College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350116

Funds: Supported by National Natural Science Foundation of China (11571074)

More Information

Author Bio:
CHEN Xiao-Yun　Professor at the College of Mathematics and Computer Science, Fuzhou University. Her research interest covers data mining,machine learning and pattern recognition. Corresponding author of this paper

CHEN Yuan　Master student at the College of Mathematics and Computer Science, Fuzhou University. Her research interest covers data mining and pattern recognition

摘要

摘要: 处理高维复杂数据的聚类问题, 通常需先降维后聚类, 但常用的降维方法未考虑数据的同类聚集性和样本间相关关系, 难以保证降维方法与聚类算法相匹配, 从而导致聚类信息损失. 非线性无监督降维方法极限学习机自编码器(Extreme learning machine, ELM-AE)因其学习速度快、泛化性能好, 近年来被广泛应用于降维及去噪. 为使高维数据投影至低维空间后仍能保持原有子空间结构, 提出基于子空间结构保持的多层极限学习机自编码器降维方法(Multilayer extreme learning machine autoencoder based on subspace structure preserving, ML-SELM-AE). 该方法在保持聚类样本多子空间结构的同时, 利用多层极限学习机自编码器捕获样本集的深层特征. 实验结果表明, 该方法在UCI数据、脑电数据和基因表达谱数据上可以有效提高聚类准确率且取得较高的学习效率.
- 多层极限学习机 /
- 自编码器 /
- 子空间学习 /
- 降维
Abstract: To deal with the clustering problem of high-dimensional complex data, it is usually reguired to reduce the dimensionality and then cluster, but the common dimensional reduction method does not consider the clustering characteristic of the data and the correlation between the samples, so it is difficult to ensure that the dimensional reduction method matches the clustering algorithm, which leads to the loss of clustering information. The nonlinear unsupervised dimensionality reduction method extreme learning machine autoencoder (ELM-AE) has been widely used in dimensionality reduction and denoising in recent years because of its fast learning speed and good generalization performance. In order to maintain the original subspace structure when high-dimensional data is projected into a low-dimensional space, the dimensional reduction method ML-SELM-AE is proposed. This method captures the deep features of the sample set by using the multi-layer extreme learning machine autoencoder while maintaining multi-subspace structure of clustered samples by self-representation model. Experimental results show that the method can effectively improve the clustering accuracy and achieve higher learning efficiency on UCI data, EEG data and gene expression data.
- Multi-layer extreme learning machine /
- autoencoder /
- subspace learning /
- dimensional reduction

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图 1 ELM-AE网络结构

Fig. 1 Network structure of ELM-AE

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图 2 SELM-AE网络结构

Fig. 2 Network structure of SELM-AE

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图 3 ML-SELM-AE网络结构

Fig. 3 Network structure of ML-SELM-AE

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图 4 人造双月数据集

Fig. 4 Artificial double moon data set

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图 5 人造双月数据集一维可视化

Fig. 5 The 1D visualization of artificial double moon data set

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图 6 IRIS数据集的二维可视化

Fig. 6 The 2D visualization of IRIS data set

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图 7 不同c和λ下的目标函数值

Fig. 7 Objective function value under different c and λ

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图 8 不同c和λ取值下的聚类准确率

Fig. 8 Clustering accuracy under different values of c and λ

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表 1 数据集描述

Table 1 The data set description

数据集	维数	样本数	类别数
IRIS	4	150	3
Data set IIb	1440	504	2
Data set II	2400	1020	2
DLBCL	5469	77	2
Colon	2 000	62	2
Prostate0	6033	102	2

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表 2 传统降维方法的聚类准确率(%) (方差, 维数)

Table 2 Comparison of clustering accuracy of traditional methods (%) (variance, dimension)

数据集	k-means	传统算法
数据集	k-means	PCA	LPP	NPE
IRIS	89.13 (0.32)	89.07 (0.34, 4)	90.27 (0.84, 2)	88.67 (0.00, 2)
Data set IIb	86.47 (2.53)	88.21 (0.61, 4)	88.69 (7.33, 4)	89.58 (6.32, 256)
Data set II	72.38 (8.94)	79.31 (4.39, 2)	82.26 (0.13, 512)	82.62 (0.71, 256)
DLBCL	68.83 (0.00)	68.83 (0.00, 2)	63.55 (1.86, 8)	69.09 (0.82, 32)
Colon	54.84 (0.00)	54.84 (0.00, 2)	54.84 (0.00, 2)	56.45 (0.00, 2)
Prostate0	56.86 (0.00)	56.83 (0.00, 2)	56.86 (0.00, 2)	56.86 (0.00, 4)

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表 3 ELM降维方法聚类准确率(%) (方差, 维数)(参数)

Table 3 Comparison of clustering accuracy of ELM methods (%) (variance, dimension)(parameters)

数据集	k-means	Unsupervised ELM			Subspace + unsupervised ELM
数据集	k-means	US-ELM(λ)	ELM-AE(c)	ML-ELM-AE (c)	SNP-ELM(λ,η,δ)	SELM-AE(c, λ)	ML-SELM-AE(c, λ)
IRIS	89.13 (0.32)	93.87 (13.78, 2) (0.1)	93.93 (1.19, 2) (10)	95.20 (1.05, 2) (0.01)	98.46 (0.32, 2) (10, 0.6, −1)	98.00 (0.00, 2) (10, 0.01)	98.40 (0.56, 2) (10, 0.01)
Data set IIb	86.47 (2.53)	91.59 (4.25, 4) (0.1)	91.98 (0.25, 4) (0.1)	92.46 (0.08, 16) (1)	92.06 (0.13, 16) (0.001, 0.8, 0.2)	95.29 (0.06, 8) (0.001, 1)	96.63 (0.00, 8) (0.001, 0.1)
Data set II	72.38 (8.94)	83.18 (0.32, 256) (10)	82.84 (0.00, 2) (0.001)	83.03 (0.00, 2) (0.1)	83.92 (1.65, 2) (10, 0.2, −0.2)	83.14 (0.00, 2) (0.01, 1)	84.22 (0.00, 2) (0.001, 10)
DLBCL	68.83 (0.00)	76.62 (0.00, 32) (0.001)	78.05 (0.73, 2) (0.001)	82.46 (0.68, 2) (0.001)	86.34 (1.78, 8) (0.001, -0.2, 0.6)	83.63 (2.51, 2) (10, 0.1)	86.71 (3.48, 2) (10, 1)
Colon	54.84 (0.00)	67.06 (4.19, 32) (0.001)	69.35 (0.00, 2) (0.001)	80.32 (1.02, 2) (0.001)	85.95 (3.69, 8) (0.001, −0.8, 1)	83.87 (0.00, 4) (10, 0.1)	85.97 (0.78, 2) (10, 0.1)
Prostate0	56.86 (0.00)	64.09 (5.83, 2) (0.01)	75.98 (0.51, 2) (0.01)	79.61 (1.01, 2) (0.01)	82.92 (2.19, 128) (0.1, 0.2, 0.8)	84.31 (0.00, 2) (10, 1)	85.29 (0.00, 2) (10, 0.01)

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表 4 运行时间对比(s)

Table 4 Comparison of running time (s)

数据集	SNP-ELM	SELM-AE	ML-SELM-AE
IRIS	4.58	0.02	0.02
Data set IIb	4.64×10³	0.16	0.33
Data set II	8.24×10³	0.65	0.76
DLBCL	7.77	0.04	0.06
Colon	3.44×10²	0.03	0.11
Prostate0	1.15×10²	0.07	0.13

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表 5 ML-SELM-AE降维前后数据的聚类准确率(%) (方差)

Table 5 Clustering accuracy before and after ML-SELM-AE dimensionality reduction (%) (variance)

数据集	k-means		LSR		LRR		LatLRR
数据集	未降维	已降维	未降维	已降维	未降维	已降维	未降维	已降维
IRIS	89.13 (0.32)	98.40 (0.00)	82.40 (0.69)	97.33 (0.00)	90.87 (0.00)	94.00 (0.83)	81.27 (1.03)	97.33 (0.00)
Data set IIb	86.47 (2.53)	93.25 (0.00)	83.13 (0.00)	86.59 (0.19)	83.13 (0.00)	86.11 (0.00)	83.13 (0.00)	86.48 (0.25)
Data set II	72.38 (8.94)	84.22 (0.00)	83.24 (0.08)	83.29 (0.05)	83.24 (0.00)	83.24 (0.00)	83.24 (0.00)	83.33 (0.00)
DLBCL	68.83 (0.00)	86.71 (3.48)	76.62 (0.00)	81.43 (0.63)	76.62 (0.00)	78.57 (0.68)	74.03 (0.00)	78.18 (3.23)
Colon	54.84 (0.00)	85.97 (0.78)	67.74 (0.00)	74.19 (0.00)	63.39 (0.00)	69.35 (0.00)	66.13 (1.67)	75.65 (4.06)
Prostate0	56.86 (0.00)	85.29 (0.00)	63.82 (1.37)	70.59 (0.00)	57.84 (0.00)	63.73 (0.00)	55.88 (0.00)	74.51 (0.00)

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表 6 三层极限学习机自编码器隐层节点数与聚类准确率(%) (方差)

Table 6 The number of hidden layer nodes and clustering accuracy for three-layer extreme learning machine autoencoder (%) (variance)

数据集	ML-ELM-AE (Multilayer ELM-AE)				ML-SELM-AE (Multilayer SELM-AE)
数据集	500-100-2	500-100-10	500-100-50	500-100-100	500-100-2	500-100-10	500-100-50	500-100-100
Data set IIb	88.69 (0.00)	91.98 (0.25)	90.89 (0.06)	87.66 (0.20)	95.44 (0.00)	94.92 (0.17)	95.44 (0.00)	94.80 (0.33)
Data set II	82.94 (0.00)	82.94 (0.00)	82.94 (0.00)	82.94 (0.00)	83.14 (0.00)	83.04 (0.00)	83.04 (0.00)	83.04 (0.00)
DLBCL	74.03 (0.00)	72.99 (3.29)	72.73 (0.00)	69.22 (0.88)	80.52 (0.00)	80.52 (0.00)	78.57 (2.05)	76.62 (0.00)
Colon	73.87 (1.67)	59.68 (0.00)	69.52 (7.35)	59.03 (0.83)	78.55 (2.53)	75.97 (7.81)	76.13 (9.46)	70.48 (4.37)
Prostate0	66.67 (0.00)	60.78 (0.00)	59.80 (0.00)	62.75 (0.00)	77.16 (0.47)	82.35 (0.00)	78.33 (6.51)	80.39 (0.00)
数据集	2-2-2	10-10-10	50-50-50	100-100-100	2-2-2	10-10-10	50-50-50	100-100-100
Data set IIb	92.46 (0.08)	90.48 (0.00)	90.16 (0.17)	90.40 (0.25)	96.63 (0.00)	95.83 (0.00)	95.44 (0.00)	94.84 (0.00)
Data set II	83.04 (0.00)	83.04 (0.00)	83.04 (0.00)	82.94 (0.00)	84.22 (0.00)	83.14 (0.00)	83.04 (0.00)	83.04 (0.00)
DLBCL	83.12 (0.00)	77.01 (0.63)	68.83 (0.00)	68.70 (0.41)	86.75 (4.23)	80.52 (0.00)	78.96 (0.82)	76.62 (0.00)
Colon	80.64 (0.00)	60.00 (2.50)	70.00 (1.36)	62.90 (0.00)	85.97 (0.78)	68.23 (0.78)	80.65 (0.00)	76.61 (9.48)
Prostate0	80.39 (0.00)	57.45 (0.83)	64.41 (0.47)	63.73 (0.00)	85.29 (0.00)	69.61 (0.00)	79.12 (6.67)	84.31 (0.00)

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