Semi-supervised Multi-view Classification via Consistency Constraints

doi:10.3778/j.issn.1673-9418.2009020

Journal of Frontiers of Computer Science and Technology ›› 2022, Vol. 16 ›› Issue (1): 242-252.DOI: 10.3778/j.issn.1673-9418.2009020

• Theory and Algorithm • Previous Articles Next Articles

Semi-supervised Multi-view Classification via Consistency Constraints

LIU Yu, MENG Min⁺(), WU Jigang

School of Computer Science and Technology, Guangdong University of Technology, Guangzhou 510006, China

Received:2020-09-08 Revised:2020-11-06 Online:2022-01-01 Published:2020-11-19
About author:LIU Yu, born in 1996, M.S. candidate. His research interests include image processing and face recognition.
MENG Min, born in 1984, Ph.D., associate professor, member of CCF. Her research interests include image processing, machine learning, etc.
WU Jigang, born in 1963, Ph.D., distinguished professor at School of Computer Science and Technology, Guangdong University of Technology, member of CCF. His research interests include network computing, cloud computing, machine intelligence and reconfigurable architecture.
Supported by:
National Natural Science Foundation of China(61702114);National Natural Science Foundation of China(61672171)

一致性约束的半监督多视图分类

刘宇, 孟敏⁺(), 武继刚

广东工业大学计算机学院,广州 510006

通讯作者: + E-mail: minmeng@gdut.edu.cn
作者简介:刘宇（1996—）,男,湖南衡阳人,硕士研究生,主要研究方向为图像处理、人脸识别。
孟敏（1984—）,女,河南汝南人,博士,副教授,CCF会员,主要研究方向为图像处理、机器学习等。
武继刚（1963—）,男,江苏沛县人,博士,广东工业大学计算机学院特聘教授,CCF会员,主要研究方向为网络计算、云计算、机器智能、可重构体系结构。
基金资助:
国家自然科学基金(61702114);国家自然科学基金(61672171)

Abstract

Abstract:

Since the traditional semi-supervised multi-view algorithms seldom take into account the diversity of information contained in different views and neglect the consistency of spatial structure between different views, they hardly achieve promising performance when dealing with multi-view data with noise and outlying entries. Although some researchers have proposed semi-supervised multi-view methods,these methods do not make full use of sample discriminant information and subspace structure information under different metric learning,which leads to the unsatisfactory classification results. To deal with the above problems,this paper proposes a semi-supervised multi-view classification via consistency constraint (SMCC) for multi-view data analysis. Firstly, the consistency constraints between different views are enhanced based on the Hilbert-Schmidt independence criteria (HSIC). Then, the dimensionality reduction is performed by feature projection to preserve the local manifold structure, which is integrated with Frobenius norm constraint to improve the robustness of the algorithm. Furthermore, the corresponding weights are adaptively assigned to different views to reduce the influence of feature information and noise pollution in different views. Finally, the proposed model can be solved efficiently using the linear alternative direction method with adaptive penalty and eigen-decomposition. The experimental results on four benchmark datasets show that the proposed algorithm can discover more effective discriminant information from multi-view data and its accuracy is improved.

Key words: multi-view, adaptive weight, consistency constraints, feature projection, semi-supervised learning

摘要：

由于传统半监督模式下的多视图算法很少考虑到不同视图中数据包含信息的差异性,且忽视了不同视图间存在着空间结构的一致性,算法在含有噪声和异常点的多视图数据中性能较差。尽管有研究者已经提出了半监督多视图方法,但这些方法没有充分利用样本判别信息以及不同度量学习下的子空间结构信息,从而导致分类结果不理想。针对以上问题,提出了一致性约束的半监督多视图分类算法（SMCC）。首先,基于希尔伯特-施密特独立性准则（HSIC）加强对不同视图之间的一致性约束。然后,通过保留原始数据的空间局部流形结构进行特征投影来降低数据空间维度,并结合F范数约束提高算法的鲁棒性。进一步,对不同视图自适应地赋予相应的权重,降低在不同视图中数据含有不同特征信息与噪声污染的影响。最后,基于线性交替方向乘子法与特征分解方法对模型进行求解。在四个基准数据集上的实验结果表明,提出的算法能够捕获多视图数据中更多的有效判别信息,准确性得到了提高。

关键词: 多视图, 自适应权重, 一致性约束, 特征投影, 半监督学习

CLC Number:

TP301.6

LIU Yu, MENG Min, WU Jigang. Semi-supervised Multi-view Classification via Consistency Constraints[J]. Journal of Frontiers of Computer Science and Technology, 2022, 16(1): 242-252.

刘宇, 孟敏, 武继刚. 一致性约束的半监督多视图分类[J]. 计算机科学与探索, 2022, 16(1): 242-252.

Figures/Tables 7

Table 1 Symbolic interpretation

符号	含义
$P v$	第v个视图的投影矩阵
$X v$	第v个视图的样本矩阵
$Y$	原始数据的标签矩阵
$F$	预测标签矩阵
$S$	相似矩阵
$L S$	拉普拉斯矩阵
$I$	单位矩阵
$1, e$	全为1的列向量
$x, y$	列向量
$\| \| · \| \| F$ 与 $\| \| · \| \| 2$	F范数与2范数
$tr (*)$	迹函数
$rank (*)$	秩函数
$α, β, λ$	超参数
$w$	权重

Table 1 Symbolic interpretation

符号	含义
$P v$	第v个视图的投影矩阵
$X v$	第v个视图的样本矩阵
$Y$	原始数据的标签矩阵
$F$	预测标签矩阵
$S$	相似矩阵
$L S$	拉普拉斯矩阵
$I$	单位矩阵
$1, e$	全为1的列向量
$x, y$	列向量
$\| \| · \| \| F$ 与 $\| \| · \| \| 2$	F范数与2范数
$tr (*)$	迹函数
$rank (*)$	秩函数
$α, β, λ$	超参数
$w$	权重

Fig.1 Flowchart of algorithm framework

Fig.2 Sample images from experimental data sets

Table 2 Performance (mean±standard deviation) of different algorithms on ORL and Yale databases

方法	ORL数据库上不同标签比例下分类准确率/%				Yale数据库上不同标签比例下分类准确率/%
方法	10%	20%	30%	40%	10%	20%	30%	40%
LP（1）	54.03±3.92	67.25±3.67	73.58±2.95	77.27±2.73	38.60±5.86	53.01±5.04	58.63±3.92	61.47±3.63
LP（2）	70.89±2.34	83.18±2.42	88.60±3.21	93.10±2.21	45.27±8.72	63.12±6.78	72.22±4.40	73.73±4.15
LP（3）	59.79±3.77	73.67±2.15	80.06±2.12	84.59±2.20	44.27±7.23	63.10±7.45	68.96±4.51	74.59±3.92
AMGL	85.67±2.00	91.22±2.03	94.66±1.05	96.26±1.42	64.72±19.2	81.64±4.82	83.20±5.28	85.20±5.76
MVAR	76.76±1.45	90.10±2.72	96.35±1.53	98.01±1.29	60.60±7.43	81.71±3.50	83.74±2.07	87.10±2.84
MLAN	71.00±3.28	80.42±2.94	85.07±2.84	88.63±2.92	58.89±15.3	70.08±9.89	77.92±3.25	81.97±4.72
FISH-MML	54.81±3.89	67.94±3.30	79.46±2.74	84.33±2.31	40.70±8.35	55.56±8.12	61.00±7.82	65.71±4.26
SMCC	84.17±2.32	92.19±1.83	95.00±1.52	97.08±1.36	74.07±9.71	82.67±7.82	85.33±4.92	89.04±3.57

Table 3 Performance (mean±standard deviation) of different algorithms on MSRCv1 and HW databases

方法	MSRCv1数据库上不同标签比例下分类准确率/%				HW数据库上不同标签比例下分类准确率/%
方法	10%	20%	30%	40%	10%	20%	30%	40%
LP（1）	62.58±5.30	69.27±5.14	75.25±3.20	78.32±3.44	97.08±1.95	97.21±1.82	97.39±1.21	97.50±0.95
LP（2）	62.95±6.65	73.29±4.85	79.32±4.54	82.97±2.14	80.22±2.19	80.33±1.90	80.38±2.07	80.93±1.25
LP（3）	59.78±5.37	66.42±4.34	70.36±2.07	71.87±4.66	74.67±2.60	76.25±2.24	77.21±1.31	77.67±1.56
LP（4）	60.22±9.99	68.91±4.46	73.92±3.73	75.73±3.41	67.89±2.28	69.31±1.95	69.71±2.52	71.17±2.14
LP（5）	n/a	n/a	n/a	n/a	67.83±3.12	69.13±2.51	69.64±1.89	71.08±1.53
LP（6）	n/a	n/a	n/a	n/a	43.89±2.34	47.31±1.50	47.93±1.02	50.92±2.36
AMGL	83.60±3.20	88.12±2.80	89.56±1.40	90.96±1.20	90.65±1.63	93.45±1.95	95.11±1.70	96.00±1.26
MVAR	86.46±3.74	90.76±1.51	91.47±1.71	93.38±1.94	85.84±2.39	88.97±1.68	90.28±1.37	91.09±0.88
MLAN	83.89±2.72	88.75±2.70	89.69±1.78	91.07±1.72	97.59±1.03	97.88±0.81	97.89±0.58	98.05±0.62
FISH-MML	77.78±3.32	84.05±1.91	86.26±1.52	87.38±1.28	93.01±0.62	94.69±1.15	95.56±1.30	96.78±1.08
SMCC	89.42±2.97	91.31±2.35	92.65±1.82	93.49±1.75	97.61±1.32	98.06±0.95	98.24±0.65	98.35±0.57

Fig.3 Relationship between value of objective function and the number of iterations on different databases

Fig.4 Influence of parameters $\beta $ and $\lambda $ on algorithm classification on different databases

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Semi-supervised Multi-view Classification via Consistency Constraints

一致性约束的半监督多视图分类

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