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摘要: 在计算机视觉和模式识别领域，随着多源信息越来越多，图像的描述方法也越来越丰富，多视图学习方法能更充分利用这种多源信息，进而提高聚类的准确率.因此，本文提出了两种基于多视图学习的方法：MultiGNMF和MultiGSemiNMF方法.该方法是在矩阵分解的基础之上，结合以往多视图学习的框架准则，并利用了样本的局部结构形成的.MultiGNMF和MultiGSemiNMF算法不仅能学习视图间的互补信息，同时能保持样本的空间结构.但是，MultiGNMF算法只适用于非负的特征矩阵.因此，考虑到SemiNMF算法相对于NMF算法具有更大的扩展性，结合多视图学习的框架，本文又提出了多视图学习的MultiGSemiNMF算法.实验结果证实了这两种方法有较好的性能.Abstract: In computer vision and pattern recognition fields, more and more data are represented by multiple views which describe different perspectives of the data. And multi-view learning methods are developed for ultilizing the information sufficiently. In this paper, we propose two novel clustering methods called MultiGNMF and MultiGSemiNMF, respectively, which are based on multiview learning with local graph regularization, where the innerview relatedness between data is taken into consideration. However, MultiGNMF is based on NMF, which only applies to non-negative matrix. To eliminate this limit, we propose MultiGSemiNMF based on SemiNMF, which is also applicable for negative matrix. The experimental results demonstrate the effectiveness of our proposed methods.
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Key words:
- Multi-view learning /
- clustering /
- matrix factorization /
- local graph regularization
1) 本文责任编委 王立威 -
图 1 在UCI Digit数据库中参数$\lambda$对本文算法的影响
Fig. 1 The influences of $\lambda$ on UCI Digit database
图 2 在CMU PIE数据库中参数$\lambda$对本文算法的影响
Fig. 2 The influences of $\lambda$ on CMU PIE database
表 1 4个数据库的资料
Table 1 The information of four databases
数据库 数量 视图个数 聚类个数 CMU PIE 2 856 2 68 UCI Digit 2 000 2 10 3-Sources 169 3 6 ORL 400 2 40 
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表 2 不同方法在4个数据库中的AC值
Table 2 The AC values by different methods in four databases
算法 UCI Digit CMU PIE 3-Sources ORL BSV ${68.5\pm.05}$ ${55.2\pm.02}$ ${60.8\pm.01}$ ${51.8\pm.02}$ WSV ${63.4\pm.04}$ ${47.6\pm.01}$ ${49.1\pm.03}$ ${42.8\pm.05}$ ConcatNMF ${67.8\pm.06}$ ${51.5\pm.00}$ ${58.6\pm.03}$ ${66.8\pm.02}$ ColNMF ${66.0\pm.05}$ ${56.3\pm.00}$ ${61.3\pm.02}$ ${66.3\pm.04}$ Co-reguSC ${86.6\pm.00}$ ${59.5\pm.02}$ ${47.8\pm.01}$ ${70.5\pm.02}$ MultiNMF ${88.1\pm.01}$ ${64.8\pm.02}$ ${68.4\pm.06}$ ${67.3\pm.03}$ SC-ML ${88.1\pm.00}$ ${72.3\pm.00}$ ${54.0\pm.00}$ ${70.8\pm.00}$ MMSC ${89.4\pm.38}$ ${61.6\pm.06}$ ${69.9\pm.04}$ ${70.7\pm.06}$ AMGL ${82.6\pm.74}$ ${63.6\pm.19}$ ${68.3\pm.12}$ ${64.2\pm.10}$ MultiGNMF ${95.1\pm.10}$ ${72.5\pm.02}$ ${73.4\pm.00}$ ${73.5\pm.00}$ MultiGSemiNMF ${95.6\pm.02}$ ${77.2\pm.12}$ ${79.3\pm.00}$ ${76.2\pm.00}$
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表 3 不同方法在4个数据库中的NMI值
Table 3 The NMI values by different methods in four databases
算法 UCI Digit CMU PIE 3-Sources ORL BSV ${63.4\pm.03}$ ${74.1\pm.00}$ ${53.0\pm.01}$ ${69.8\pm.01}$ WSV ${60.3\pm.03}$ ${69.1\pm.02}$ ${44.1\pm.02}$ ${65.4\pm.04}$ ConcatNMF ${60.3\pm.03}$ ${70.5\pm.00}$ ${51.7\pm.03}$ ${85.1\pm.01}$ ColNMF ${62.1\pm.03}$ ${68.3\pm.00}$ ${55.2\pm.02}$ ${84.5\pm.03}$ Co-reguSC ${77.0\pm.00}$ ${80.5\pm.01}$ ${41.4\pm.01}$ ${80.5\pm.01}$ MultiNMF ${80.4\pm.01}$ ${82.2\pm.02}$ ${60.2\pm.06}$ ${87.6\pm.01}$ SC-ML ${87.6\pm.00}$ ${85.1\pm.00}$ ${45.5\pm.00}$ ${85.3\pm.00}$ MMSC ${88.0\pm.05}$ ${80.3\pm.01}$ ${66.3\pm.09}$ ${85.9\pm.01}$ AMGL ${84.9\pm.33}$ ${81.8\pm.10}$ ${56.9\pm.11}$ ${81.9\pm.02}$ MultiGNMF ${90.1\pm.04}$ ${90.2\pm.01}$ ${65.4\pm.00}$ ${88.5\pm.00}$ MultiGSemiNMF ${91.2\pm.01}$ ${93.8\pm.05}$ ${73.4\pm.00}$ ${89.9\pm.00}$
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