基于双约束非负矩阵分解的多视角聚类

发布时间：2018-05-11 23:34

本文选题：多视角聚类 + 非负矩阵分解　；参考：《大连理工大学》2016年硕士论文

【摘要】：聚类一直是机器学习领域一个非常重要的内容,各种各样高效的聚类算法被不断地提出。另一方面,伴随着网络的发展,数据的获取也变得越来越容易,一组相同的样本经常被不同的特征描述。如何有效地利用不同维度空间下的数据来提高聚类的准确率是国内外众多学者研究的课题,这就使得多视角聚类在近些年来取得了迅速的发展。鉴于非负矩阵分解(NMF)可解释性强、算法实现简单,基于NMF的聚类算法受到了广泛地关注。不仅如此,实验证明基于NMF的聚类算法无论在聚类的准确率还是在聚类的稳定性方面都可以媲美其他的聚类算法。伴随着NMF在聚类方面的成功,大批的学者将NMF应用到了多视角聚类中。基于NMF的多视角聚类算法继承了NMF的优点并较大幅度地提升了聚类的准确率。当然,基于NMF的多视角聚类算法也有着以下缺陷。首先,非负矩阵分解得到的分解结果并不唯一；其次非负矩阵分解的多视角聚类算法并没有为每一个视角得到一个标准的正交基；最后非负矩阵分解并没有保留数据的局部信息。为了弥补上述的三个不足,本文提出了一个基于双约束非负矩阵分解(DCNMF)的多视角聚类算法。先在每个视角下的基矩阵施加正交约束,之后使用矩阵转置相乘来进一步改进算法,以得到标准的正交基并避免正交性带来的高算法复杂度。进一步的,为了保留不同视图之间的局部信息,在目标函数中添加流形正则项。最后,本文提出了一个流形正则项参数的迭代规则,这样做能够平衡矩阵分解的重构误差和流形正则项,此外还可以加快算法的收敛速度。之后文章从理论和实验两个方面证明了算法的收敛性,并设计实验证明DCNMF的优越性。与其他算法相比,DCNMF在算法的准确率和运行效率上都有显著的提高。
[Abstract]:Clustering has been a very important part of the field of machine learning. All kinds of efficient clustering algorithms are constantly proposed. On the other hand, with the development of the network, the acquisition of data is becoming more and more easy. A group of identical samples are often described by different features. For example, how to effectively use data in different dimensional space Improving the accuracy of clustering is the subject of many scholars at home and abroad. This makes multi view clustering make rapid development in recent years. In view of the strong interpretability of the non negative matrix decomposition (NMF) and the simple implementation of the algorithm, the clustering algorithm based on NMF has received extensive attention. Not only that, the experiment proves that the clustering algorithm based on NMF is the same. The accuracy of clustering and the stability of clustering can be compared to other clustering algorithms. With the success of NMF in clustering, a large number of scholars have applied NMF to multi view clustering. The multi view clustering algorithm based on NMF inherits the advantages of NMF and greatly improves the accuracy of clustering. Of course, NMF based on NMF The multi view clustering algorithm also has the following defects. First, the decomposition results obtained by the non negative matrix decomposition are not unique; secondly, the multi view clustering algorithm with non negative matrix decomposition does not get a standard orthogonal basis for every angle of view; finally, the non negative matrix decomposition does not retain the local information of the data. In order to make up the above three In this paper, a multi view clustering algorithm based on double constraint non negative matrix decomposition (DCNMF) is proposed in this paper. First, the orthogonal constraints are applied to the base matrix in each view. Then the algorithm is further improved by using matrix transposed multiplication to obtain the standard orthogonal basis and avoid the high algorithmic complexity caused by orthogonality. The local information between different views is retained and the manifold regular items are added to the objective function. Finally, an iterative rule of the regular parameter of the manifold is proposed in this paper, which can balance the reconstruction error of the matrix decomposition and the regular term of the manifold. In addition, the convergence speed of the algorithm can be accelerated. After that, the article proves two aspects of theory and experiment. The convergence of the algorithm is clear, and the design experiment proves the superiority of DCNMF. Compared with other algorithms, DCNMF has a remarkable improvement in the accuracy and efficiency of the algorithm.

【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TP181;TP311.13

【参考文献】