基于图半监督学习的球面嵌入算法 Alternative Title Spherical Embedding Algorithm Based On Graph Semi Supervised Learning 王琦 Thesis Advisor 董国雄 2018-04-20 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 学士 Keyword 球面嵌入 极大完全子图 半监督学习 Abstract 针对现有的球面嵌入算法在部分点间的距离缺失的情况下不能准确嵌入的 问题,本文 出了一种基于图半监督学习的球面嵌入算法,它能够在数据集只有 近邻点间或部分点间的距离的情形下,将数据集嵌入到单位球面上。该算法首先 将给定的数据集表示为一个无向带权图并找到该图中的极大完全子图,进而利用 现有的基于 MDS 的球面嵌入算法将这一完全图嵌入到单位球面上,最后使用图半 监督学习的方法,对数据集的整体分布进行估计,进而得到其他点在球面上的位置。为检验算法的性能,本文生成了两个测试数据集对算法进行测试,一个数据 集为球面上均匀分布的数据集,另一个数据集为球面 Fisher–Bingham 分布的数 据集。实验结果表明,本文 出的算法在两类数据集下均较为准确的将数据嵌入 到了球面空间上。因此,本文 出的方法可以较好的实现对数据在低维球面空间 上的嵌入,这对于计算机视觉及模式识别等领域中的诸多问题都能有所帮助。 Other Abstract Aiming at the problem that the existing spherical embedding algorithm cannot embed accurately when the distance between some points is missing,this paper proposes a new spherical embedding algorithm that only the distance between neighboring points or part of points is available.The algorithm first expresses a given data set as an undirected weighted graph and finds the maximal complete sub-graph in the graph, and then uses the existing MDS-based spherical embedding algorithm to embed this complete graph on the unit sphere. Finally, the semi-supervised learning method is used to estimate the overall distribution of the data set, and then obtain the position of other points on the sphere.To test the performance of the algorithm, two test data sets were generated to test the algorithm. One data set was a data set that was uniformly distributed on the sphere,and the other data set was a Fisher-Bingham distributed data set.Experimental results show that the proposed algorithm embeds data into spherical space more accurately in both data sets. Therefore,the method proposed in this paper can achieve better embedding of data in low-dimensional spherical space,which can be helpful for many problems in the fields of computer vision and pattern recognition. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/225107 Collection 数学与统计学院 Recommended CitationGB/T 7714 王琦. 基于图半监督学习的球面嵌入算法[D]. 兰州. 兰州大学,2018.
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