计算机科学
半监督学习
图形
拉普拉斯矩阵
地点
非线性降维
聚类分析
数据点
理论计算机科学
可扩展性
光谱聚类
人工智能
机器学习
作者
Yan-Ming Zhang,Kaizhu Huang,Xinwen Hou,Cheng-Lin Liu
出处
期刊:IEEE transactions on cybernetics
[Institute of Electrical and Electronics Engineers]
日期:2014-07-08
被引量:28
标识
DOI:10.1109/tcyb.2014.2300489
摘要
Machine learning based on graph representation, or manifold learning, has attracted great interest in recent years. As the discrete approximation of data manifold, the graph plays a crucial role in these kinds of learning approaches. In this paper, we propose a novel learning method for graph construction, which is distinct from previous methods in that it solves an optimization problem with the aim of directly preserving the local information of the original data set. We show that the proposed objective has close connections with the popular Laplacian Eigenmap problem, and is hence well justified. The optimization turns out to be a quadratic programming problem with n(n-1)/2 variables (n is the number of data points). Exploiting the sparsity of the graph, we further propose a more efficient cutting plane algorithm to solve the problem, making the method better scalable in practice. In the context of clustering and semi-supervised learning, we demonstrated the advantages of our proposed method by experiments.
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