更改

超图已被广泛用于机器学习中，常作为一种数据结构或一种正则化属性分类器 classifier regularization。 <ref>{{citation| last1 = Zhou | first1 = Dengyong| last2 = Huang | first2 = Jiayuan | last3=Scholkopf | first3=Bernhard| issue = 2| journal = Advances in Neural Information Processing Systems| pages = 1601–1608| title = Learning with hypergraphs: clustering, classification, and embedding| year = 2006}}</ref> 这些应用包括推荐系统  recommender system (社团作为超边)<ref>{{citation|last1=Tan | first1=Shulong | last2=Bu | first2=Jiajun | last3=Chen | first3=Chun | last4=Xu | first4=Bin | last5=Wang | first5=Can | last6=He | first6=Xiaofei|issue = 1| journal = ACM Transactions on Multimedia Computing, Communications, and Applications| title = Using rich social media information for music recommendation via hypergraph model| year = 2013|url=https://www.researchgate.net/publication/226075153| bibcode=2011smma.book..213T }}</ref>、图像检索 image retrieval(相关性作为超边) <ref>{{citation|last1=Liu | first1=Qingshan | last2=Huang | first2=Yuchi | last3=Metaxas | first3=Dimitris N. |issue = 10–11| journal = Pattern Recognition| title = Hypergraph with sampling for image retrieval| pages=2255–2262| year = 2013| doi=10.1016/j.patcog.2010.07.014 | volume=44}}</ref> 、和生物信息学(生物、化学分子间相互作用作为超边)<ref>{{citation|last1=Patro |first1=Rob | last2=Kingsoford | first2=Carl| issue = 10–11| journal = Bioinformatics| title = Predicting protein interactions via parsimonious network history inference| year = 2013| pages=237–246|doi=10.1093/bioinformatics/btt224 |pmid=23812989 |pmc=3694678 | volume=29}}</ref>。比较典型的超图机器学习方法包括：超图谱聚类法 spectral clustering（用拉普拉斯超图 hypergraph Laplacian 扩展光谱图理论 spectral graph theory）<ref>{{citation|last1=Gao | first1=Tue | last2=Wang | first2=Meng | last3=Zha|first3=Zheng-Jun|last4=Shen|first4=Jialie|last5=Li|first5=Xuelong|last6=Wu|first6=Xindong|issue = 1| journal = IEEE Transactions on Image Processing| volume=22 | title = Visual-textual joint relevance learning for tag-based social image search| year = 2013| pages=363–376|url=http://ink.library.smu.edu.sg/cgi/viewcontent.cgi?article=2510&context=sis_research | doi=10.1109/tip.2012.2202676| pmid=22692911 | bibcode=2013ITIP...22..363Y }}</ref> 和超图半监督学习 semi-supervised learning（通过引入超图结构来对结果进行限定）。<ref>{{citation|last1=Tian|first1=Ze|last2=Hwang|first2=TaeHyun|last3=Kuang|first3=Rui|issue = 21| journal = Bioinformatics| title = A hypergraph-based learning algorithm for classifying gene expression and arrayCGH data with prior knowledge| year = 2009| pages=2831–2838|doi=10.1093/bioinformatics/btp467|pmid=19648139| volume=25|doi-access=free}}</ref>对于大尺寸的超图，可以使用Apache Spark构建的分布式框架<ref name=hyperx />。

超图已被广泛用于机器学习中，常作为一种数据结构或一种正则化属性分类器 classifier regularization。 <ref>{{citation| last1 = Zhou | first1 = Dengyong| last2 = Huang | first2 = Jiayuan | last3=Scholkopf | first3=Bernhard| issue = 2| journal = Advances in Neural Information Processing Systems| pages = 1601–1608| title = Learning with hypergraphs: clustering, classification, and embedding| year = 2006}}</ref> 这些应用包括推荐系统  recommender system (社团作为超边)<ref>{{citation|last1=Tan | first1=Shulong | last2=Bu | first2=Jiajun | last3=Chen | first3=Chun | last4=Xu | first4=Bin | last5=Wang | first5=Can | last6=He | first6=Xiaofei|issue = 1| journal = ACM Transactions on Multimedia Computing, Communications, and Applications| title = Using rich social media information for music recommendation via hypergraph model| year = 2013|url=https://www.researchgate.net/publication/226075153| bibcode=2011smma.book..213T }}</ref>、图像检索 image retrieval(相关性作为超边) <ref>{{citation|last1=Liu | first1=Qingshan | last2=Huang | first2=Yuchi | last3=Metaxas | first3=Dimitris N. |issue = 10–11| journal = Pattern Recognition| title = Hypergraph with sampling for image retrieval| pages=2255–2262| year = 2013| doi=10.1016/j.patcog.2010.07.014 | volume=44}}</ref> 、和生物信息学(生物、化学分子间相互作用作为超边)<ref>{{citation|last1=Patro |first1=Rob | last2=Kingsoford | first2=Carl| issue = 10–11| journal = Bioinformatics| title = Predicting protein interactions via parsimonious network history inference| year = 2013| pages=237–246|doi=10.1093/bioinformatics/btt224 |pmid=23812989 |pmc=3694678 | volume=29}}</ref>。比较典型的超图机器学习方法包括：超图谱聚类法 spectral clustering（用拉普拉斯超图 hypergraph Laplacian 扩展光谱图理论 spectral graph theory）<ref>{{citation|last1=Gao | first1=Tue | last2=Wang | first2=Meng | last3=Zha|first3=Zheng-Jun|last4=Shen|first4=Jialie|last5=Li|first5=Xuelong|last6=Wu|first6=Xindong|issue = 1| journal = IEEE Transactions on Image Processing| volume=22 | title = Visual-textual joint relevance learning for tag-based social image search| year = 2013| pages=363–376|url=http://ink.library.smu.edu.sg/cgi/viewcontent.cgi?article=2510&context=sis_research | doi=10.1109/tip.2012.2202676| pmid=22692911 | bibcode=2013ITIP...22..363Y }}</ref> 和超图半监督学习 semi-supervised learning（通过引入超图结构来对结果进行限定）。<ref>{{citation|last1=Tian|first1=Ze|last2=Hwang|first2=TaeHyun|last3=Kuang|first3=Rui|issue = 21| journal = Bioinformatics| title = A hypergraph-based learning algorithm for classifying gene expression and arrayCGH data with prior knowledge| year = 2009| pages=2831–2838|doi=10.1093/bioinformatics/btp467|pmid=19648139| volume=25|doi-access=free}}</ref>对于大尺寸的超图，可以使用Apache Spark构建的分布式框架<ref name=hyperx />。

==See also==

==进一步阅读==

* [[Simplicial complex]]

* [https://en.wikipedia.org/wiki/Simplicial_complex Simplicial complex 简单复合体]

* [[Combinatorial design]]

* [https://en.wikipedia.org/wiki/Combinatorial_design Combinatorial design 组合设计]

* [[Factor graph]]

* [https://en.wikipedia.org/wiki/Factor_graph Factor graph 因子图]

* [[Greedoid]]

* [https://en.wikipedia.org/wiki/Greedoid Greedoid 序阵]

* [[Incidence structure]]

* [https://en.wikipedia.org/wiki/Incidence_structure Incidence structure 入射结构 ]

* [[Matroid]]

* [https://en.wikipedia.org/wiki/Matroid Matroid 拟阵]

* [[Multigraph]]

* [https://en.wikipedia.org/wiki/Multigraph Multigraph 多重图]

* [[P system]]

* [https://en.wikipedia.org/wiki/P_system P system P系统]

* [[Sparse matrix-vector multiplication]]

* [https://en.wikipedia.org/wiki/Sparse_matrix-vector_multiplication Sparse matrix-vector multiplication 稀疏矩阵-向量乘法]

*[[Matching in hypergraphs]]

*[https://en.wikipedia.org/wiki/Matching_(graph_theory)#Matching_in_hypergraphs Matching in hypergraphs 超图中的匹配]

==参考文献==

==参考文献==