聚类分析
歧管(流体力学)
斯蒂弗尔流形
歧管对齐
子空间拓扑
非线性降维
图形
迭代函数
数学
计算机科学
算法
理论计算机科学
人工智能
纯数学
降维
数学分析
工程类
机械工程
作者
Aparajita Khan,Pradipta Maji
出处
期刊:IEEE transactions on neural networks and learning systems
[Institute of Electrical and Electronics Engineers]
日期:2022-08-01
卷期号:33 (8): 3895-3907
被引量:10
标识
DOI:10.1109/tnnls.2021.3054789
摘要
The meaningful patterns embedded in high-dimensional multi-view data sets typically tend to have a much more compact representation that often lies close to a low-dimensional manifold. Identification of hidden structures in such data mainly depends on the proper modeling of the geometry of low-dimensional manifolds. In this regard, this article presents a manifold optimization-based integrative clustering algorithm for multi-view data. To identify consensus clusters, the algorithm constructs a joint graph Laplacian that contains denoised cluster information of the individual views. It optimizes a joint clustering objective while reducing the disagreement between the cluster structures conveyed by the joint and individual views. The optimization is performed alternatively over $k$ -means and Stiefel manifolds. The Stiefel manifold helps to model the nonlinearities and differential clusters within the individual views, whereas $k$ -means manifold tries to elucidate the best-fit joint cluster structure of the data. A gradient-based movement is performed separately on the manifold of each view so that individual nonlinearity is preserved while looking for shared cluster information. The convergence of the proposed algorithm is established over the manifold and asymptotic convergence bound is obtained to quantify theoretically how fast the sequence of iterates generated by the algorithm converges to an optimal solution. The integrative clustering on benchmark and multi-omics cancer data sets demonstrates that the proposed algorithm outperforms state-of-the-art multi-view clustering approaches.
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