scholarly journals High-Order Entropy-Based Closures for Linear Transport in Slab Geometry II: A Computational Study of the Optimization Problem

2012 ◽  
Vol 34 (4) ◽  
pp. B361-B391 ◽  
Author(s):  
Graham W. Alldredge ◽  
Cory D. Hauck ◽  
André L. Tits
Keyword(s):  
Optimization Problem ◽  
Computational Study ◽  
High Order ◽  
Slab Geometry ◽  
Linear Transport

scholarly journals Multi-View Spectral Clustering with Optimal Neighborhood Laplacian Matrix

2020 ◽  
Vol 34 (04) ◽  
pp. 6965-6972
Author(s):  
Sihang Zhou ◽  
Xinwang Liu ◽  
Jiyuan Liu ◽  
Xifeng Guo ◽  
Yawei Zhao ◽  
...  
Keyword(s):  
Spectral Clustering ◽  
Optimization Problem ◽  
State Of The Art ◽  
Laplacian Matrix ◽  
High Order ◽  
Insufficient Information ◽  
Complementary Information ◽  
First Order ◽  
Laplacian Matrices ◽  
Group Data

Multi-view spectral clustering aims to group data into different categories by optimally exploring complementary information from multiple Laplacian matrices. However, existing methods usually linearly combine a group of pre-specified first-order Laplacian matrices to construct an optimal Laplacian matrix, which may result in limited representation capability and insufficient information exploitation. In this paper, we propose a novel optimal neighborhood multi-view spectral clustering (ONMSC) algorithm to address these issues. Specifically, the proposed algorithm generates an optimal Laplacian matrix by searching the neighborhood of both the linear combination of the first-order and high-order base Laplacian matrices simultaneously. This design enhances the representative capacity of the optimal Laplacian and better utilizes the hidden high-order connection information, leading to improved clustering performance. An efficient algorithm with proved convergence is designed to solve the resultant optimization problem. Extensive experimental results on 9 datasets demonstrate the superiority of our algorithm against state-of-the-art methods, which verifies the effectiveness and advantages of the proposed ONMSC.

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