Manifold Optimization-based Hybrid TX/RX Precoding for FD Relay mmWave Systems

2018 ◽  
Author(s):  
Shunya Nishikawa ◽  
Giuseppe Abreu
Keyword(s):  
Manifold Optimization

scholarly journals Heterogeneous Tensor Decomposition for Clustering via Manifold Optimization

2016 ◽  
Vol 38 (3) ◽  
pp. 476-489 ◽  
Author(s):  
Yanfeng Sun ◽  
Junbin Gao ◽  
Xia Hong ◽  
Bamdev Mishra ◽  
Baocai Yin
Keyword(s):  
Tensor Decomposition ◽  
Manifold Optimization

scholarly journals A Brief Introduction to Manifold Optimization

2020 ◽  
Vol 8 (2) ◽  
pp. 199-248 ◽  
Author(s):  
Jiang Hu ◽  
Xin Liu ◽  
Zai-Wen Wen ◽  
Ya-Xiang Yuan
Keyword(s):  
Manifold Optimization

Simultaneous clustering of multiview biomedical data using manifold optimization

2019 ◽  
Vol 35 (20) ◽  
pp. 4029-4037 ◽  
Author(s):  
Yun Yu ◽  
Lei-Hong Zhang ◽  
Shuqin Zhang
Keyword(s):  
Search Algorithm ◽  
Real Data ◽  
Supplementary Information ◽  
Stiefel Manifold ◽  
Biomedical Data ◽  
Clustering Methods ◽  
Multiple Cancer ◽  
Cancer Subtypes ◽  
Kegg Pathways ◽  
Manifold Optimization

Abstract Motivation Multiview clustering has attracted much attention in recent years. Several models and algorithms have been proposed for finding the clusters. However, these methods are developed either to find the consistent/common clusters across different views, or to identify the differential clusters among different views. In reality, both consistent and differential clusters may exist in multiview datasets. Thus, development of simultaneous clustering methods such that both the consistent and the differential clusters can be identified is of great importance. Results In this paper, we proposed one method for simultaneous clustering of multiview data based on manifold optimization. The binary optimization model for finding the clusters is relaxed to a real value optimization problem on the Stiefel manifold, which is solved by the line-search algorithm on manifold. We applied the proposed method to both simulation data and four real datasets from TCGA. Both studies show that when the underlying clusters are consistent, our method performs competitive to the state-of-the-art algorithms. When there are differential clusters, our method performs much better. In the real data study, we performed experiments on cancer stratification and differential cluster (module) identification across multiple cancer subtypes. For the patients of different subtypes, both consistent clusters and differential clusters are identified at the same time. The proposed method identifies more clusters that are enriched by gene ontology and KEGG pathways. The differential clusters could be used to explain the different mechanisms for the cancer development in the patients of different subtypes. Availability and implementation Codes can be downloaded from: http://homepage.fudan.edu.cn/sqzhang/files/2018/12/MVCMOcode.zip. Supplementary information Supplementary data are available at Bioinformatics online.

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