A Nesterov-type Acceleration with Adaptive Localized Cayley Parametrization for Optimization over the Stiefel Manifold

Whitehead products in the complex Stiefel manifolds

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091500016941 ◽

1983 ◽

Vol 26 (2) ◽

pp. 241-251 ◽

Cited By ~ 1

Author(s):

Yasukuni Furukawa

Keyword(s):

Stiefel Manifold ◽

Isotropy Group ◽

Homotopy Groups ◽

Stiefel Manifolds

The complex Stiefel manifoldWn,k, wheren≦k≦1, is a space whose points arek-frames inCn. By using the formula of McCarty [4], we will make the calculations of the Whitehead products in the groups π*(Wn,k). The case of real and quaternionic will be treated by Nomura and Furukawa [7]. The product [[η],j1l] appears as generator of the isotropy group of the identity map of Stiefel manifolds. In this note we use freely the results of the 2-components of the homotopy groups of real and complex Stiefel manifolds such as Paechter [8], Hoo-Mahowald [1], Nomura [5], Sigrist [9] and Nomura-Furukawa [6].

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Blind Data Detection in Massive MIMO via ℓ3-norm Maximization over the Stiefel Manifold

IEEE Transactions on Wireless Communications ◽

10.1109/twc.2020.3033699 ◽

2020 ◽

pp. 1-1

Author(s):

Ye Xue ◽

Yifei Shen ◽

Vincent Lau ◽

Jun Zhang ◽

Khaled B. Letaief

Keyword(s):

Massive Mimo ◽

Stiefel Manifold ◽

Data Detection

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Clustering of cancer data based on Stiefel manifold for multiple views

BMC Bioinformatics ◽

10.1186/s12859-021-04195-4 ◽

2021 ◽

Vol 22 (1) ◽

Author(s):

Jing Tian ◽

Jianping Zhao ◽

Chunhou Zheng

Keyword(s):

Optimization Problem ◽

Nearest Neighbor ◽

Search Algorithm ◽

Stiefel Manifold ◽

Omics Data ◽

K Nearest Neighbor ◽

Cancer Data ◽

Clustering Problem ◽

Multiple Datasets ◽

Cluster Class

Abstract Background In recent years, various sequencing techniques have been used to collect biomedical omics datasets. It is usually possible to obtain multiple types of omics data from a single patient sample. Clustering of omics data plays an indispensable role in biological and medical research, and it is helpful to reveal data structures from multiple collections. Nevertheless, clustering of omics data consists of many challenges. The primary challenges in omics data analysis come from high dimension of data and small size of sample. Therefore, it is difficult to find a suitable integration method for structural analysis of multiple datasets. Results In this paper, a multi-view clustering based on Stiefel manifold method (MCSM) is proposed. The MCSM method comprises three core steps. Firstly, we established a binary optimization model for the simultaneous clustering problem. Secondly, we solved the optimization problem by linear search algorithm based on Stiefel manifold. Finally, we integrated the clustering results obtained from three omics by using k-nearest neighbor method. We applied this approach to four cancer datasets on TCGA. The result shows that our method is superior to several state-of-art methods, which depends on the hypothesis that the underlying omics cluster class is the same. Conclusion Particularly, our approach has better performance than compared approaches when the underlying clusters are inconsistent. For patients with different subtypes, both consistent and differential clusters can be identified at the same time.

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