A Proof of the Frobenius Rank Equality

1980 ◽  
Vol 87 (6) ◽  
pp. 481 ◽  
Author(s):  
Donald W. Robinson
Keyword(s):  
Rank Equality

A Proof of the Frobenius Rank Equality

1980 ◽  
Vol 87 (6) ◽  
pp. 481-482 ◽  
Author(s):  
Donald W. Robinson
Keyword(s):  
Rank Equality

scholarly journals The Frobenius rank equality for morphisms

1980 ◽  
Vol 29 ◽  
pp. 413-421
Author(s):  
Donald W. Robinson
Keyword(s):  
Rank Equality

scholarly journals Robust Ordinal Embedding from Contaminated Relative Comparisons

2019 ◽  
Vol 33 ◽  
pp. 7908-7915 ◽  
Author(s):  
Ke Ma ◽  
Qianqian Xu ◽  
Xiaochun Cao
Keyword(s):  
Exact Solution ◽  
Optimal Solutions ◽  
Unified Framework ◽  
Real World Data ◽  
Traditional Methods ◽  
Promising Tool ◽  
Multi Stage ◽  
Relative Comparisons ◽  
Rank Equality ◽  
Embedding Methods

Existing ordinal embedding methods usually follow a twostage routine: outlier detection is first employed to pick out the inconsistent comparisons; then an embedding is learned from the clean data. However, learning in a multi-stage manner is well-known to suffer from sub-optimal solutions. In this paper, we propose a unified framework to jointly identify the contaminated comparisons and derive reliable embeddings. The merits of our method are three-fold: (1) By virtue of the proposed unified framework, the sub-optimality of traditional methods is largely alleviated; (2) The proposed method is aware of global inconsistency by minimizing a corresponding cost, while traditional methods only involve local inconsistency; (3) Instead of considering the nuclear norm heuristics, we adopt an exact solution for rank equality constraint. Our studies are supported by experiments with both simulated examples and real-world data. The proposed framework provides us a promising tool for robust ordinal embedding from the contaminated comparisons.

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