Computing Colourful Simplicial Depth and Median in ℝ2

2022 ◽  
Author(s):  
Greg Aloupis ◽  
Tamon Stephen ◽  
Olga Zasenko
Keyword(s):  
Simplicial Depth ◽  
Colourful Simplicial Depth

scholarly journals A Combinatorial Approach to Colourful Simplicial Depth

2014 ◽  
Vol 28 (1) ◽  
pp. 306-322 ◽  
Author(s):  
Antoine Deza ◽  
Frédéric Meunier ◽  
Pauline Sarrabezolles
Keyword(s):  
Combinatorial Approach ◽  
Simplicial Depth ◽  
Colourful Simplicial Depth

scholarly journals Colourful Simplicial Depth

2006 ◽  
Vol 35 (4) ◽  
pp. 597-615 ◽  
Author(s):  
Antoine Deza ◽  
Sui Huang ◽  
Tamon Stephen ◽  
Tamas Terlaky
Keyword(s):  
Simplicial Depth ◽  
Colourful Simplicial Depth

scholarly journals A quadratic lower bound for colourful simplicial depth

2008 ◽  
Vol 16 (4) ◽  
pp. 324-327 ◽  
Author(s):  
Tamon Stephen ◽  
Hugh Thomas
Keyword(s):  
Lower Bound ◽  
Simplicial Depth ◽  
Colourful Simplicial Depth

scholarly journals The colourful simplicial depth conjecture

2015 ◽  
Vol 130 ◽  
pp. 119-128 ◽  
Author(s):  
Pauline Sarrabezolles
Keyword(s):  
Simplicial Depth ◽  
Colourful Simplicial Depth

scholarly journals A Note on Lower Bounds for Colourful Simplicial Depth

Symmetry ◽  
2013 ◽  
Vol 5 (1) ◽  
pp. 47-53 ◽  
Author(s):  
Antoine Deza ◽  
Tamon Stephen ◽  
Feng Xie
Keyword(s):  
Lower Bounds ◽  
Simplicial Depth ◽  
Colourful Simplicial Depth

scholarly journals Computing Simplicial Depth by Using Importance Sampling Algorithm and Its Application

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Fanyu Meng ◽  
Wei Shao ◽  
Yuxia Su
Keyword(s):  
Importance Sampling ◽  
Testing Machine ◽  
Exact Algorithm ◽  
Real Data ◽  
Exact Algorithms ◽  
Approximate Algorithm ◽  
Sampling Algorithm ◽  
Simplicial Depth ◽  
Low Efficiency ◽  
Np Problem

Simplicial depth (SD) plays an important role in discriminant analysis, hypothesis testing, machine learning, and engineering computations. However, the computation of simplicial depth is hugely challenging because the exact algorithm is an NP problem with dimension d and sample size n as input arguments. The approximate algorithm for simplicial depth computation has extremely low efficiency, especially in high-dimensional cases. In this study, we design an importance sampling algorithm for the computation of simplicial depth. As an advanced Monte Carlo method, the proposed algorithm outperforms other approximate and exact algorithms in accuracy and efficiency, as shown by simulated and real data experiments. Furthermore, we illustrate the robustness of simplicial depth in regression analysis through a concrete physical data experiment.

scholarly journals Simplified simplicial depth for regression and autoregressive growth processes

2016 ◽  
Vol 173 ◽  
pp. 125-146 ◽  
Author(s):  
Christoph P. Kustosz ◽  
Christine H. Müller ◽  
Martin Wendler
Keyword(s):  
Growth Processes ◽  
Simplicial Depth
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