Hypercomplex Widely Linear Estimation Through the Lens of Underpinning Geometry

2019 ◽  
Vol 67 (15) ◽  
pp. 3985-3994 ◽  
Author(s):  
Tohru Nitta ◽  
Masaki Kobayashi ◽  
Danilo P. Mandic
2019 ◽  
Vol 356 (5) ◽  
pp. 3115-3138 ◽  
Author(s):  
Jesús Navarro-Moreno ◽  
Rosa María Fernández-Alcalá ◽  
José Domingo Jiménez-López ◽  
Juan Carlos Ruiz-Molina

2017 ◽  
Vol 136 ◽  
pp. 92-101 ◽  
Author(s):  
José Domingo Jiménez-López ◽  
Rosa María Fernández-Alcalá ◽  
Jesús Navarro-Moreno ◽  
Juan Carlos Ruiz-Molina

Author(s):  
Tohru Nitta

This chapter reviews the widely linear estimation for complex numbers, quaternions, and geometric algebras (or Clifford algebras) and their application examples. It was proved effective mathematically to add , the complex conjugate number of , as an explanatory variable in estimation of complex-valued data in 1995. Thereafter, the technique has been extended to higher-dimensional algebras. The widely linear estimation improves the accuracy and the efficiency of estimation, then expands the scalability of the estimation framework, and is applicable and useful for many fields including neural computing with high-dimensional parameters.


2019 ◽  
Vol 26 (9) ◽  
pp. 1344-1348
Author(s):  
Min Xiang ◽  
Yili Xia ◽  
Danilo P. Mandic

2015 ◽  
Vol 63 (11) ◽  
pp. 4501-4509 ◽  
Author(s):  
Maximilian Matthe ◽  
Luciano Leonel Mendes ◽  
Nicola Michailow ◽  
Dan Zhang ◽  
Gerhard Fettweis

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