Next Article in Journal
A Novel Cost-Efficient Framework for Critical Heartbeat Task Scheduling Using the Internet of Medical Things in a Fog Cloud System
Previous Article in Journal
Iterative Learning-Based Path and Speed Profile Optimization for an Unmanned Surface Vehicle
Previous Article in Special Issue
A Novel Methodology for Series Arc Fault Detection by Temporal Domain Visualization and Convolutional Neural Network
Open AccessArticle

Lie Group Methods in Blind Signal Processing

by Dariusz Mika 1,* and Jerzy Jozwik 2,*
1
Institute of Technical Sciences and Aviation, The State School of Higher Education in Chelm, 22-100 Chelm, Poland
2
Faculty of Mechanical Engineering, Lublin University of Technology, 20-618 Lublin, Poland
*
Authors to whom correspondence should be addressed.
Sensors 2020, 20(2), 440; https://doi.org/10.3390/s20020440
Received: 31 October 2019 / Revised: 27 December 2019 / Accepted: 7 January 2020 / Published: 13 January 2020
This paper deals with the use of Lie group methods to solve optimization problems in blind signal processing (BSP), including Independent Component Analysis (ICA) and Independent Subspace Analysis (ISA). The paper presents the theoretical fundamentals of Lie groups and Lie algebra, the geometry of problems in BSP as well as the basic ideas of optimization techniques based on Lie groups. Optimization algorithms based on the properties of Lie groups are characterized by the fact that during optimization motion, they ensure permanent bonding with a search space. This property is extremely significant in terms of the stability and dynamics of optimization algorithms. The specific geometry of problems such as ICA and ISA along with the search space homogeneity enable the use of optimization techniques based on the properties of the Lie groups O ( n ) and S O ( n ) . An interesting idea is that of optimization motion in one-parameter commutative subalgebras and toral subalgebras that ensure low computational complexity and high-speed algorithms. View Full-Text
Keywords: geometric optimization; Independent Component Analysis; independent subspace analysis; Lie groups; Lie algebra; toral subalgebra; sensors geometric optimization; Independent Component Analysis; independent subspace analysis; Lie groups; Lie algebra; toral subalgebra; sensors
Show Figures

Figure 1

MDPI and ACS Style

Mika, D.; Jozwik, J. Lie Group Methods in Blind Signal Processing. Sensors 2020, 20, 440.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop