Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Linear Approximation in Time Domain

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...

Linear Approximation in Frequency Domain

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

The collection of speech data for the assessment of cognition remotely: Balancing ethical and practical challenges.

Alzheimer's & dementia (Amsterdam, Netherlands)·2026

Same author

Improving LIME Stability via Density-Awareness: Evaluation and Comparison of AKDE-LIME.

Applied artificial intelligence : AAI·2026

Same author

Biomarkers.

Alzheimer's & dementia : the journal of the Alzheimer's Association·2025

Same author

Perimeter Security Utilizing Thermal Object Detection.

Sensors (Basel, Switzerland)·2025

Same author

A hybrid neuromarketing approach exploiting EEG graph signal processing and gaze dynamic patterning.

Brain informatics·2025

Same author

Comparative analysis of muscle synergies in gait of stroke patients and healthy controls.

Frontiers in human neuroscience·2025

Same journal

Cortex-anchored sensor-space harmonics for event-related EEG.

Journal of neural engineering·2026

Same journal

Neural mechanisms of mixed speech and grasp representation in sensorimotor cortices.

Journal of neural engineering·2026

Same journal

Developing a binary communication protocol between biological neural networks using virtual white matter.

Journal of neural engineering·2026

Same journal

Spatiotemporally distinctive astrocytic and neuronal responses to repetitive intracortical microstimulation.

Journal of neural engineering·2026

Same journal

A neural mass modelling framework for evaluating EEG source localisation of seizure activity.

Journal of neural engineering·2026

Same journal

Functional and effective connectivity methods from SEEG for characterizing epileptogenic networks in refractory epilepsy: a comprehensive review and future directions.

Journal of neural engineering·2026

See all related articles

Search research articles

Related Experiment Video

Updated: Aug 16, 2025

Simultaneous Scalp Electroencephalography EEG, Electromyography EMG, and Whole-body Segmental Inertial Recording for Multi-modal Neural Decoding

Simultaneous Scalp Electroencephalography EEG, Electromyography EMG, and Whole-body Segmental Inertial Recording for Multi-modal Neural Decoding

Published on: July 26, 2013

Revisiting Riemannian geometry-based EEG decoding through approximate joint diagonalization.

Fotis P Kalaganis¹, Nikos A Laskaris², Vangelis P Oikonomou¹

¹Centre for Research and Technology Hellas, Information Technologies Institute, Multimedia Knowledge and Social Media Analytics Laboratory, Thermi-Thessaloniki 57001, Greece.

Journal of Neural Engineering

|December 21, 2022

Summary

This summary is machine-generated.

This study simplifies complex Riemannian geometry for electroencephalography (EEG) analysis by reconstructing spatial covariance matrices. The new method reduces computational load, making advanced neuroscientific explorations more accessible and efficient.

Keywords:

EEG Riemannian geometry approximate joint diagonalization covariance electroencephalography manifold

More Related Videos

Mapping Cortical Dynamics Using Simultaneous MEG/EEG and Anatomically-constrained Minimum-norm Estimates: an Auditory Attention Example

Mapping Cortical Dynamics Using Simultaneous MEG/EEG and Anatomically-constrained Minimum-norm Estimates: an Auditory Attention Example

Published on: October 24, 2012

EEG Mu Rhythm in Typical and Atypical Development

EEG Mu Rhythm in Typical and Atypical Development

Published on: April 9, 2014

Related Experiment Videos

Last Updated: Aug 16, 2025

Simultaneous Scalp Electroencephalography EEG, Electromyography EMG, and Whole-body Segmental Inertial Recording for Multi-modal Neural Decoding

Simultaneous Scalp Electroencephalography EEG, Electromyography EMG, and Whole-body Segmental Inertial Recording for Multi-modal Neural Decoding

Published on: July 26, 2013

Mapping Cortical Dynamics Using Simultaneous MEG/EEG and Anatomically-constrained Minimum-norm Estimates: an Auditory Attention Example

Mapping Cortical Dynamics Using Simultaneous MEG/EEG and Anatomically-constrained Minimum-norm Estimates: an Auditory Attention Example

Published on: October 24, 2012

EEG Mu Rhythm in Typical and Atypical Development

EEG Mu Rhythm in Typical and Atypical Development

Published on: April 9, 2014

Area of Science:

Computational Neuroscience
Signal Processing
Machine Learning

Background:

Riemannian geometry offers advanced analytical tools for electroencephalography (EEG) data.
Widespread adoption is limited by mathematical complexity and high computational demands.

Purpose of the Study:

To simplify Riemannian geometry concepts for EEG processing.
To develop an efficient and comprehensible scheme for neuroscientific exploration.
To reduce computational complexity in Riemannian geometry applications.

Main Methods:

Reconstruction of spatial covariance matrices using approximate joint diagonalization.
Identification of a common eigenspace to simplify Riemannian geometry computations.
Validation using real and synthetic EEG data.

Main Results:

The reconstruction process adheres to physiologically plausible assumptions.
Significantly reduced computational complexity for Riemannian geometry schemes.
Bridged the gap between mathematical rigor and computational neuroscience.

Conclusions:

The developed approach facilitates robust and efficient neuroscientific explorations using Riemannian geometry.
Reformulated and reintroduced 'Symmetric Positive Definite (SPD) Matrix Quantization' and 'Coding over SPD Atoms'.
Paves the way for broader application of Riemannian geometry in EEG analysis.