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

Multi-input and Multi-variable systems

Multi-input and Multi-variable systems

Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence...

Linear time-invariant Systems

Linear time-invariant Systems

A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...

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,...

Multicompartment Models: Overview

Multicompartment Models: Overview

Multicompartment models are mathematical constructs that depict how drugs are distributed and eliminated within the body. They segment the body into several compartments, symbolizing various physiological or anatomical areas connected through drug transfer processes such as absorption, metabolism, distribution, and elimination.
These models offer a more comprehensive representation of drug behavior in the body than one-compartment models. They accommodate the complexity of drug distribution,...

Discrete-Time Fourier Series

Discrete-Time Fourier Series

The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
For a discrete-time periodic signal x[n]...

Discrete-time Fourier transform

Discrete-time Fourier transform

The Discrete-Time Fourier Transform (DTFT) is an essential mathematical tool for analyzing discrete-time signals, converting them from the time domain to the frequency domain. This transformation allows for examining the frequency components of discrete signals, providing insights into their spectral characteristics. In the DTFT, the continuous integral used in the continuous-time Fourier transform is replaced by a summation to accommodate the discrete nature of the signal.
One of the notable...

You might also read

Related Articles

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

Sort by

Same author

Stimulation of soy seeds using environmentally friendly magnetic and electric fields.

Scientific reports·2023

Same author

Structured multi-criteria model of self-managed motivation in organizations based on happiness at work: pandemic related study.

Scientific reports·2023

Same author

Impact of electromagnetic stimulation on the mechanical and photophysical properties of alfalfa leaves.

Scientific reports·2022

Same author

Entropy and Ergodicity of Boole-Type Transformations.

Entropy (Basel, Switzerland)·2021

Same author

Chemometric approach to characterization of the selected grape seed oils based on their fatty acids composition and FTIR spectroscopy.

Scientific reports·2021

Same author

Geometric Aspects of the Isentropic Liquid Dynamics and Vorticity Invariants.

Entropy (Basel, Switzerland)·2020

Search research articles

Related Experiment Video

Updated: Sep 17, 2025

Basics of Multivariate Analysis in Neuroimaging Data

Basics of Multivariate Analysis in Neuroimaging Data

Published on: July 24, 2010

4D hypercomplex-valued neural network in multivariate time series forecasting.

Radosław Kycia¹, Agnieszka Niemczynowicz²

¹Faculty of Computer Science and Telecommunications, Cracow University of Technology, Kraków, Poland.

Scientific Reports

|July 3, 2025

Summary

This summary is machine-generated.

Hypercomplex neural networks (NNs) offer efficient multivariate time series forecasting. Architectures with dense hypercomplex layers provide comparable accuracy to other models but require fewer parameters, enabling faster data processing.

Keywords:

4D hypercomplex algebras Clifford algebras Convolutional neural networks Coquaternions Hypercomplex-valued neural networks Hyperparametrs optimization LSTM Quaternions Times series forecasting

More Related Videos

Using Informational Connectivity to Measure the Synchronous Emergence of fMRI Multi-voxel Information Across Time

Using Informational Connectivity to Measure the Synchronous Emergence of fMRI Multi-voxel Information Across Time

Published on: July 1, 2014

Cross-Modal Multivariate Pattern Analysis

Cross-Modal Multivariate Pattern Analysis

Published on: November 9, 2011

Related Experiment Videos

Last Updated: Sep 17, 2025

Basics of Multivariate Analysis in Neuroimaging Data

Basics of Multivariate Analysis in Neuroimaging Data

Published on: July 24, 2010

Using Informational Connectivity to Measure the Synchronous Emergence of fMRI Multi-voxel Information Across Time

Using Informational Connectivity to Measure the Synchronous Emergence of fMRI Multi-voxel Information Across Time

Published on: July 1, 2014

Cross-Modal Multivariate Pattern Analysis

Cross-Modal Multivariate Pattern Analysis

Published on: November 9, 2011

Area of Science:

Artificial Intelligence
Machine Learning
Financial Forecasting

Background:

Multivariate time series forecasting is crucial in finance.
Traditional neural network architectures can be computationally intensive.

Purpose of the Study:

To evaluate hypercomplex neural network architectures for multivariate time series forecasting.
To compare the performance of different input layer types (convolutional, LSTM, dense) within hypercomplex models.

Main Methods:

Testing three classes of four-dimensional (4D) hypercomplex neural network architectures.
Utilizing four related Stock Market multivariate time series datasets.
Performing hyperparameter optimization for each architecture class.

Main Results:

Hypercomplex dense layers achieved comparable Mean Absolute Error (MAE) accuracy to other architectures.
Models with hypercomplex dense layers had significantly fewer trainable parameters.
Hypercomplex neural networks processed time series data faster.

Conclusions:

Hypercomplex neural networks are effective for multivariate time series forecasting.
Dense hypercomplex layers offer an efficient alternative with reduced computational cost.
Input time series ordering impacts model performance.