https://github.com/mostafaelhoushi/fos
Implementation of Fast Orthogonal Search (FOS) Algorithm in MATLAB
https://github.com/mostafaelhoushi/fos
polynomial-regression regression signal-analysis system-identification
Last synced: 2 months ago
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Implementation of Fast Orthogonal Search (FOS) Algorithm in MATLAB
- Host: GitHub
- URL: https://github.com/mostafaelhoushi/fos
- Owner: mostafaelhoushi
- Created: 2017-11-09T06:26:58.000Z (over 7 years ago)
- Default Branch: master
- Last Pushed: 2019-08-04T15:09:47.000Z (almost 6 years ago)
- Last Synced: 2025-03-28T02:37:51.447Z (3 months ago)
- Topics: polynomial-regression, regression, signal-analysis, system-identification
- Language: MATLAB
- Homepage:
- Size: 2.35 MB
- Stars: 14
- Watchers: 4
- Forks: 2
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
Awesome Lists containing this project
README
[//]: # (Image References)
[fos_model]: ./docs/fos_model.png "FOS Model"
# Fast Orthogonal Search (FOS) Algorithm
Implementation of Fast Orthogonal Search (FOS) Algorithm as described in this paper:
```
@article{Korenberg:1989:ROA:2733743.2733908,
author = {Korenberg, M. J.},
title = {A Robust Orthogonal Algorithm for System Identification and Time-series Analysis},
journal = {Biol. Cybern.},
issue_date = {February 1989},
volume = {60},
number = {4},
month = feb,
year = {1989},
issn = {0340-1200},
pages = {267--276},
numpages = {10},
url = {http://dx.doi.org/10.1007/BF00204124},
doi = {10.1007/BF00204124},
acmid = {2733908},
publisher = {Springer-Verlag New York, Inc.},
address = {Secaucus, NJ, USA},
}
```
## What is FOS?
![FOS Model][fos_model]
FOS tries to provide a mathematical model to map the input signal of a system to its output signal, using a time-series polynomail equation.
For a system that produces, at epoch 
, output 
for input 
, FOS tries to model the output as a summation of polynomial terms:
where each polyomial term, 
is a product of inputs and/or outputs, possibly at different epochs:
such that:
The FOS algorithm aims to minimize the error 
between the actual output, and the predicted output, 
.
, 
and 
are paremeters to the FOS algorithm and are therefore determined by the user:
- is the maximum order of the polynomial
- is the maximum lag in input that the current output can depend on
- is the maximum lag in output that the current output can depend on
If, and are set to zero, then FOS will aim to find the relationship between the input and output for a time-independent system.
## Getting Started
We advise you to run tests `test1.m` and `test2.m` and go through their code to understand how to train and evaluate a model using FOS.
## Citing Author
If you find this code useful in your work, please cite the following paper by the author of the code:
```
@article{ElhoushiSurvvey2017,
author = {Elhoushi, Mostafa and Georgy, Jacques and Noureldin, Aboelmagd and Korenberg, Michael J.},
title = {A Survey on Approaches of Motion Mode Recognition Using Sensors},
journal = {IEEE Trans. Intelligent Transportation Systems},
keywords = {activity_recognition},
number = 7,
pages = {1662-1686},
url = {https://ieeexplore.ieee.org/document/7726001},
volume = 18,
year = 2017
}
```