RAFF - Robust Algebraic Fitting Function
This package implements a robust method to fit a given function (described by its parameters) to input data. The method is based on the LOVO algorithm  and also in a suitable voting strategy in order automatically eliminate outliers.
Potential use of this package is in statistical problems which depend on fitting functions or in more specific fields like computer vision for problems related shape detection.
For a brief description of the potential of this program and the difference between related strategies in the literature, like least square, consider the following dataset
A=[-2.0 5.0; -1.5 3.25; -1.0 2.0 ; -0.5 1.25; 0.0 1.0 ; 0.5 2.55; 1.0 2.0 ; 1.5 3.25; 2.0 5.0 ;]
Let us assume that we wish to find a fitting function given by parameters
x, x and the model
f(t[i])≈A[i,2] in the least square sense. When we apply a least square strategy we obtain
and when we apply RAFF strategy we get
Note that RAFF detects (automatically) the model
f(t)=1.0*t^2 +1.0 that is, RAFF detects the point
(0.5,2.55) like an outlier and excludes the influence of this point for determine
Consequently, RAFF detects the number of possible outliers and in the same time, which their are. This fact distinguishes RAFF from other techniques like  or classical least square.
Other useful examples are found in the documentation and also in directory
RAFF is a package registered in the
General repository. Consequently, in order to install
RAFF, just type in
julia> ] add RAFF
Several files with test problems are provided inside directory
test/test_problems. We also provide some
scripts to create new random test problems, visualize and solve them
RAFF. Those files can be found in
test/scripts. For a detailed explanation of each
script file, please refer to the
Any suggestions or contributions to
RAFF are very welcome.
a open-source software available through the MIT license, so users are
free to create their own versions of the software. Users are specially
encouraged to participate on the project in the following ways:
- Modifications to the code can be submitter as pull requests to the
- Bugs, suggestions and questions can be raised as issues in the project's Github page.
- General doubts can also be sent directly to
fncsobral at uem dot br.
The following table outlines the results found by the current version
RAFF in the test set.
|Name||Dim.||N Points||N Outl.||Found||Correct||Time (s)||Status||Solution|
|C1||4||10||2||2||2||0.0006||1||[ 1.999e+00, 1.142e-02, -4.023e+00, -1.053e+01]|
|C2||4||10||2||1||1||0.0005||1||[ 1.575e+00, 2.635e+00, 3.434e+01, -7.821e+00]|
|C3||4||10||2||2||1||0.0005||1||[ 4.221e-01, -1.596e+01, 2.388e+01, 2.146e+02]|
|C4||4||10||1||1||1||0.0005||1||[ 2.701e+00, 2.556e+00, -5.914e+01, -1.021e+02]|
|C5||4||100||1||9||1||0.0210||1||[ 2.114e+00, 1.160e+00, -6.590e+00, -1.971e+01]|
|CI1||3||25||2||2||2||0.0020||1||[ 9.741e-01, 9.769e-01, 5.020e+00]|
|E1||3||20||1||1||0||0.0263||1||[ 3.271e+03, -9.884e+01, 5.507e+01]|
|E2||3||10||1||2||0||0.0110||1||[ 2.137e+03, 2.760e+03, 2.369e+02]|
|E3||3||100||1||1||1||0.2297||1||[ 9.590e+02, 9.632e+03, 3.940e-01]|
|E4||3||100||10||1||1||0.2308||1||[ 1.139e+03, 9.370e+03, 4.206e-01]|
|LOG1||4||10||1||0||0||0.0042||1||[ 1.479e+03, 2.201e+03, 6.611e+01, -2.075e+02]|
- Francisco Sobral (Leader)
- Emerson Vitor Castelani
- Ronaldo Lopes
- Wesley Shirabayashi
The authors of this package were sponsored by Fundação Araucária, project number 002/17 - 47223. If you would like to cite this package, please use
Castelani, E. V., Lopes, R., Shirabayashi, W., & Sobral, F. N. C. (2019). RAFF.jl: Robust Algebraic Fitting Function in Julia. Journal of Open Source Software, 4(39), 1385. https://doi.org/10.21105/joss.01385
 Andreani, R., Martínez, J. M., Martínez, L., & Yano, F. S. (2009). Low order-value optimization and applications. Journal of Global Optimization, 43(1), 1-22.