L1AdaptiveTrendFilter.jl is a Julia package for filtering and identifying unknown underlying trends of a given noisy signal. It is originally a supplemental material for our paper "L1 Adaptive Trend Filter via Fast Coordinate Descent".
In order to use it, download the package in the julia prompt with the command:
Pkg.clone("git://github.com/joaquimg/L1AdaptiveTrendFilter.jl.git")
Then simply include the command using L1AdaptiveTrendFilter to import the package.
The function l1_adaptive_trend_filter performs the filtering via coordinate descent and takes the following required inputs:
- y : Signal or time-series to be filtered; (Must be a vector of reals)
- components: List of integers corresponding to the types of components to be considered. (must be a vector of integers containing some of the following numbers: 1 = Step, 2 = Spike, 3 = Slope, 4 = Sine, 5 = Cossine )
Optional inputs:
- f: Vector of overcomplete frequencies (Default=ø);
- numλ: Size of the regularizer path for the parameter λ (Default=40);
- numγ: Size of the regularizer path for the parameter γ (Default=10);
- MAXITER: Maximum number of iterations (Default=500);
- verbose: Boolean flag for displaying progress of algorithm (Default=false);
- lower_bounds: List of lower bounds for each component type (Default=[-∞,-∞,-∞,-∞,-∞]);
- upper_bounds: List of upper bpunds for each component type (Default=[+∞,+∞,+∞,+∞,+∞]).
This function returns:
- β_path: Path of components coefficients;
- y_path: Path of filtered signals;
- β_best: Best components coefficients according to the EBIC criteria;
- y_best: Best filtered signal according to the EBIC criteria;
- λ_best: Best value for the λ regularizer according to the EBIC criteria;
- γ_best: Best value for the γ regularizer according to the EBIC criteria.
# after initializing the package with
# Pkg.clone("git://github.com/joaquimg/L1AdaptiveTrendFilter.jl.git")
#You must include the library with:
using L1AdaptiveTrendFilter
y = rand(18) # some inputs
components = [1,3] #(meaning we only consider step and slope components)
# run the algorithm
beta_path, y_path, beta_best, y_best, lambda_best, gamma_best = l1_adaptive_trend_filter(y,components)
one option is to remove the package and add it again:
Pkg.rm("L1AdaptiveTrendFilter")
workspace()
Pkg.clone("git://github.com/joaquimg/L1AdaptiveTrendFilter.jl.git")
Please use the following Bibtex reference:
@article{souto2016ell_1,
title={$$\backslash$ ell\_1 $ Adaptive Trend Filter via Fast Coordinate Descent},
author={Souto, Mario and Garcia, Joaquim D and Amaral, Gustavo C},
journal={arXiv preprint arXiv:1603.03799},
year={2016}
}