L1AdaptiveTrendFilter.jl

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".

Installing

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.

Filtering

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.

Example

# 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)

Re-installing

one option is to remove the package and add it again:

Pkg.rm("L1AdaptiveTrendFilter")
workspace()
Pkg.clone("git://github.com/joaquimg/L1AdaptiveTrendFilter.jl.git")

Citing this package

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}
}