C++ package for learning optimal wavelet bases using a neural network approach.
The functional basis is expressed in terms of a set of filter coefficients (known from wavelet analyses) and the learning is implemented using a neural network with gradient descent. The composite entity is called a Wavenet1 below and is desribed in more detail in the companion note [1].
This package implements the wavenet transform using matrix algebra, for which we rely on the Armadillo C++ linear algebra library [2]. If the HepMC package [3] for experimental particile physics event records is installed, a specialised Generator class, converting HepMC::GenEvent's to Armadillo matrices, can be used. Finally, if the ROOT library [4] is installed, some of the bundled examples allow for producing output graphics showing the results of the learning process
Generally, this package is developed for UNIX-based operating system. Therefore, getting it installed in MacOS and Linux should be relatively smooth. Windows is not supported, but feel free to give it a try if you're feeling brave.
To install the base package itself, simply do:
$ git clone https://github.com/asogaard/Wavenet.git
$ cd Wavenet
That was easy.
However, as mentioned above, the package depends on a few external packages that need to be installed and configured before you can
$ make
and run the Wavenet package. How this is done is described below
LAPACK, BLAS, and Boost [5-7]. Recommended. Improves performance of matrix algebra in Armadillo (below). Pre-installed on MacOS systems. On Linux, install using APT as
$ sudo apt-get install liblapack-dev
$ sudo apt-get install libblas-dev
$ sudo apt-get install libboost-dev
Armadillo [2]. Necessary. The Wavenet package comes bundled with a utility script for downloading and installing Armadillo. Simply call
$ source scripts/downloadArmadillo.sh
This scripts installs the Armadillo package to ./external/ and updates the appropriate path (ARMAPATH) in the Makefile. See also the caveat below.
Alternatively, available on Linux using APT as
$ sudo apt-get install libarmadillo-dev
on MacOS using Homebrew as
$ brew install homebrew/science/armadillo
and through manual installation, cf. the official webpage. If installed in this way, the variable ARMAPATH at the top of the Makefile needs to be updated to the installation directory and the DYLD_LIBRARY_PATH environment variable might need to be set manually, see below.
ROOT [4]. Recommended. High energy physics framework. Used for plotting graphical results. Must be installed manually, following the instructions on the official webpage.
HepMC [3]. Optional. Event record for high energy physics collision simulations. The Wavenet package comes bundled with a utility script for downloading and installing HepMC. Simply call
$ source scripts/downloadHepMC.sh
This scripts installs the HepMC package to ./external/ and updates the appropriate path (HEPMCPATH) in the Makefile. See also the caveat below.
Alternatively, can be installed manually, cf. the official webpage. If installed in this way, the variable HEPMCPATH at the top of the Makefile needs to be updated to the installation directory and the DYLD_LIBRARY_PATH environment variable might need to be set manually, see below.
If the external shared libraries, Armadillo and (optionally) HepMC, are not installed in standard locations (e.g. /usr/local/) the programs might be unable to find these by default. This is the case if the packages are installed using the bundled utility download scripts. In this case, you need to call
$ source scripts/setup.sh
which updates the environment variable DYLD_LIBRARY_PATH to point to the install directories in ./external/, where the scripts install the external packages by default. This needs to be done in every new shell, so it might be smart to perform this call as part of the bash initialisation (i.e. put it in ~/.bash_profile or similar). If you forget, the programs will let you know by throwing errors when you try to run.
If the packages are installed in another non-standard location, manually, make sure to set the appropriate environment variable(s) yourself.
The central object in this package is the Wavenet class, which performs
- forward transforms of input (1- or 2-dimensional) data into a set of neural network node activations or wavelet coefficients,
- inverse transforms or a set of wavelet coefficients into a "position-space" signal,
- backpropagation of sparisty errors on the wavelet coefficient, and
- learning updates based on the backpropagated errors from training examples.
The function for computing the sparsity- and regularisation costs, as well as the associated gradients, are located in CostFunctions.
The LowpassOperator and HighpassOperator classes, both deriving from the basic MatrixOperator class, are responsible for the implementation of the low- and high-pass filter operations in the Wavenet transforms.
The Coach class manages the training1 of Wavenet objects, possibly utilising more advanced learning methods such as adaptive learning rates and batch sizes as well as a variant of simulated annealing.
The training examples which go into the training are provided by a collection of Generators, all deriving from the GeneratorBase class. By default, five generators come bundled with the package: NeedleGenerator, UniformGenerator, GaussianGenerator, CSVGenerator, and (optionally) HepMCGenerator. For specialised use, the user can added additional generator classes by following the provided examples.
The Wavenet objects can be save to, and loaded from, file using the Snapshot class, which also allows for easy iteration between save files from successive iterations, which the Coach class automatically takes care of.
The remaining files (Logger, Type, and Utilities) take care of pretty printing, type checking, and convenient utility functions.
Below is a minimal working example of the Wavenet code in action:
#include "Wavenet/Generators.h" /* wavenet::NeedleGenerator */
#include "Wavenet/Wavenet.h" /* wavenet::Wavenet */
#include "Wavenet/Coach.h" /* wavevent::Coach */
int main (int argc, char* argv[]) {
// Create Generator instance; here NeedleGenerator.
wavenet::NeedleGenerator ng;
ng.setShape({16,16});
// Create Wavenet instance.
wavenet::Wavenet wn;
// Create Coach instance.
wavenet::Coach coach ("Example00");
coach.setGenerator(&ng);
coach.setWavenet (&wn);
// Run the training.
coach.run();
return 1;
}
This is the same code as in examples/Example00.cxx. For examples of graphical output generated with this package, please see media.
© Andreas Søgaard, 2016. Licensed under an MIT License. If you use this package in your work (commerical, research, or otherwise), please give proper credit to the authors, e.g. through [1].
[1] A. Søgaard, Learning optimal wavelet bases using a neural network approach, 2016. [arXiv:xxxx.yyyyy]
[2] C. Sanderson and R. Curtin, Armadillo: a template-based C++ library for linear algebra, Journal of Open Source Software 1 (2016) 26
[3] M. Dobbs and J. B. Hansen, The HepMC C++ Monte Carlo Event Record for High Energy Physics, Comput. Phys. Commun. 134 (2001) 41
[4] R. Brun and F. Rademakers, ROOT - An Object Oriented Data Analysis Framework,
Proceedings AIHENP'96 Workshop, Lausanne, Sep. 1996, Nucl. Inst. & Meth. in Phys. Res. A 389 (1997) 81-86. See also http://root.cern.ch/
[5] E. Anderson et al., LAPACK Users' Guide, 3rd ed., SIAM (1999). [http://www.netlib.org/lapack]
[6] L. S. Blackford et al., An Updated Set of Basic Linear Algebra Subprograms (BLAS), ACM Trans. Math. Soft., 28-2 (2002) 135—151. [http://www.netlib.org/blas]
[7] Boost C++ Libraries, http://www.boost.org
1 Cute, right?