SPAMS (SPArse Modeling Software) is an open-source optimization toolbox for
sparse estimation with licence GPLv3. It implements algorithms for solving
machine learning and signal processing problems involving sparse
The library is coded in C++, is compatible with Linux, Mac, and Windows 32bits
and 64bits Operating Systems. It is interfaced with Matlab, R and Python, but
can be called from any C++ application (by hacking the code a bit).
It requires an implementation of BLAS and LAPACK for performing linear algebra
operations. The ones shipped with matlab and R can be used, but also external
libraries such as atlas, the netlib implementation, or the Intel Math Kernel
Library can be used. It also exploits multi-core CPUs when this feature is
supported by the compiler, through OpenMP.
The current licence is GPLv3, which is available at
http://www.gnu.org/licenses/gpl.html. For other licensing possibilities
allowing its use in proprietary softwares, please contact the author.
Version 2.5 of SPAMS is divided into several “toolboxes” and has a few
additional miscellaneous functions:
The Dictionary learning and matrix factorization toolbox
contains the online learning technique of [20, 21] and its
variants for solving various matrix factorization problems:
dictionary Learning for sparse coding;
- sparse principal component analysis (seen as a sparse matrix factorization problem);
- non-negative matrix factorization;
- non-negative sparse coding;
- dictionary learning with structured sparsity;
- archetypal analysis [7, 37].
- The Sparse decomposition toolbox contains efficient implementations of
Orthogonal Matching Pursuit, (or Forward Selection) [35, 27];
- the LARS/homotopy algorithm [30, 9] (variants for solving Lasso and Elastic-Net problems);
- a weighted version of LARS;
- OMP and LARS when data comes with a binary mask;
- a coordinate-descent algorithm for ℓ1-decomposition problems [12, 10, 36];
- a greedy solver for simultaneous signal approximation as defined in [34, 33] (SOMP);
- a solver for simulatneous signal approximation with ℓ1/ℓ2-regularization based on block-coordinate descent;
- a homotopy method for the Fused-Lasso Signal Approximation as defined in  with the homotopy method presented in the appendix of ;
- a tool for projecting efficiently onto a few convex sets
inducing sparsity such as the ℓ1-ball using the method of
[3, 18, 8], and Elastic-Net or Fused Lasso constraint sets as
proposed in the appendix of .
- an active-set algorithm for simplex decomposition problems .
- The Proximal toolbox: An implementation of proximal methods
(ISTA and FISTA ) for solving a large class of sparse approximation
problems with different combinations of loss and regularizations. One of the main
features of this toolbox is to provide a robust stopping criterion based on
duality gaps to control the quality of the optimization, whenever
possible. It also handles sparse feature matrices for large-scale problems. The following regularizations are implemented:
All of these regularization functions can be used with the following losses
Tikhonov regularization (squared ℓ2-norm);
- ℓ1-norm, ℓ2, ℓ∞-norms;
- Elastic-Net ;
- Fused Lasso ;
- tree-structured sum of ℓ2-norms (see [15, 16]);
- tree-structured sum of ℓ∞-norms (see [15, 16]);
- general sum of ℓ∞-norms (see [22, 23]);
- mixed ℓ1/ℓ2-norms on matrices [38, 29];
- mixed ℓ1/ℓ∞-norms on matrices [38, 29];
- mixed ℓ1/ℓ2-norms on matrices plus ℓ1 [31, 11];
- mixed ℓ1/ℓ∞-norms on matrices plus ℓ1;
- group-lasso with ℓ2 or ℓ∞-norms;
- multi-task tree-structured sum of ℓ∞-norms (see [22, 23]);
- trace norm;
- ℓ0 pseudo-norm (only with ISTA);
- tree-structured ℓ0 (only with ISTA);
- rank regularization for matrices (only with ISTA);
- the path-coding penalties of .
This toolbox can also enforce non-negativity constraints, handle intercepts and
sparse matrices. There are also a few additional undocumented functionalities,
which are available in the source code.
For some combinations of loss and regularizers, stochastic and incremental proximal
gradient solvers are also implemented [26, 25].
- square loss with missing observations;
- logistic loss, weighted logistic loss;
- multi-class logistic.
- A few tools for performing linear algebra operations such as a
conjugate gradient algorithm, manipulating sparse matrices and graphs.
The toolbox was written by Julien Mairal at INRIA, with the collaboration of
Francis Bach (INRIA), Jean Ponce (Ecole Normale Supérieure), Guillermo Sapiro
(University of Minnesota), Guillaume Obozinski (INRIA) and Rodolphe Jenatton
R and Python interfaces have been written by Jean-Paul Chieze (INRIA).
The archetypal analysis implementation was written by Yuansi Chen, during
an internship at INRIA, with the collaboration of Zaid Harchaoui.