1 Introduction
SPAMS (SPArse Modeling Software) is an opensource optimization toolbox for
sparse estimation with licence GPLv3. It implements algorithms for solving
machine learning and signal processing problems involving sparse
regularizations.
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 multicore 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);
 nonnegative matrix factorization;
 nonnegative 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 ElasticNet problems);
 a weighted version of LARS;
 OMP and LARS when data comes with a binary mask;
 a coordinatedescent algorithm for ℓ_{1}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 ℓ_{1}/ℓ_{2}regularization based on blockcoordinate descent;
 a homotopy method for the FusedLasso Signal Approximation as defined in [10] with the homotopy method presented in the appendix of [21];
 a tool for projecting efficiently onto a few convex sets
inducing sparsity such as the ℓ_{1}ball using the method of
[3, 18, 8], and ElasticNet or Fused Lasso constraint sets as
proposed in the appendix of [21].
 an activeset algorithm for simplex decomposition problems [37].
 The Proximal toolbox: An implementation of proximal methods
(ISTA and FISTA [1]) 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 largescale problems. The following regularizations are implemented:

Tikhonov regularization (squared ℓ_{2}norm);
 ℓ_{1}norm, ℓ_{2}, ℓ_{∞}norms;
 ElasticNet [39];
 Fused Lasso [32];
 treestructured sum of ℓ_{2}norms (see [15, 16]);
 treestructured sum of ℓ_{∞}norms (see [15, 16]);
 general sum of ℓ_{∞}norms (see [22, 23]);
 mixed ℓ_{1}/ℓ_{2}norms on matrices [38, 29];
 mixed ℓ_{1}/ℓ_{∞}norms on matrices [38, 29];
 mixed ℓ_{1}/ℓ_{2}norms on matrices plus ℓ_{1} [31, 11];
 mixed ℓ_{1}/ℓ_{∞}norms on matrices plus ℓ_{1};
 grouplasso with ℓ_{2} or ℓ_{∞}norms;
 grouplasso+ℓ_{1};
 multitask treestructured sum of ℓ_{∞}norms (see [22, 23]);
 trace norm;
 ℓ_{0} pseudonorm (only with ISTA);
 treestructured ℓ_{0} (only with ISTA);
 rank regularization for matrices (only with ISTA);
 the pathcoding penalties of [24].
All of these regularization functions can be used with the following losses

square loss;
 square loss with missing observations;
 logistic loss, weighted logistic loss;
 multiclass logistic.
This toolbox can also enforce nonnegativity 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].
 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
(INRIA).
R and Python interfaces have been written by JeanPaul Chieze (INRIA).
The archetypal analysis implementation was written by Yuansi Chen, during
an internship at INRIA, with the collaboration of Zaid Harchaoui.