libsdca

libsdca is a library for multiclass classification based on stochastic dual coordinate ascent (SDCA).

Below is a brief overview of supported training objectives, inputs, proximal operators, and interfaces.

Multiclass objectives:

• Multiclass SVM of Crammer and Singer [1]
• Multiclass SVM with smoothed hinge loss
• Top-k Multiclass SVM [4]
  • top-k hinge loss alpha (non-smooth and smooth)
  • top-k hinge loss beta (non-smooth and smooth)
• Multiclass cross-entropy loss (softmax loss)
• Top-k entropy loss [5]

Multilabel objectives:

• Multilabel SVM of Crammer and Singer [2]
• Multilabel SVM with smoothed hinge loss
• Multilabel cross-entropy loss

Input data:

• features
• kernels
• float or double precision
• multiple datasets at once (e.g. to monitor performance on a validation set)

Proximal operators and more (e.g. compute projections onto various sets):

• simplex (implements the algorithm of [3])
• top-k simplex
• top-k cone
• entropic projections
• Lambert W function of the exponent (computes W(exp(x))
• Further details: matsdca_prox('help','prox')

Interfaces:

• C++11 headers (simply include and use; no additional libraries to compile and link)
• Matlab mex files
• Python support is only partial at the moment, see PR #2

For the truncated top-k entropy loss [5], see libsdca_gd in a previous release v0.2.0.

Installation instructions

libsdca can be installed on Linux and OS X in two ways.

• Using a make script in Matlab:

run matlab/make.m

• Using CMake (requires CMake version >= 2.8.9):

mkdir build && cd build && cmake .. && make install -j4

The Matlab interface is installed in the directory matlab and provides two mex files:

• matsdca_fit - solvers;
• matsdca_prox - proximal operators.

The directory should be added to the Matlab search path with addpath matlab.

Quick start

Using the library is as easy as

model = matsdca_fit(X, Y, opts);

A quick demo script is available at matlab/demo.m.

Type matsdca_fit('help') and matsdca_prox('help') for help.

References and citation

Please cite libsdca in your publications if it helps your research.

• Top-k Multiclass SVM (top-k hinge loss alpha and beta):

@inproceedings{lapin2015topk,
  title = {Top-k Multiclass {SVM}},
  author = {Lapin, Maksim and Hein, Matthias and Schiele, Bernt},
  booktitle = {NIPS},
  year = {2015}
}

• Smooth top-k losses and cross-entropy losses:

@inproceedings{lapin2016loss,
  title = {Loss Functions for Top-k Error: Analysis and Insights},
  author = {Lapin, Maksim and Hein, Matthias and Schiele, Bernt},
  booktitle = {CVPR},
  year = {2016}
}

References

^{[1] K. Crammer and Y. Singer. On the Algorithmic Implementation of Multiclass Kernel-based Vector Machines. In JMLR, 2001.
[2] K. Crammer and Y. Singer. A family of additive online algorithms for category ranking. In JMLR, 2003.
[3] K.C. Kiwiel. Variable fixing algorithms for the continuous quadratic knapsack problem. In JOTA, 2008.
[4] M. Lapin, M. Hein, and B. Schiele. Top-k multiclass SVM. In NIPS, 2015.
[5] M. Lapin, M. Hein, and B. Schiele. Loss Functions for Top-k Error: Analysis and Insights. In CVPR, 2016.}