Solving MultiClass Support Vector Machines with LaRank

Abstract: Optimization algorithms for large margin multiclass recognizers are often too costly to handle ambitious problems with structured outputs and exponential numbers of classes. Optimization algorithms that rely on the full gradient are not effective because, unlike the solution, the gradient is not sparse and is very large. The LaRank algorithm sidesteps this difficulty by relying on a randomized exploration inspired by the perceptron algorithm. We show that this approach is competitive with gradient based optimizers on simple multiclass problems. Furthermore, a single LaRank pass over the training examples delivers test error rates that are nearly as good as those of the final solution.

Antoine Bordes, Léon Bottou, Patrick Gallinari and Jason Weston: Solving MultiClass Support Vector Machines with LaRank, Proceedings of the 24th International Machine Learning Conference, 89-96, Edited by Zoubin Ghahramani, OmniPress, Corvallis, Oregon, 2007.

icml-2007.djvu icml-2007.pdf icml-2007.ps.gz 

@inproceedings{bordes-2007,
  author = {Bordes, Antoine and Bottou, L\'{e}on and Gallinari, Patrick and Weston, Jason},
  title = {Solving MultiClass Support Vector Machines with LaRank},
  booktitle = {Proceedings of the 24th International Machine Learning Conference},
  pages = {89-96},
  year = {2007},
  editor = {Ghahramani, Zoubin},
  address = {Corvallis, Oregon},
  publisher = {OmniPress},
  url = {http://leon.bottou.org/papers/bordes-2007},
}

Implementation

Antoine Bordes provides an implementation of the LaRank algorithm. This new implementation runs slightly faster than the code we have used for the paper. In addition there is a special version for the case of linear kernels.