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Support Vector Machine

SVMlight: Support Vector Machine


Author: Thorsten Joachims <thorsten@ls8.cs.uni-dortmund.de>
University of Dortmund, Informatik, AI-Unit
Collaborative Research Center on 'Complexity Reduction in Multivariate Data' (SFB475)
Version: 3.02
Date: 16.11.99




Overview

SVMlight is an implementation of Support Vector Machines (SVMs) in C. The main features of the program are the following: 
  • fast optimization algorithm
    • working set selection based on steepest feasible descent
    • "shrinking" heuristic
    • caching of kernel evaluations
    • use of folding in the linear case
  • includes algorithm for approximately training large transductive SVMs (TSVMs)
  • can train SVMs with cost models
  • handles many thousands of support vectors
  • handles several ten-thousands of training examples
  • supports standard kernel functions and lets you define your own
  • uses sparse vector representation
There is also a regression support vector machine based on SVMlight available at the AI-Unit: mySVM.

Description

SVMlight is an implementation of Vapnik's Support Vector Machine [Vapnik, 1995] for the problem of pattern recognition. The optimization algorithm used in SVMlight is described in [Joachims, 1999a]. The algorithm has scalable memory requirements and can handle problems with many thousands of support vectors efficiently. This new version also includes a new algorithm for training large-scale transductive SVMs. The algorithm proceeds by solving a sequence of optimization problems lower-bounding the solution using a form of local search. A detailed description of the algorithm can be found in [Joachims, 1999c]. You can now also use SVMs with cost models (see [Morik et al., 1999]). The code has been used on a large range of problems, including text classification [Joachims, 1999c][Joachims, 1998a], several image recognition tasks, and medical applications. Many tasks have the property of sparse instance vectors. This implementation makes use of this property which leads to a very compact and efficient representation. 

Source Code

The source code is free for scientific use. Please contact me, if you are planning to use the software for commercial purposes. The software must not be modified and distributed without prior permission of the author. If you use SVMlight in your scientific work, please cite as 
  • T. Joachims, Making large-Scale SVM Learning Practical. Advances in Kernel Methods - Support Vector Learning, B. Schölkopf and C. Burges and A. Smola (ed.), MIT-Press, 1999.

    • [PDF] [Postscript (gz)]
I would also appreciate, if you sent me (a link to) your papers so that I can learn about your research. The implementation was developed on Solaris 2.5 with gcc, but compiles also on SunOS 3.1.4, Solaris 2.7, Linux, IRIX, Windows NT, and Powermac (after small modifications, see FAQ). The source code is available at the following location:  Please send me email and let me know that you got svm-light. I will put you on my mailing list to inform you about new versions and bug-fixes. SVMlight comes with a quadratic programming tool for solving small intermediate quadratic programming problems. It is based on the method of Hildreth and D'Espo and solves small quadratic programs very efficiently. Nevertheless, if for some reason you want to use another solver, the new version still comes with an interface to PR_LOQO. The PR_LOQO optimizer was written by A. Smola. It can be requested from http://www.kernel-machines.org/code/prloqo.tar.gz.

Installation

To install SVMlight you need to download svm_light.tar.gz. Create a new directory: 
    mkdir svm_light
Move svm_light.tar.gz to this directory and unpack it with 
    gunzip -c svm_light.tar.gz | tar xvf -
Now execute 
    make    or    make all
which compiles the system and creates the two executables 
    svm_learn       (learning module)
    svm_classify    (classification module)
If you do not want to use the built-in optimizer but PR_LOQO instead, create a subdirectory in the svm_light directory with 
    mkdir pr_loqo
and copy the files pr_loqo.c and pr_loqo.h (which you received by email) in there. Now execute
    make svm_learn_loqo
If the system does not compile properly, check this FAQ. 

How to use

This section explains how to use the SVMlight software. A good introduction to the theory of SVMs is Chris Burges' tutorial.

SVMlight consists of a learning module (svm_learn) and a classification module (svm_classify). The classification module can be used to apply the learned model to new examples. See also the examples below for how to use svm_learn and svm_classify.

svm_learn is called with the following parameters: 

    svm_learn [options] example_file model_file
Available options are: 
    General options:
             -?          -> this help
             -v [0..3]   -> verbosity level (default 1)
    Learning options:
             -c float    -> C: trade-off between training error
                            and margin (default 1000)
             -j float    -> Cost: cost-factor, by which training errors on
                            positive examples outweight errors on negative
                            examples (default 1)
             -b [0,1]    -> use biased hyperplane (i.e. x*w+b>0) instead
                            of unbiased hyperplane (i.e. x*w>0) (default 1)
             -i [0,1]    -> remove inconsistent training examples
                            and retrain (default 0)
    Transduction options:
             -p [0..1]   -> fraction of unlabeled examples to be classified
                            into the positive class (default is the ratio of
                            positive and negative examples in the training data)
    Kernel options:
             -t int      -> type of kernel function:
                            0: linear (default)
                            1: polynomial (s a*b+c)^d
                            2: radial basis function exp(-gamma ||a-b||^2)
                            3: sigmoid tanh(s a*b + c)
                            4: user defined kernel from kernel.h
             -d int      -> parameter d in polynomial kernel
             -g float    -> parameter gamma in rbf kernel
             -s float    -> parameter s in sigmoid/poly kernel
             -r float    -> parameter c in sigmoid/poly kernel
             -u string   -> parameter of user defined kernel
    Optimization options:
             -q [2..400] -> maximum size of QP-subproblems (default 10)
             -m [5..]    -> size of cache for kernel evaluations in MB (default 40)
                            The larger the faster...
             -e float    -> eps: Allow that error for termination criterion
                            [y [w*x+b] - 1] >= eps (default 0.001)
             -h [5..]    -> number of iterations a variable needs to be
                            optimal before considered for shrinking (default 100)
             -f [0,1]    -> do final optimality check for variables removed
                            by shrinking. Although this test is usually 
                            positive, there is no guarantee that the optimum
                            was found if the test is omitted. (default 1)
    Output options:
             -l char     -> file to write predicted labels of unlabeled
                            examples into after transductive learning
             -a char     -> write all alphas to this file after learning
                            (in the same order as in the training set)












































The input file example_file contains the training examples. The first lines may contain comments and are ignored if they start with #. Each of the following lines represents one training example and is of the following format: 
    <class> .=. +1 | -1  |  0
    <feature> .=. integer
    <value> .=. real
    <line> .=. <class> <feature>:<value> <feature>:<value> ... <feature>:<value>


The class label and each of the feature/value pairs are separated by a space character. Feature/value pairs MUST be ordered by increasing feature number. Features with value zero can be skipped. The +1 as class label marks a positive example, -1 a negative example respectively. A class label of 0 indicates that this example should be classified using transduction. The predictions for the examples classified by transduction are written to the file specified through the -l option. The order of the predictions is the same as in the training data. 

The result of svm_learn is the model which is learned from the training data in example_file. The model is written to model_file. To classify test examples, svm_classify reads this file. svm_classify is called with the following parameters: 

    svm_classify [options] example_file model_file output_file
Available options are: 
    -h         -> Help.
    -v [0..3]  -> Verbosity level (default 2).
    -f [0,1]   -> 0: old output format of V1.0
                  1: output the value of decision function (default)


All test examples in example_file are classified and the predicted classes are written to output_file. There is one line per test example in output_file containing the value of the decision function on that example. The test example file has the same format as the one for svm_learn. Again, <class> can have the value zero indicating unknown. 

If you want to find out more, try this FAQ. 

Getting started: an Example Problem

Inductive SVM

You will find an example text classification problem at  Download this file into your svm_light directory and unpack it with 
    gunzip -c example1.tar.gz | tar xvf -
This will create a subdirectory example1. Documents are represented as feature vectors. Each feature corresponds to a word stem (9947 features). The task is to learn which Reuters articles are about "corporate acquisitions". There are 1000 positive and 1000 negative examples in the file train.dat.  The file test.dat contains 600 test examples. The feature numbers correspond to the line numbers in the file words. To run the example, execute the commands: 
    svm_learn example1/train.dat example1/model
    svm_classify example1/test.dat example1/model example1/predictions
The accuracy on the test set is printed to stdout. 

Transductive SVM

To try out the transductive learner, you can use the following dataset. I compiled it from the same Reuters articles as used in the example for the inductive SVM. The dataset consists of only 10 training examples (5 positive and 5 negative) and the same 600 test examples as above. You find it at  Download this file into your svm_light directory and unpack it with 
    gunzip -c example2.tar.gz | tar xvf -
This will create a subdirectory example2. To run the example, execute the commands: 
    svm_learn example2/train_transduction.dat example2/model
    svm_classify example2/test.dat example2/model example2/predictions
The classification module is called only to get the accuracy printed. The transductive learner is invoced automatically, since  train_transduction.dat contains unlabeled examples (i. e. the 600 test examples). You can compare the results to those of the inductive SVM by running:
svm_learn example2/train_induction.dat example2/model
svm_classify example2/test.dat example2/model example2/predictions
The file train_induction.dat contains the same 10 (labeled) training examples as train_transduction.dat.

Extensions and Additions

Questions and Bug Reports

If you find bugs or you have problems with the code you cannot solve by yourself, please contact me via email <svm-light@ls8.cs.uni-dortmund.de>. 

Disclaimer

This software is free only for non-commercial use. It must not be modified and distributed without prior permission of the author. The author is not responsible for implications from the use of this software. 

History

V3.01 -> V3.02

  • Now examples can be read in correctly on SGIs.

V3.00 -> V3.01

  • Fixed rare convergence bug for Hildreth and D'Espo solver.

V2.01 -> V3.00

  • Training algorithm for transductive Support Vector Machines.
  • Integrated core QP-solver based on the method of Hildreth and D'Espo.
  • Uses folding in the linear case, which speeds up linear SVM training by an order of magnitude.
  • Allows linear cost models.
  • Faster in general.

V2.00 -> V2.01

V1.00 -> V2.00

  • Learning is much faster especially for large training sets.
  • Working set selection based on steepest feasible descent.
  • "Shrinking" heuristic.
  • Improved caching.
  • New solver for intermediate QPs.
  • Lets you set the size of the cache in MB.
  • Simplified output format of svm_classify.
  • Data files may contain comments.

V0.91 -> V1.00

  • Learning is more than 4 times faster.
  • Smarter caching and optimization.
  • You can define your own kernel function.
  • Lets you set the size of the cache.
  • VCdim is now estimated based on the radius of the support vectors.
  • The classification module is more memory efficient.
  • The f2c library is available from here.
  • Adaptive precision tuning makes optimization more robust.
  • Includes some small bug fixes and is more robust.
  • Source code for SVMlight V1.00

V0.9 -> V0.91

  • Fixed small bug which appears for very small C. Optimization did not converge.

References

Joachims/99a Joachims, Thorsten (1999). Making large-Scale SVM Learning Practical. In Advances in Kernel Methods - Support Vector Learning, chapter 11. MIT Press. [.ps.gz] [.pdf]
Joachims/99c Thorsten Joachims (1999). Transductive Inference for Text Classification using Support Vector Machines. In International Conference on Machine Learning (ICML). . [.ps.gz] [.pdf]
Scheffer/Joachims/99a Tobias Scheffer and Thorsten Joachims (1999). Expected Error Analysis for Model Selection. In International Conference on Machine Learning (ICML). .
Joachims/98a Joachims, Thorsten (1998). Text Categorization with Support Vector Machines: Learning with Many Relevant Features. In Claire N\'edellec and C\'eline Rouveirol, editor(s), Proceedings of the European Conference on Machine Learning, pages 137 -- 142. Springer. [.ps.gz] [.pdf]
Joachims/98c Thorsten Joachims (1998). Making large-Scale SVM Learning Practical. Technical report, Universität Dortmund, LS VIII-Report. [.ps.gz] [.pdf]
Scheffer/Joachims/98a Tobias Scheffer and Thorsten Joachims (1998). Estimating the expected error of empirical minimizers for model selection. Technical report, TU-Berlin. [.ps]
Cortes/Vapnik/95a Cortes, Corinna and Vapnik, Vladimir N. (1995). Support--Vector Networks. Machine Learning Journal, 20 pages 273--297.
Vapnik/95a Vladimir N. Vapnik (1995). The Nature of Statistical Learning Theory. Springer.

Other SVM Resources

Last modified July 7th, 2000 by Thorsten Joachims <thorsten@ls8.cs.uni-dortmund.de>