## SVM
^{rank} ## Support Vector Machine for RankingAuthor: Thorsten Joachims <thorsten@joachims.org> Version: 1.00 |

*SVM ^{rank}* is an instance of

If you are looking for Propensity SVM-Rank for learning from incomplete and biased data, please go here.

- T. Joachims,
*Training Linear SVMs in Linear Time,*Proceedings of the ACM Conference on Knowledge Discovery and Data Mining (KDD), 2006. [Postscript (gz)] [PDF]

The implementation was developed on Linux with gcc, but compiles also on Solaris, Cygwin, Windows (using MinGW) and Mac (after small modifications, see FAQ). The source code is available at the following location:

https://osmot.cs.cornell.edu/svm_rank/current/svm_rank.tar.gz

- Linux (32-bit): https://osmot.cs.cornell.edu/svm_rank/current/svm_rank_linux32.tar.gz
- Linux (64-bit): https://osmot.cs.cornell.edu/svm_rank/current/svm_rank_linux64.tar.gz
- Cygwin: https://osmot.cs.cornell.edu/svm_rank/current/svm_rank_cygwin.tar.gz
- Windows: https://osmot.cs.cornell.edu/svm_rank/current/svm_rank_windows.zip

Please send me email and let me know that you got it. The archive contains the source code of the most recent version of *SVM ^{rank}*, which includes the source code of

gunzip –c svm_rank.tar.gz | tar xvf –This expands the archive into the current directory, which now contains all relevant files. You can compile

makeThis will produce the executables

SVM* ^{rank}* consists of a learning module (

svm_rank_learn -c 20.0 train.dat model.datwhich trains a Ranking SVM on the training set

General Options: -? -> this help -v [0..3] -> verbosity level (default 1) -y [0..3] -> verbosity level for svm_light (default 0) Learning Options: -c float -> C: trade-off between training error and margin (default 0.01) -p [1,2] -> L-norm to use for slack variables. Use 1 for L1-norm, use 2 for squared slacks. (default 1) -o [1,2] -> Rescaling method to use for loss. 1: slack rescaling 2: margin rescaling (default 2) -l [0..] -> Loss function to use. 0: zero/one loss ?: see below in application specific options (default 1) Optimization Options (see [2][5]): -w [0,..,9] -> choice of structural learning algorithm (default 3): 0: n-slack algorithm described in [2] 1: n-slack algorithm with shrinking heuristic 2: 1-slack algorithm (primal) described in [5] 3: 1-slack algorithm (dual) described in [5] 4: 1-slack algorithm (dual) with constraint cache [5] 9: custom algorithm in svm_struct_learn_custom.c -e float -> epsilon: allow that tolerance for termination criterion (default 0.001000) -k [1..] -> number of new constraints to accumulate before recomputing the QP solution (default 100) (-w 0 and 1 only) -f [5..] -> number of constraints to cache for each example (default 5) (used with -w 4) -b [1..100] -> percentage of training set for which to refresh cache when no epsilon violated constraint can be constructed from current cache (default 100%) (used with -w 4) SVM-light Options for Solving QP Subproblems (see [3]): -n [2..q] -> number of new variables entering the working set in each svm-light iteration (default n = q). Set n < q to prevent zig-zagging. -m [5..] -> size of svm-light cache for kernel evaluations in MB (default 40) (used only for -w 1 with kernels) -h [5..] -> number of svm-light iterations a variable needs to be optimal before considered for shrinking (default 100) -# int -> terminate svm-light QP subproblem optimization, if no progress after this number of iterations. (default 100000) 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 Output Options: -a string -> write all alphas to this file after learning (in the same order as in the training set) Application-Specific Options: The following loss functions can be selected with the -l option: 1 Total number of swapped pairs summed over all queries. 2 Fraction of swapped pairs averaged over all queries. NOTE: SVM-light in '-z p' mode and SVM-rank with loss 1 are equivalent for c_light = c_rank/n, where n is the number of training rankings (i.e. queries).

SVM^{rank} learns an unbiased linear classification rule (i.e.
a rule `w*x` without explicit threshold). The loss function to be
optimized is selected using the '-l' option. Loss function '1' is identical to
the one used in the ranking mode of SVM^{light}, and it optimizes
the total number of swapped pairs. Loss function '2' is a normalized version of
'1'. For each query, it divides the number of swapped pairs by the maximum
number of possibly swapped pairs for that query.

You can in principle use kernels in SVM^{rank} using the '-t'
option just like in SVM^{light}, but it is painfully slow and you
are probably better off using SVM^{light}.

The file format of the training and test files is the same as for *SVM ^{light}*
(see here for further details), with the exception that
the lines in the input files have to be sorted by increasing qid. 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:

<qid> .=. <positive integer>

The target value 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 target value defines the order of
the examples for each query. Implicitly,
the target values are used to generated pairwise preference constraints as
described in
[Joachims, 2002c].
A preference constraint is included for all pairs of examples in the `example_file`,
for which the target value differs. The special feature "qid" can be used to
restrict the generation of constraints. Two examples are considered for a
pairwise preference constraint only if the value of "qid" is the same. For
example, given the `example_file`

3 qid:1 1:1 2:1 3:0 4:0.2 5:0 # 1A

2 qid:1 1:0 2:0 3:1 4:0.1 5:1 # 1B

1 qid:1 1:0 2:1 3:0 4:0.4 5:0 # 1C

1 qid:1 1:0 2:0 3:1 4:0.3 5:0 # 1D

1 qid:2 1:0 2:0 3:1 4:0.2 5:0 # 2A

2 qid:2 1:1 2:0 3:1 4:0.4 5:0 # 2B

1 qid:2 1:0 2:0 3:1 4:0.1 5:0 # 2C

1 qid:2 1:0 2:0 3:1 4:0.2 5:0 # 2D

2 qid:3 1:0 2:0 3:1 4:0.1 5:1 # 3A

3 qid:3 1:1 2:1 3:0 4:0.3 5:0 # 3B

4 qid:3 1:1 2:0 3:0 4:0.4 5:1 # 3C

1 qid:3 1:0 2:1 3:1 4:0.5 5:0 # 3D

the following set of pairwise constraints is generated (examples are referred to by the info-string after the # character):

1A>1B, 1A>1C, 1A>1D, 1B>1C, 1B>1D, 2B>2A, 2B>2C, 2B>2D, 3C>3A, 3C>3B, 3C>3D, 3B>3A, 3B>3D, 3A>3D

The result of `svm_rank_learn` is the model that is learned from the training data in
`train.dat`. The model is written to `model.dat`. To make predictions on test examples, `svm_rank_classify` reads this file. `svm_rank_classify` is called as follows:

svm_rank_classify test.dat model.dat predictions

For each line in `test.dat,` the predicted ranking score is written to
the file `predictions`. There is one line per test example in `predictions` in the same order as in
`test.dat`.
From these scores, the ranking can be recovered via sorting.

You will find an example problem at

https://osmot.cs.cornell.edu/svm_light/examples/example3.tar.gz

It consists of 3 rankings (i.e. queries) with 4 examples each. It also contains a file with 4 test examples. Unpack the archive with

gunzip -c example3.tar.gz | tar xvf -

This will create a subdirectory `example3`.
To run the example, execute the commands:

`svm_rank_learn -c 3 example3/train.dat example3/model`

`svm_rank_classify example3/test.dat example3/model example3/predictions`

The output in the predictions file can be used to rank the test examples. If you do so, you will see that it predicts the correct ranking. The values in the predictions file do not have a meaning in an absolute sense - they are only used for ordering. The equivalent call for SVM-light is

`svm_learn -z p -c 1 example3/train.dat example3/model`

Note the different value for c, since we have 3 training rankings.

It can also be interesting to look at the "training error" of the ranking SVM. The equivalent of training error for a ranking SVM is the number of training pairs that are misordered by the learned model. To find those pairs, one can apply the model to the training file:

svm_rank_classify example3/train.dat example3/model example3/predictions.train

Again, the predictions file shows the ordering implied by the model. The model ranks all training examples correctly.

Note that ranks are comparable only between examples with the same qid. Note also that the target value (first value in each line of the data files) is only used to define the order of the examples. Its absolute value does not matter, as long as the ordering relative to the other examples with the same qid remains the same.

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

- none

- none

**[1] **T. Joachims, *Training Linear SVMs in Linear Time,* Proceedings of
the ACM Conference on Knowledge Discovery and Data Mining (KDD), 2006.
[Postscript] [PDF]

**[2]** T. Joachims, *A Support
Vector Method for Multivariate Performance Measures*, Proceedings of the
International Conference on Machine Learning (ICML), 2005.
[Postscript] [PDF]

**[3]** Tsochantaridis, T. Joachims, T. Hofmann, and Y. Altun, Large Margin
Methods for Structured and Interdependent Output Variables, Journal of Machine
Learning Research (JMLR), 6(Sep):1453-1484, 2005.
[PDF]

**[4] **I. Tsochantaridis, T. Hofmann, T. Joachims, Y. Altun. *Support Vector
Machine Learning for Interdependent and Structured Output Spaces*.
International Conference on Machine Learning (ICML), 2004.
[Postscript] [PDF]

**[5] **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.
[Postscript (gz)]
[PDF]

**[6]** T. Joachims, T. Finley, Chun-Nam Yu, Cutting-Plane Training of
Structural SVMs, Machine Learning Journal, 2009.
[PDF]

[7]
T. Joachims, *Optimizing Search
Engines Using Clickthrough Data*, Proceedings of the ACM Conference on
Knowledge Discovery and Data Mining (KDD), ACM, 2002.
[Postscript] [PDF]