OpenKernel Quick Tour

Under construction.

Using the library

In this quick tour, we will focus on the command-line utilities and LIBSVM plugin. The command-line utilities are available in the kernel/bin sub-directory.

Preparing your data

In order to use the library, you need to represent each point in your dataset as an fst, i.e., a weighted transducer (or automaton) represented in the binary format used by the OpenFst library. The OpenFst quick tour contains the relevant information for accomplishing this.

A dataset is then represented by a Fst archive (far file) or by a text file containing a list of fst file (specified using an absolute path). The i -th entry in the far archive or in the fst list being the fst representing the i -th point in the dataset.

This dataset should contain both your training and testing data.

An example of dataset, a subset of Reuters-21578, is provided with the library and can be used to become familiar with its usage.

Creating an n -gram kernel

The klngram utility can be used to generate an n-gram kernel. The -order option specifies the n-gram order and the -sigma option the size of the alphabet (i.e. the maximum label id). The fst.list specifies the dataset the kernel is operating on. The output of klngram is a kar file (for kernel archive) that contains both the kernel function and the dataset it is defined on.

$ klngram -order=3 -sigma=2  data.far > 3-gram.kar

In addition to n-gram kernels, the library provides tools for the creation of gappy n-gram kernels (klngram), mismatch kernels (klmismatch) and arbitrary rational kernels (klrational).

Kernels can also be combined by taking their sum (klsum) or product (klproduct) or can be composed with a polynomial (klpolynomial), a gaussian (klgaussian) or a sigmoid (klsigmoid).

Generating a kernel matrix

The kernel matrix corresponding to the evaluation of the kernel on the specified dataset can be computed using the kleval utility as shown here:

$ kleval 3-gram.kar > 3-gram.matrix

Assuming the size of the dataset is n, the result will be a text file with n lines and n floats on each line. The j -th value on the i -th line correspond to the value of the kernel for the i -th and j -th points in the dataset.

The kernel matrix can be partially computed by restricting the set of values to be evaluated using the -xmin, -xmax, -ymin and -ymax flags. Assuming the lines and columns are indexed from 0 to n - 1, the following command can be used to only compute the (i, j) value if and only if 10 ≤ i, j < 20:

kleval -xmin=10 -ymin=10 -xmax=20 -ymax=20 3-gram.kar

Using the -libsvm option will generate a file in the format used by LIBSVM to specify precomputed kernels. LIBSVM users are however encouraged to use the LIBSVM plugin as described below.

Finally, the -kar option allows the kernel matrix to be stored in a kar file in addition to the kernel function and dataset.

$ kleval 3-gram.kar > 3-gram.matrix.kar

Using the LIBSVM plugin

The OpenKernel library package includes a modified version of LIBSVM that allows the definition of arbitrary plugins to handle the kernel computations. This version of LIBSVM is available in the libsvm sub-directory. A specific plugin to allow the use of the OpenKernel library with libsvm is provided in the kernel/plugin sub-directory. In order to use this plugin, you need to add the path to the kernel/plugin sub-directory to your dynamic loader path (LD_LIBRARY_PATH on Linux, DYLD_LIBRARY_PATH on MacOS X).

The training and test dataset need to be specified in the usual LIBSVM format (if you are not familiar with LIBSVM check out the official website or the README file in the libsvm directory). For instance a text file train such as:

1 1:1.0
-1 2:1.0
1 4:1.0

specifies that the 1st, 2nd and 4th points of the dataset are in the training set with labels 1, -1 and 1. And a text file test such as:

-1 3:1.0
1 5:1.0

specifies that the 3rd and 5th points of the dataset are in the test set (the labels are optional here and will only be used for scoring).

The svm-train utility needs to be called with two additional options. The -k option specifies the type of kernel and should be openkernel when using the OpenKernel library. The -K option specifies the kar file defining the kernel and dataset to be used. All the other svm-train options are still available. For example:

$ svm-train -k openkernel -K 3-gram.kar train 3-gram.model

The svm-predict utility does not required any additional options. The kernel information is included in the model file:

$ svm-predict test 3-gram.model 3-gram.pred

When using the LIBSVM plugin, the kernel values are computed "on the fly" as requested by the LIBSVM utilities. When performing several experiments using the same kernel (on the same dataset), it is recommended, in order to avoid unnecessary computations, to first compute the (partial) kernel matrix using kleval -kar and use the resulting kar file as a parameter to the LIBSVM utilities.

-- CyrilAllauzen - 08 Oct 2007