Package weka.classifiers.functions.supportVector

Class StringKernel

java.lang.Object
weka.classifiers.functions.supportVector.Kernel
weka.classifiers.functions.supportVector.StringKernel
All Implemented Interfaces:
Serializable, CapabilitiesHandler, OptionHandler, RevisionHandler, TechnicalInformationHandler
public class StringKernel extends Kernel implements TechnicalInformationHandler
Implementation of the subsequence kernel (SSK) as described in [1] and of the subsequence kernel with lambda pruning (SSK-LP) as described in [2].

For more information, see

Huma Lodhi, Craig Saunders, John Shawe-Taylor, Nello Cristianini, Christopher J. C. H. Watkins (2002). Text Classification using String Kernels. Journal of Machine Learning Research. 2:419-444.

F. Kleedorfer, A. Seewald (2005). Implementation of a String Kernel for WEKA. Wien, Austria.

BibTeX: 

 @article{Lodhi2002,
    author = {Huma Lodhi and Craig Saunders and John Shawe-Taylor and Nello Cristianini and Christopher J. C. H. Watkins},
    journal = {Journal of Machine Learning Research},
    pages = {419-444},
    title = {Text Classification using String Kernels},
    volume = {2},
    year = {2002},
    HTTP = {http://www.jmlr.org/papers/v2/lodhi02a.html}
 }
 
 @techreport{Kleedorfer2005,
    address = {Wien, Austria},
    author = {F. Kleedorfer and A. Seewald},
    institution = {Oesterreichisches Forschungsinstitut fuer Artificial Intelligence},
    number = {TR-2005-13},
    title = {Implementation of a String Kernel for WEKA},
    year = {2005}
 }

Valid options are: 

 -D
  Enables debugging output (if available) to be printed.
  (default: off)
 
 -P <0|1>
  The pruning method to use:
  0 = No pruning
  1 = Lambda pruning
  (default: 0)
 
 -C <num>
  The size of the cache (a prime number).
  (default: 250007)
 
 -IC <num>
  The size of the internal cache (a prime number).
  (default: 200003)
 
 -L <num>
  The lambda constant. Penalizes non-continuous subsequence
  matches. Must be in (0,1).
  (default: 0.5)
 
 -ssl <num>
  The length of the subsequence.
  (default: 3)
 
 -ssl-max <num>
  The maximum length of the subsequence.
  (default: 9)
 
 -N
  Use normalization.
  (default: no)

Theory

Overview

The algorithm computes a measure of similarity between two texts based on the number and form of their common subsequences, which need not be contiguous. This method can be parametrized by specifying the subsequence length k, the penalty factor lambda, which penalizes non-contiguous matches, and optional 'lambda pruning', which takes maxLambdaExponent, m, as parameter. Lambda pruning causes very 'stretched' substring matches not to be counted, thus speeding up the computation. The functionality of SSK and SSK-LP is explained in the following using simple examples.

Explanation & Examples

for all of the following examples, we assume these parameter values: 
 k=2
 lambda=0.5
 m=8 (for SSK-LP examples)

SSK

Example 1

 SSK(2,"ab","axb")=0.5^5 = 0,03125
There is one subsequence of the length of 2 that both strings have in common, "ab". The result of SSK is computed by raising lambda to the power of L, where L is the length of the subsequence match in the one string plus the length of the subsequence match in the other, in our case: 
    ab    axb
 L= 2  +   3 = 5
hence, the kernel yields 0.5^5 = 0,03125

Example 2

 SSK(2,"ab","abb")=0.5^5 + 0.5^4 = 0,09375
Here, we also have one subsequence of the length of 2 that both strings have in common, "ab". The result of SSK is actually computed by summing over all values computed for each occurrence of a common subsequence match. In this example, there are two possible cases: 
 ab    abb
 --    --  L=4
 --    - - L=5
we have two matches, one of the length of 2+2=4, one of the length of 2+3=5, so we get the result 0.5^5 + 0.5^4 = 0,09375.

SSK-LP

Without lambda pruning, the string kernel finds *all* common subsequences of the given length, whereas with lambda pruning, common subsequence matches that are too much stretched in both strings are not taken into account. It is argued that the value yielded for such a common subsequence is too low ( lambda ^(length[match_in_s] + length[match_in_t]) . Tests have shown that a tremendous speedup can be achieved using this technique while suffering from very little quality loss.
Lambda pruning is parametrized by the maximum lambda exponent. It is a good idea to choose that value to be about 3 or 4 times the subsequence length as a rule of thumb. YMMV.

Example 3

Without lambda pruning, one common subsequence, "AB" would be found in the following two strings. (With k=2) 
 SSK(2,"ab","axb")=0.5^14 = 0,00006103515625
lambda pruning allows for the control of the match length. So, if m (the maximum lambda exponent) is e.g. 8, these two strings would yield a kernel value of 0: 
 with lambda pruning:    SSK-LP(2,8,"AxxxxxxxxxB","AyB")= 0
 without lambda pruning: SSK(2,"AxxxxxxxxxB","AyB")= 0.5^14 = 0,00006103515625
This is because the exponent for lambda (=the length of the subsequence match) would be 14, which is > 8. In Contrast, the next result is > 0 
 m=8
 SSK-LP(2,8,"AxxB","AyyB")=0.5^8 = 0,00390625
because the lambda exponent would be 8, which is just accepted by lambda pruning.

Normalization

When the string kernel is used for its main purpose, as the kernel of a support vector machine, it is not normalized. The normalized kernel can be switched on by -F (feature space normalization) but is much slower. Like most unnormalized kernels, K(x,x) is not a fixed value, see the next example.

Example 4

 SSK(2,"ab","ab")=0.5^4 = 0.0625
 SSK(2,"AxxxxxxxxxB","AxxxxxxxxxB") = 12.761724710464478
SSK is evaluated twice, each time for two identical strings. A good measure of similarity would produce the same value in both cases, which should indicate the same level of similarity. The value of the normalized SSK would be 1.0 in both cases. So for the purpose of computing string similarity the normalized kernel should be used. For SVM the unnormalized kernel is usually sufficient.

Complexity of SSK and SSK-LP

The time complexity of this method (without lambda pruning and with an infinitely large cache) is
 O(k*|s|*|t|)
Lambda Pruning has a complexity (without caching) of
 O(m*binom(m,k)^2*(|s|+n)*|t|)
 

 k...          subsequence length (ssl)
 s,t...        strings
 |s|...        length of string s
 binom(x,y)... binomial coefficient (x!/[(x-y)!y!])
 m...          maxLambdaExponent (ssl-max)
Keep in mind that execution time can increase fast for long strings and big values for k, especially if you don't use lambda pruning. With lambda pruning, computation is usually so fast that switching on the cache leads to slower computation because of setup costs. Therefore caching is switched off for lambda pruning.

For details and qualitative experiments about SSK, see [1]
For details about lambda pruning and performance comparison of SSK and SSK-LP (SSK with lambda pruning), see [2] Note that the complexity estimation in [2] assumes no caching of intermediate results, which has been implemented in the meantime and greatly improves the speed of the SSK without lambda pruning.

Notes for usage within Weka

Only instances of the following form can be processed using string kernels: 
 +----------+-------------+---------------+
 |attribute#|     0       |       1       |
 +----------+-------------+---------------+
 | content  | [text data] | [class label] |
 +----------------------------------------+
  ... or ...
 +----------+---------------+-------------+
 |attribute#|     0         |     1       |
 +----------+---------------+-------------+
 | content  | [class label] | [text data] |
 +----------------------------------------+
Version:
$Revision: 14512 $
Author:
Florian Kleedorfer (kleedorfer@austria.fm), Alexander K. Seewald (alex@seewald.at)
See Also:

  • Field Details

    • PRUNING_NONE

      public static final int PRUNING_NONE
      Pruning method: No Pruning
      See Also:

    • PRUNING_LAMBDA

      public static final int PRUNING_LAMBDA
      Pruning method: Lambda See [2] for details.
      See Also:

    • TAGS_PRUNING

      public static final Tag[] TAGS_PRUNING
      Pruning methods

  • Constructor Details

    • StringKernel

      public StringKernel()
      default constructor

    • StringKernel

      public StringKernel(Instances data, int cacheSize, int subsequenceLength, double lambda, boolean debug) throws Exception
      creates a new StringKernel object. Initializes the kernel cache and the 'lambda cache', i.e. the precalculated powers of lambda from lambda^2 to lambda^MAX_POWER_OF_LAMBDA
      Parameters:
      data - the dataset to use
      cacheSize - the size of the cache
      subsequenceLength - the subsequence length
      lambda - the lambda value
      debug - whether to output debug information
      Throws:
      Exception - if something goes wrong

  • Method Details

    • globalInfo

      public String globalInfo()
      Returns a string describing the kernel
      Specified by:
      globalInfo in class Kernel
      Returns:
      a description suitable for displaying in the explorer/experimenter gui

    • getTechnicalInformation

      public TechnicalInformation getTechnicalInformation()
      Returns an instance of a TechnicalInformation object, containing detailed information about the technical background of this class, e.g., paper reference or book this class is based on.
      Specified by:
      getTechnicalInformation in interface TechnicalInformationHandler
      Returns:
      the technical information about this class

    • listOptions

      public Enumeration<Option> listOptions()
      Returns an enumeration describing the available options.
      Specified by:
      listOptions in interface OptionHandler
      Overrides:
      listOptions in class Kernel
      Returns:
      an enumeration of all the available options.

    • setOptions

      public void setOptions(String[] options) throws Exception
      Parses a given list of options.

      Valid options are: 

       -D
  Enables debugging output (if available) to be printed.
  (default: off)
 
       -P <0|1>
  The pruning method to use:
  0 = No pruning
  1 = Lambda pruning
  (default: 0)
 
       -C <num>
  The size of the cache (a prime number).
  (default: 250007)
 
       -IC <num>
  The size of the internal cache (a prime number).
  (default: 200003)
 
       -L <num>
  The lambda constant. Penalizes non-continuous subsequence
  matches. Must be in (0,1).
  (default: 0.5)
 
       -ssl <num>
  The length of the subsequence.
  (default: 3)
 
       -ssl-max <num>
  The maximum length of the subsequence.
  (default: 9)
 
       -N
  Use normalization.
  (default: no)
      Specified by:
      setOptions in interface OptionHandler
      Overrides:
      setOptions in class Kernel
      Parameters:
      options - the list of options as an array of strings
      Throws:
      Exception - if an option is not supported

    • getOptions

      public String[] getOptions()
      Gets the current settings of the Kernel.
      Specified by:
      getOptions in interface OptionHandler
      Overrides:
      getOptions in class Kernel
      Returns:
      an array of strings suitable for passing to setOptions

    • pruningMethodTipText

      public String pruningMethodTipText()
      Returns the tip text for this property
      Returns:
      tip text for this property suitable for displaying in the explorer/experimenter gui

    • setPruningMethod

      public void setPruningMethod(SelectedTag value)
      Sets the method used to for pruning.
      Parameters:
      value - the pruning method to use.

    • getPruningMethod

      public SelectedTag getPruningMethod()
      Gets the method used for pruning.
      Returns:
      the pruning method to use.

    • setCacheSize

      public void setCacheSize(int value)
      Sets the size of the cache to use (a prime number)
      Parameters:
      value - the size of the cache

    • getCacheSize

      public int getCacheSize()
      Gets the size of the cache
      Returns:
      the cache size

    • cacheSizeTipText

      public String cacheSizeTipText()
      Returns the tip text for this property
      Returns:
      tip text for this property suitable for displaying in the explorer/experimenter gui

    • setInternalCacheSize

      public void setInternalCacheSize(int value)
      sets the size of the internal cache for intermediate results. Memory consumption is about 16x this amount in bytes. Only use when lambda pruning is switched off.
      Parameters:
      value - the size of the internal cache

    • getInternalCacheSize

      public int getInternalCacheSize()
      Gets the size of the internal cache
      Returns:
      the cache size

    • internalCacheSizeTipText

      public String internalCacheSizeTipText()
      Returns the tip text for this property
      Returns:
      tip text for this property suitable for displaying in the explorer/experimenter gui

    • setSubsequenceLength

      public void setSubsequenceLength(int value)
      Sets the length of the subsequence.
      Parameters:
      value - the length

    • getSubsequenceLength

      public int getSubsequenceLength()
      Returns the length of the subsequence
      Returns:
      the length

    • subsequenceLengthTipText

      public String subsequenceLengthTipText()
      Returns the tip text for this property
      Returns:
      tip text for this property suitable for displaying in the explorer/experimenter gui

    • setMaxSubsequenceLength

      public void setMaxSubsequenceLength(int value)
      Sets the maximum length of the subsequence.
      Parameters:
      value - the maximum length

    • getMaxSubsequenceLength

      public int getMaxSubsequenceLength()
      Returns the maximum length of the subsequence
      Returns:
      the maximum length

    • maxSubsequenceLengthTipText

      public String maxSubsequenceLengthTipText()
      Returns the tip text for this property
      Returns:
      tip text for this property suitable for displaying in the explorer/experimenter gui

    • setLambda

      public void setLambda(double value)
      Sets the lambda constant used in the string kernel
      Parameters:
      value - the lambda value to use

    • getLambda

      public double getLambda()
      Gets the lambda constant used in the string kernel
      Returns:
      the current lambda constant

    • lambdaTipText

      public String lambdaTipText()
      Returns the tip text for this property
      Returns:
      tip text for this property suitable for displaying in the explorer/experimenter gui

    • setUseNormalization

      public void setUseNormalization(boolean value)
      Sets whether to use normalization. Each time this value is changed, the kernel cache is cleared.
      Parameters:
      value - whether to use normalization

    • getUseNormalization

      public boolean getUseNormalization()
      Returns whether normalization is used.
      Returns:
      true if normalization is used

    • useNormalizationTipText

      public String useNormalizationTipText()
      Returns the tip text for this property
      Returns:
      tip text for this property suitable for displaying in the explorer/experimenter gui

    • eval

      public double eval(int id1, int id2, Instance inst1) throws Exception
      Computes the result of the kernel function for two instances. If id1 == -1, eval use inst1 instead of an instance in the dataset.
      Specified by:
      eval in class Kernel
      Parameters:
      id1 - the index of the first instance in the dataset
      id2 - the index of the second instance in the dataset
      inst1 - the instance corresponding to id1 (used if id1 == -1)
      Returns:
      the result of the kernel function
      Throws:
      Exception - if something goes wrong

    • clean

      public void clean()
      Frees the memory used by the kernel. (Useful with kernels which use cache.) This function is called when the training is done. i.e. after that, eval will be called with id1 == -1.
      Specified by:
      clean in class Kernel

    • numEvals

      public int numEvals()
      Returns the number of kernel evaluation performed.
      Specified by:
      numEvals in class Kernel
      Returns:
      the number of kernel evaluation performed.

    • numCacheHits

      public int numCacheHits()
      Returns the number of dot product cache hits.
      Specified by:
      numCacheHits in class Kernel
      Returns:
      the number of dot product cache hits, or -1 if not supported by this kernel.

    • normalizedKernel

      public double normalizedKernel(char[] s, char[] t)
      evaluates the normalized kernel between s and t. See [1] for details about the normalized SSK.
      Parameters:
      s - first input string
      t - second input string
      Returns:
      a double indicating their distance, or similarity

    • unnormalizedKernel

      public double unnormalizedKernel(char[] s, char[] t)
      evaluates the unnormalized kernel between s and t. See [1] for details about the unnormalized SSK.
      Parameters:
      s - first input string
      t - second input string
      Returns:
      a double indicating their distance, or similarity

    • getCapabilities

      public Capabilities getCapabilities()
      Returns the Capabilities of this kernel.
      Specified by:
      getCapabilities in interface CapabilitiesHandler
      Overrides:
      getCapabilities in class Kernel
      Returns:
      the capabilities of this object
      See Also:

    • buildKernel

      public void buildKernel(Instances data) throws Exception
      builds the kernel with the given data.
      Overrides:
      buildKernel in class Kernel
      Parameters:
      data - the data to base the kernel on
      Throws:
      Exception - if something goes wrong, e.g., the data does not consist of one string attribute and the class

    • getRevision

      public String getRevision()
      Returns the revision string.
      Specified by:
      getRevision in interface RevisionHandler
      Overrides:
      getRevision in class Kernel
      Returns:
      the revision