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: 14534 $
Author:
  Florian Kleedorfer (kleedorfer@austria.fm), Alexander K. Seewald (alex@seewald.at)
See Also:
  - Serialized Form

- ## Field Summary

  Fields
  Modifier and Type
  Field
  Description
  `static final int`
  `PRUNING_LAMBDA`
  Pruning method: Lambda See [2] for details.
  `static final int`
  `PRUNING_NONE`
  Pruning method: No Pruning
  `static final Tag[]`
  `TAGS_PRUNING`
  Pruning methods

- ## Constructor Summary

  Constructors
  Constructor
  Description
  `StringKernel()`
  default constructor
  `StringKernel(Instances data, int cacheSize, int subsequenceLength, double lambda, boolean debug)`
  creates a new StringKernel object.

- ## Method Summary

  Modifier and Type
  Method
  Description
  `void`
  `buildKernel(Instances data)`
  builds the kernel with the given data.
  `String`
  `cacheSizeTipText()`
  Returns the tip text for this property
  `void`
  `clean()`
  Frees the memory used by the kernel.
  `double`
  `eval(int id1, int id2, Instance inst1)`
  Computes the result of the kernel function for two instances.
  `int`
  `getCacheSize()`
  Gets the size of the cache
  `Capabilities`
  `getCapabilities()`
  Returns the Capabilities of this kernel.
  `int`
  `getInternalCacheSize()`
  Gets the size of the internal cache
  `double`
  `getLambda()`
  Gets the lambda constant used in the string kernel
  `int`
  `getMaxSubsequenceLength()`
  Returns the maximum length of the subsequence
  `String[]`
  `getOptions()`
  Gets the current settings of the Kernel.
  `SelectedTag`
  `getPruningMethod()`
  Gets the method used for pruning.
  `String`
  `getRevision()`
  Returns the revision string.
  `int`
  `getSubsequenceLength()`
  Returns the length of the subsequence
  `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.
  `boolean`
  `getUseNormalization()`
  Returns whether normalization is used.
  `String`
  `globalInfo()`
  Returns a string describing the kernel
  `String`
  `internalCacheSizeTipText()`
  Returns the tip text for this property
  `String`
  `lambdaTipText()`
  Returns the tip text for this property
  `Enumeration<Option>`
  `listOptions()`
  Returns an enumeration describing the available options.
  `String`
  `maxSubsequenceLengthTipText()`
  Returns the tip text for this property
  `double`
  `normalizedKernel(char[] s, char[] t)`
  evaluates the normalized kernel between s and t.
  `int`
  `numCacheHits()`
  Returns the number of dot product cache hits.
  `int`
  `numEvals()`
  Returns the number of kernel evaluation performed.
  `String`
  `pruningMethodTipText()`
  Returns the tip text for this property
  `void`
  `setCacheSize(int value)`
  Sets the size of the cache to use (a prime number)
  `void`
  `setInternalCacheSize(int value)`
  sets the size of the internal cache for intermediate results.
  `void`
  `setLambda(double value)`
  Sets the lambda constant used in the string kernel
  `void`
  `setMaxSubsequenceLength(int value)`
  Sets the maximum length of the subsequence.
  `void`
  `setOptions(String[] options)`
  Parses a given list of options.
  `void`
  `setPruningMethod(SelectedTag value)`
  Sets the method used to for pruning.
  `void`
  `setSubsequenceLength(int value)`
  Sets the length of the subsequence.
  `void`
  `setUseNormalization(boolean value)`
  Sets whether to use normalization.
  `String`
  `subsequenceLengthTipText()`
  Returns the tip text for this property
  `double`
  `unnormalizedKernel(char[] s, char[] t)`
  evaluates the unnormalized kernel between s and t.
  `String`
  `useNormalizationTipText()`
  Returns the tip text for this property

  ### Methods inherited from class weka.classifiers.functions.supportVector.Kernel

  `debugTipText, forName, getChecksTurnedOff, getDebug, getDoNotCheckCapabilities, makeCopies, makeCopy, setChecksTurnedOff, setDebug, setDoNotCheckCapabilities`

  ### Methods inherited from class java.lang.Object

  `equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

- ## Field Details

  - ### PRUNING_NONE

    public static final int PRUNING_NONE
    Pruning method: No Pruning
    See Also:
      - Constant Field Values

  - ### PRUNING_LAMBDA

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

  - ### 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:
      - `Capabilities`

  - ### 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