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Text Segmentation Metrics

1. Windowdiff

Pevzner, L., and Hearst, M., A Critique and Improvement of
  an Evaluation Metric for Text Segmentation,
  Computational Linguistics 28, 19-36


2. Generalized Hamming Distance

Bookstein A., Kulyukin V.A., Raita T.
Generalized Hamming Distance
Information Retrieval 5, 2002, pp 353-375

Baseline implementation in C++
http://digital.cs.usu.edu/~vkulyukin/vkweb/software/ghd/ghd.html

Study describing benefits of Generalized Hamming Distance Versus
WindowDiff for evaluating text segmentation tasks
Begsten, Y.  Quel indice pour mesurer l'efficacite en segmentation de textes ?
TALN 2009


3. Pk text segmentation metric

Beeferman D., Berger A., Lafferty J. (1999)
Statistical Models for Text Segmentation
Machine Learning, 34, 177-210
é    NÚ1Fc                 C   sª   t | ƒt |ƒkrtdƒ‚|t | ƒkrtdƒ‚d}tt | ƒ| d ƒD ](}t| ||| …  |¡|||| …  |¡ ƒ}|rC||7 }q"|td|ƒ7 }q"|t | ƒ| d  S )aW  
    Compute the windowdiff score for a pair of segmentations.  A
    segmentation is any sequence over a vocabulary of two items
    (e.g. "0", "1"), where the specified boundary value is used to
    mark the edge of a segmentation.

        >>> s1 = "000100000010"
        >>> s2 = "000010000100"
        >>> s3 = "100000010000"
        >>> '%.2f' % windowdiff(s1, s1, 3)
        '0.00'
        >>> '%.2f' % windowdiff(s1, s2, 3)
        '0.30'
        >>> '%.2f' % windowdiff(s2, s3, 3)
        '0.80'

    :param seg1: a segmentation
    :type seg1: str or list
    :param seg2: a segmentation
    :type seg2: str or list
    :param k: window width
    :type k: int
    :param boundary: boundary value
    :type boundary: str or int or bool
    :param weighted: use the weighted variant of windowdiff
    :type weighted: boolean
    :rtype: float
    z!Segmentations have unequal lengthzCWindow width k should be smaller or equal than segmentation lengthsr   é   ç      ð?)ÚlenÚ
ValueErrorÚrangeÚabsÚcountÚmin)Zseg1Zseg2ÚkÚboundaryZweightedÚwdÚiZndiff© r   úH/var/www/auris/lib/python3.10/site-packages/nltk/metrics/segmentation.pyÚ
windowdiff1   s   ÿ0
r   c                 C   sF   t  | |f¡}|t  |¡ |dd d …f< |t  | ¡ |d d …df< |S )Nr   )ÚnpÚemptyZarange)ZnrowsZncolsÚins_costÚdel_costÚmatr   r   r   Ú	_init_matb   s   r   c                 C   s¦   t |ƒD ]L\}}t |ƒD ]C\}}	|t||	 ƒ | ||f  }
||	kr)| ||f }n||	kr8|| ||d f  }n
|| |d |f  }t||
ƒ| |d |d f< qqd S )Nr   )Ú	enumerater   r
   )r   ZrowvZcolvr   r   Úshift_cost_coeffr   ZrowiÚjZcoljZ
shift_costZtcostr   r   r   Ú_ghd_auxi   s   õÿr   ç       @r   c                    s´   ‡ fdd„t | ƒD ƒ}‡ fdd„t |ƒD ƒ}t|ƒ}t|ƒ}	|dkr(|	dkr(dS |dkr4|	dkr4|| S |dkr@|	dkr@|	| S t|	d |d ||ƒ}
t|
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d ƒS )av  
    Compute the Generalized Hamming Distance for a reference and a hypothetical
    segmentation, corresponding to the cost related to the transformation
    of the hypothetical segmentation into the reference segmentation
    through boundary insertion, deletion and shift operations.

    A segmentation is any sequence over a vocabulary of two items
    (e.g. "0", "1"), where the specified boundary value is used to
    mark the edge of a segmentation.

    Recommended parameter values are a shift_cost_coeff of 2.
    Associated with a ins_cost, and del_cost equal to the mean segment
    length in the reference segmentation.

        >>> # Same examples as Kulyukin C++ implementation
        >>> ghd('1100100000', '1100010000', 1.0, 1.0, 0.5)
        0.5
        >>> ghd('1100100000', '1100000001', 1.0, 1.0, 0.5)
        2.0
        >>> ghd('011', '110', 1.0, 1.0, 0.5)
        1.0
        >>> ghd('1', '0', 1.0, 1.0, 0.5)
        1.0
        >>> ghd('111', '000', 1.0, 1.0, 0.5)
        3.0
        >>> ghd('000', '111', 1.0, 2.0, 0.5)
        6.0

    :param ref: the reference segmentation
    :type ref: str or list
    :param hyp: the hypothetical segmentation
    :type hyp: str or list
    :param ins_cost: insertion cost
    :type ins_cost: float
    :param del_cost: deletion cost
    :type del_cost: float
    :param shift_cost_coeff: constant used to compute the cost of a shift.
        ``shift cost = shift_cost_coeff * |i - j|`` where ``i`` and ``j``
        are the positions indicating the shift
    :type shift_cost_coeff: float
    :param boundary: boundary value
    :type boundary: str or int or bool
    :rtype: float
    c                    ó   g | ]
\}}|ˆ kr|‘qS r   r   ©Ú.0r   Úval©r   r   r   Ú
<listcomp>§   ó    zghd.<locals>.<listcomp>c                    r   r   r   r   r!   r   r   r"   ¨   r#   r   g        r   )éÿÿÿÿr$   )r   r   r   r   Úfloat)ÚrefÚhypr   r   r   r   Zref_idxZhyp_idxZ
nref_boundZ
nhyp_boundr   r   r!   r   Úghdy   s   .r(   c                 C   sœ   |du rt tt| ƒ|  |¡d  ƒƒ}d}tt| ƒ| d ƒD ]$}| ||| …  |¡dk}|||| …  |¡dk}||krC|d7 }q|t| ƒ| d  S )aù  
    Compute the Pk metric for a pair of segmentations A segmentation
    is any sequence over a vocabulary of two items (e.g. "0", "1"),
    where the specified boundary value is used to mark the edge of a
    segmentation.

    >>> '%.2f' % pk('0100'*100, '1'*400, 2)
    '0.50'
    >>> '%.2f' % pk('0100'*100, '0'*400, 2)
    '0.50'
    >>> '%.2f' % pk('0100'*100, '0100'*100, 2)
    '0.00'

    :param ref: the reference segmentation
    :type ref: str or list
    :param hyp: the segmentation to evaluate
    :type hyp: str or list
    :param k: window size, if None, set to half of the average reference segment length
    :type boundary: str or int or bool
    :param boundary: boundary value
    :type boundary: str or int or bool
    :rtype: float
    Nr   r   r   r   )ÚintÚroundr   r	   r   )r&   r'   r   r   Úerrr   ÚrÚhr   r   r   Úpk¼   s   €r.   )r   F)r   r   r   r   )Nr   )	Ú__doc__Únumpyr   ÚImportErrorr   r   r   r(   r.   r   r   r   r   Ú<module>   s   
 ÿ
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