231 lines
7 KiB
Python
231 lines
7 KiB
Python
# Natural Language Toolkit: Text Segmentation Metrics
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#
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# Copyright (C) 2001-2018 NLTK Project
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# Author: Edward Loper <edloper@gmail.com>
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# Steven Bird <stevenbird1@gmail.com>
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# David Doukhan <david.doukhan@gmail.com>
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# URL: <http://nltk.org/>
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# For license information, see LICENSE.TXT
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"""
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Text Segmentation Metrics
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1. Windowdiff
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Pevzner, L., and Hearst, M., A Critique and Improvement of
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an Evaluation Metric for Text Segmentation,
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Computational Linguistics 28, 19-36
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2. Generalized Hamming Distance
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Bookstein A., Kulyukin V.A., Raita T.
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Generalized Hamming Distance
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Information Retrieval 5, 2002, pp 353-375
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Baseline implementation in C++
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http://digital.cs.usu.edu/~vkulyukin/vkweb/software/ghd/ghd.html
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Study describing benefits of Generalized Hamming Distance Versus
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WindowDiff for evaluating text segmentation tasks
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Begsten, Y. Quel indice pour mesurer l'efficacite en segmentation de textes ?
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TALN 2009
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3. Pk text segmentation metric
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Beeferman D., Berger A., Lafferty J. (1999)
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Statistical Models for Text Segmentation
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Machine Learning, 34, 177-210
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"""
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try:
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import numpy as np
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except ImportError:
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pass
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from six.moves import range
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def windowdiff(seg1, seg2, k, boundary="1", weighted=False):
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"""
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Compute the windowdiff score for a pair of segmentations. A
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segmentation is any sequence over a vocabulary of two items
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(e.g. "0", "1"), where the specified boundary value is used to
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mark the edge of a segmentation.
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>>> s1 = "000100000010"
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>>> s2 = "000010000100"
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>>> s3 = "100000010000"
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>>> '%.2f' % windowdiff(s1, s1, 3)
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'0.00'
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>>> '%.2f' % windowdiff(s1, s2, 3)
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'0.30'
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>>> '%.2f' % windowdiff(s2, s3, 3)
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'0.80'
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:param seg1: a segmentation
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:type seg1: str or list
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:param seg2: a segmentation
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:type seg2: str or list
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:param k: window width
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:type k: int
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:param boundary: boundary value
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:type boundary: str or int or bool
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:param weighted: use the weighted variant of windowdiff
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:type weighted: boolean
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:rtype: float
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"""
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if len(seg1) != len(seg2):
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raise ValueError("Segmentations have unequal length")
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if k > len(seg1):
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raise ValueError("Window width k should be smaller or equal than segmentation lengths")
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wd = 0
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for i in range(len(seg1) - k + 1):
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ndiff = abs(seg1[i:i+k].count(boundary) - seg2[i:i+k].count(boundary))
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if weighted:
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wd += ndiff
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else:
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wd += min(1, ndiff)
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return wd / (len(seg1) - k + 1.)
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# Generalized Hamming Distance
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def _init_mat(nrows, ncols, ins_cost, del_cost):
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mat = np.empty((nrows, ncols))
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mat[0, :] = ins_cost * np.arange(ncols)
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mat[:, 0] = del_cost * np.arange(nrows)
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return mat
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def _ghd_aux(mat, rowv, colv, ins_cost, del_cost, shift_cost_coeff):
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for i, rowi in enumerate(rowv):
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for j, colj in enumerate(colv):
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shift_cost = shift_cost_coeff * abs(rowi - colj) + mat[i, j]
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if rowi == colj:
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# boundaries are at the same location, no transformation required
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tcost = mat[i, j]
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elif rowi > colj:
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# boundary match through a deletion
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tcost = del_cost + mat[i, j + 1]
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else:
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# boundary match through an insertion
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tcost = ins_cost + mat[i + 1, j]
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mat[i + 1, j + 1] = min(tcost, shift_cost)
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def ghd(ref, hyp, ins_cost=2.0, del_cost=2.0, shift_cost_coeff=1.0, boundary='1'):
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"""
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Compute the Generalized Hamming Distance for a reference and a hypothetical
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segmentation, corresponding to the cost related to the transformation
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of the hypothetical segmentation into the reference segmentation
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through boundary insertion, deletion and shift operations.
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A segmentation is any sequence over a vocabulary of two items
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(e.g. "0", "1"), where the specified boundary value is used to
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mark the edge of a segmentation.
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Recommended parameter values are a shift_cost_coeff of 2.
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Associated with a ins_cost, and del_cost equal to the mean segment
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length in the reference segmentation.
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>>> # Same examples as Kulyukin C++ implementation
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>>> ghd('1100100000', '1100010000', 1.0, 1.0, 0.5)
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0.5
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>>> ghd('1100100000', '1100000001', 1.0, 1.0, 0.5)
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2.0
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>>> ghd('011', '110', 1.0, 1.0, 0.5)
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1.0
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>>> ghd('1', '0', 1.0, 1.0, 0.5)
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1.0
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>>> ghd('111', '000', 1.0, 1.0, 0.5)
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3.0
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>>> ghd('000', '111', 1.0, 2.0, 0.5)
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6.0
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:param ref: the reference segmentation
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:type ref: str or list
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:param hyp: the hypothetical segmentation
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:type hyp: str or list
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:param ins_cost: insertion cost
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:type ins_cost: float
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:param del_cost: deletion cost
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:type del_cost: float
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:param shift_cost_coeff: constant used to compute the cost of a shift.
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shift cost = shift_cost_coeff * |i - j| where i and j are
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the positions indicating the shift
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:type shift_cost_coeff: float
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:param boundary: boundary value
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:type boundary: str or int or bool
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:rtype: float
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"""
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ref_idx = [i for (i, val) in enumerate(ref) if val == boundary]
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hyp_idx = [i for (i, val) in enumerate(hyp) if val == boundary]
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nref_bound = len(ref_idx)
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nhyp_bound = len(hyp_idx)
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if nref_bound == 0 and nhyp_bound == 0:
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return 0.0
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elif nref_bound > 0 and nhyp_bound == 0:
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return nref_bound * ins_cost
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elif nref_bound == 0 and nhyp_bound > 0:
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return nhyp_bound * del_cost
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mat = _init_mat(nhyp_bound + 1, nref_bound + 1, ins_cost, del_cost)
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_ghd_aux(mat, hyp_idx, ref_idx, ins_cost, del_cost, shift_cost_coeff)
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return mat[-1, -1]
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# Beeferman's Pk text segmentation evaluation metric
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def pk(ref, hyp, k=None, boundary='1'):
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"""
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Compute the Pk metric for a pair of segmentations A segmentation
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is any sequence over a vocabulary of two items (e.g. "0", "1"),
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where the specified boundary value is used to mark the edge of a
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segmentation.
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>>> '%.2f' % pk('0100'*100, '1'*400, 2)
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'0.50'
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>>> '%.2f' % pk('0100'*100, '0'*400, 2)
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'0.50'
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>>> '%.2f' % pk('0100'*100, '0100'*100, 2)
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'0.00'
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:param ref: the reference segmentation
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:type ref: str or list
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:param hyp: the segmentation to evaluate
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:type hyp: str or list
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:param k: window size, if None, set to half of the average reference segment length
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:type boundary: str or int or bool
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:param boundary: boundary value
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:type boundary: str or int or bool
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:rtype: float
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"""
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if k is None:
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k = int(round(len(ref) / (ref.count(boundary) * 2.)))
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err = 0
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for i in range(len(ref)-k +1):
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r = ref[i:i+k].count(boundary) > 0
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h = hyp[i:i+k].count(boundary) > 0
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if r != h:
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err += 1
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return err / (len(ref)-k +1.)
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# skip doctests if numpy is not installed
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def setup_module(module):
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from nose import SkipTest
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try:
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import numpy
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except ImportError:
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raise SkipTest("numpy is required for nltk.metrics.segmentation")
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