264 lines
8.3 KiB
Python
264 lines
8.3 KiB
Python
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# Natural Language Toolkit: Gale-Church Aligner
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#
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# Copyright (C) 2001-2023 NLTK Project
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# Author: Torsten Marek <marek@ifi.uzh.ch>
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# Contributor: Cassidy Laidlaw, Liling Tan
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# URL: <https://www.nltk.org/>
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# For license information, see LICENSE.TXT
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"""
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A port of the Gale-Church Aligner.
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Gale & Church (1993), A Program for Aligning Sentences in Bilingual Corpora.
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https://aclweb.org/anthology/J93-1004.pdf
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"""
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import math
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try:
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from norm import logsf as norm_logsf
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from scipy.stats import norm
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except ImportError:
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def erfcc(x):
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"""Complementary error function."""
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z = abs(x)
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t = 1 / (1 + 0.5 * z)
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r = t * math.exp(
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-z * z
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- 1.26551223
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+ t
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* (
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1.00002368
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+ t
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* (
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0.37409196
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+ t
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* (
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0.09678418
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+ t
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* (
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-0.18628806
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+ t
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* (
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0.27886807
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+ t
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* (
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-1.13520398
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+ t
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* (1.48851587 + t * (-0.82215223 + t * 0.17087277))
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)
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)
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)
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)
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)
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)
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)
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if x >= 0.0:
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return r
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else:
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return 2.0 - r
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def norm_cdf(x):
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"""Return the area under the normal distribution from M{-∞..x}."""
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return 1 - 0.5 * erfcc(x / math.sqrt(2))
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def norm_logsf(x):
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try:
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return math.log(1 - norm_cdf(x))
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except ValueError:
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return float("-inf")
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LOG2 = math.log(2)
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class LanguageIndependent:
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# These are the language-independent probabilities and parameters
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# given in Gale & Church
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# for the computation, l_1 is always the language with less characters
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PRIORS = {
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(1, 0): 0.0099,
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(0, 1): 0.0099,
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(1, 1): 0.89,
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(2, 1): 0.089,
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(1, 2): 0.089,
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(2, 2): 0.011,
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}
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AVERAGE_CHARACTERS = 1
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VARIANCE_CHARACTERS = 6.8
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def trace(backlinks, source_sents_lens, target_sents_lens):
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"""
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Traverse the alignment cost from the tracebacks and retrieves
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appropriate sentence pairs.
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:param backlinks: A dictionary where the key is the alignment points and value is the cost (referencing the LanguageIndependent.PRIORS)
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:type backlinks: dict
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:param source_sents_lens: A list of target sentences' lengths
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:type source_sents_lens: list(int)
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:param target_sents_lens: A list of target sentences' lengths
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:type target_sents_lens: list(int)
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"""
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links = []
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position = (len(source_sents_lens), len(target_sents_lens))
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while position != (0, 0) and all(p >= 0 for p in position):
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try:
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s, t = backlinks[position]
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except TypeError:
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position = (position[0] - 1, position[1] - 1)
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continue
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for i in range(s):
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for j in range(t):
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links.append((position[0] - i - 1, position[1] - j - 1))
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position = (position[0] - s, position[1] - t)
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return links[::-1]
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def align_log_prob(i, j, source_sents, target_sents, alignment, params):
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"""Returns the log probability of the two sentences C{source_sents[i]}, C{target_sents[j]}
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being aligned with a specific C{alignment}.
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@param i: The offset of the source sentence.
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@param j: The offset of the target sentence.
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@param source_sents: The list of source sentence lengths.
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@param target_sents: The list of target sentence lengths.
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@param alignment: The alignment type, a tuple of two integers.
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@param params: The sentence alignment parameters.
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@returns: The log probability of a specific alignment between the two sentences, given the parameters.
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"""
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l_s = sum(source_sents[i - offset - 1] for offset in range(alignment[0]))
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l_t = sum(target_sents[j - offset - 1] for offset in range(alignment[1]))
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try:
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# actually, the paper says l_s * params.VARIANCE_CHARACTERS, this is based on the C
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# reference implementation. With l_s in the denominator, insertions are impossible.
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m = (l_s + l_t / params.AVERAGE_CHARACTERS) / 2
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delta = (l_s * params.AVERAGE_CHARACTERS - l_t) / math.sqrt(
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m * params.VARIANCE_CHARACTERS
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)
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except ZeroDivisionError:
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return float("-inf")
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return -(LOG2 + norm_logsf(abs(delta)) + math.log(params.PRIORS[alignment]))
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def align_blocks(source_sents_lens, target_sents_lens, params=LanguageIndependent):
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"""Return the sentence alignment of two text blocks (usually paragraphs).
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>>> align_blocks([5,5,5], [7,7,7])
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[(0, 0), (1, 1), (2, 2)]
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>>> align_blocks([10,5,5], [12,20])
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[(0, 0), (1, 1), (2, 1)]
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>>> align_blocks([12,20], [10,5,5])
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[(0, 0), (1, 1), (1, 2)]
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>>> align_blocks([10,2,10,10,2,10], [12,3,20,3,12])
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[(0, 0), (1, 1), (2, 2), (3, 2), (4, 3), (5, 4)]
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@param source_sents_lens: The list of source sentence lengths.
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@param target_sents_lens: The list of target sentence lengths.
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@param params: the sentence alignment parameters.
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@return: The sentence alignments, a list of index pairs.
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"""
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alignment_types = list(params.PRIORS.keys())
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# there are always three rows in the history (with the last of them being filled)
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D = [[]]
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backlinks = {}
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for i in range(len(source_sents_lens) + 1):
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for j in range(len(target_sents_lens) + 1):
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min_dist = float("inf")
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min_align = None
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for a in alignment_types:
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prev_i = -1 - a[0]
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prev_j = j - a[1]
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if prev_i < -len(D) or prev_j < 0:
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continue
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p = D[prev_i][prev_j] + align_log_prob(
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i, j, source_sents_lens, target_sents_lens, a, params
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)
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if p < min_dist:
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min_dist = p
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min_align = a
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if min_dist == float("inf"):
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min_dist = 0
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backlinks[(i, j)] = min_align
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D[-1].append(min_dist)
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if len(D) > 2:
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D.pop(0)
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D.append([])
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return trace(backlinks, source_sents_lens, target_sents_lens)
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def align_texts(source_blocks, target_blocks, params=LanguageIndependent):
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"""Creates the sentence alignment of two texts.
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Texts can consist of several blocks. Block boundaries cannot be crossed by sentence
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alignment links.
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Each block consists of a list that contains the lengths (in characters) of the sentences
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in this block.
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@param source_blocks: The list of blocks in the source text.
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@param target_blocks: The list of blocks in the target text.
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@param params: the sentence alignment parameters.
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@returns: A list of sentence alignment lists
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"""
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if len(source_blocks) != len(target_blocks):
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raise ValueError(
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"Source and target texts do not have the same number of blocks."
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)
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return [
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align_blocks(source_block, target_block, params)
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for source_block, target_block in zip(source_blocks, target_blocks)
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]
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# File I/O functions; may belong in a corpus reader
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def split_at(it, split_value):
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"""Splits an iterator C{it} at values of C{split_value}.
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Each instance of C{split_value} is swallowed. The iterator produces
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subiterators which need to be consumed fully before the next subiterator
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can be used.
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"""
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def _chunk_iterator(first):
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v = first
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while v != split_value:
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yield v
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v = it.next()
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while True:
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yield _chunk_iterator(it.next())
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def parse_token_stream(stream, soft_delimiter, hard_delimiter):
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"""Parses a stream of tokens and splits it into sentences (using C{soft_delimiter} tokens)
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and blocks (using C{hard_delimiter} tokens) for use with the L{align_texts} function.
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"""
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return [
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[
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sum(len(token) for token in sentence_it)
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for sentence_it in split_at(block_it, soft_delimiter)
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]
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for block_it in split_at(stream, hard_delimiter)
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]
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