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774 lines
28 KiB
Python
774 lines
28 KiB
Python
# Natural Language Toolkit: Dependency Grammars
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#
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# Copyright (C) 2001-2020 NLTK Project
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# Author: Jason Narad <jason.narad@gmail.com>
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#
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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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import math
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import logging
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from nltk.parse.dependencygraph import DependencyGraph
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logger = logging.getLogger(__name__)
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#################################################################
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# DependencyScorerI - Interface for Graph-Edge Weight Calculation
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#################################################################
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class DependencyScorerI(object):
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"""
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A scorer for calculated the weights on the edges of a weighted
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dependency graph. This is used by a
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``ProbabilisticNonprojectiveParser`` to initialize the edge
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weights of a ``DependencyGraph``. While typically this would be done
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by training a binary classifier, any class that can return a
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multidimensional list representation of the edge weights can
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implement this interface. As such, it has no necessary
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fields.
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"""
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def __init__(self):
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if self.__class__ == DependencyScorerI:
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raise TypeError("DependencyScorerI is an abstract interface")
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def train(self, graphs):
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"""
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:type graphs: list(DependencyGraph)
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:param graphs: A list of dependency graphs to train the scorer.
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Typically the edges present in the graphs can be used as
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positive training examples, and the edges not present as negative
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examples.
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"""
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raise NotImplementedError()
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def score(self, graph):
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"""
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:type graph: DependencyGraph
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:param graph: A dependency graph whose set of edges need to be
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scored.
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:rtype: A three-dimensional list of numbers.
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:return: The score is returned in a multidimensional(3) list, such
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that the outer-dimension refers to the head, and the
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inner-dimension refers to the dependencies. For instance,
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scores[0][1] would reference the list of scores corresponding to
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arcs from node 0 to node 1. The node's 'address' field can be used
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to determine its number identification.
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For further illustration, a score list corresponding to Fig.2 of
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Keith Hall's 'K-best Spanning Tree Parsing' paper:
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scores = [[[], [5], [1], [1]],
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[[], [], [11], [4]],
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[[], [10], [], [5]],
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[[], [8], [8], []]]
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When used in conjunction with a MaxEntClassifier, each score would
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correspond to the confidence of a particular edge being classified
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with the positive training examples.
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"""
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raise NotImplementedError()
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#################################################################
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# NaiveBayesDependencyScorer
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#################################################################
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class NaiveBayesDependencyScorer(DependencyScorerI):
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"""
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A dependency scorer built around a MaxEnt classifier. In this
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particular class that classifier is a ``NaiveBayesClassifier``.
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It uses head-word, head-tag, child-word, and child-tag features
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for classification.
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>>> from nltk.parse.dependencygraph import DependencyGraph, conll_data2
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>>> graphs = [DependencyGraph(entry) for entry in conll_data2.split('\\n\\n') if entry]
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>>> npp = ProbabilisticNonprojectiveParser()
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>>> npp.train(graphs, NaiveBayesDependencyScorer())
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>>> parses = npp.parse(['Cathy', 'zag', 'hen', 'zwaaien', '.'], ['N', 'V', 'Pron', 'Adj', 'N', 'Punc'])
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>>> len(list(parses))
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1
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"""
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def __init__(self):
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pass # Do nothing without throwing error
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def train(self, graphs):
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"""
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Trains a ``NaiveBayesClassifier`` using the edges present in
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graphs list as positive examples, the edges not present as
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negative examples. Uses a feature vector of head-word,
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head-tag, child-word, and child-tag.
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:type graphs: list(DependencyGraph)
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:param graphs: A list of dependency graphs to train the scorer.
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"""
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from nltk.classify import NaiveBayesClassifier
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# Create training labeled training examples
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labeled_examples = []
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for graph in graphs:
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for head_node in graph.nodes.values():
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for child_index, child_node in graph.nodes.items():
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if child_index in head_node["deps"]:
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label = "T"
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else:
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label = "F"
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labeled_examples.append(
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(
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dict(
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a=head_node["word"],
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b=head_node["tag"],
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c=child_node["word"],
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d=child_node["tag"],
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),
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label,
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)
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)
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self.classifier = NaiveBayesClassifier.train(labeled_examples)
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def score(self, graph):
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"""
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Converts the graph into a feature-based representation of
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each edge, and then assigns a score to each based on the
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confidence of the classifier in assigning it to the
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positive label. Scores are returned in a multidimensional list.
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:type graph: DependencyGraph
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:param graph: A dependency graph to score.
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:rtype: 3 dimensional list
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:return: Edge scores for the graph parameter.
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"""
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# Convert graph to feature representation
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edges = []
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for head_node in graph.nodes.values():
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for child_node in graph.nodes.values():
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edges.append(
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(
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dict(
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a=head_node["word"],
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b=head_node["tag"],
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c=child_node["word"],
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d=child_node["tag"],
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)
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)
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)
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# Score edges
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edge_scores = []
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row = []
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count = 0
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for pdist in self.classifier.prob_classify_many(edges):
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logger.debug("%.4f %.4f", pdist.prob("T"), pdist.prob("F"))
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# smoothing in case the probability = 0
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row.append([math.log(pdist.prob("T") + 0.00000000001)])
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count += 1
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if count == len(graph.nodes):
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edge_scores.append(row)
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row = []
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count = 0
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return edge_scores
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#################################################################
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# A Scorer for Demo Purposes
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#################################################################
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# A short class necessary to show parsing example from paper
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class DemoScorer(DependencyScorerI):
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def train(self, graphs):
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print("Training...")
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def score(self, graph):
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# scores for Keith Hall 'K-best Spanning Tree Parsing' paper
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return [
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[[], [5], [1], [1]],
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[[], [], [11], [4]],
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[[], [10], [], [5]],
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[[], [8], [8], []],
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]
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#################################################################
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# Non-Projective Probabilistic Parsing
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#################################################################
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class ProbabilisticNonprojectiveParser(object):
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"""A probabilistic non-projective dependency parser.
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Nonprojective dependencies allows for "crossing branches" in the parse tree
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which is necessary for representing particular linguistic phenomena, or even
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typical parses in some languages. This parser follows the MST parsing
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algorithm, outlined in McDonald(2005), which likens the search for the best
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non-projective parse to finding the maximum spanning tree in a weighted
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directed graph.
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>>> class Scorer(DependencyScorerI):
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... def train(self, graphs):
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... pass
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...
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... def score(self, graph):
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... return [
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... [[], [5], [1], [1]],
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... [[], [], [11], [4]],
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... [[], [10], [], [5]],
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... [[], [8], [8], []],
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... ]
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>>> npp = ProbabilisticNonprojectiveParser()
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>>> npp.train([], Scorer())
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>>> parses = npp.parse(['v1', 'v2', 'v3'], [None, None, None])
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>>> len(list(parses))
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1
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Rule based example
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------------------
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>>> from nltk.grammar import DependencyGrammar
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>>> grammar = DependencyGrammar.fromstring('''
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... 'taught' -> 'play' | 'man'
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... 'man' -> 'the' | 'in'
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... 'in' -> 'corner'
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... 'corner' -> 'the'
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... 'play' -> 'golf' | 'dachshund' | 'to'
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... 'dachshund' -> 'his'
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... ''')
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>>> ndp = NonprojectiveDependencyParser(grammar)
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>>> parses = ndp.parse(['the', 'man', 'in', 'the', 'corner', 'taught', 'his', 'dachshund', 'to', 'play', 'golf'])
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>>> len(list(parses))
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4
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"""
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def __init__(self):
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"""
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Creates a new non-projective parser.
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"""
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logging.debug("initializing prob. nonprojective...")
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def train(self, graphs, dependency_scorer):
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"""
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Trains a ``DependencyScorerI`` from a set of ``DependencyGraph`` objects,
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and establishes this as the parser's scorer. This is used to
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initialize the scores on a ``DependencyGraph`` during the parsing
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procedure.
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:type graphs: list(DependencyGraph)
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:param graphs: A list of dependency graphs to train the scorer.
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:type dependency_scorer: DependencyScorerI
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:param dependency_scorer: A scorer which implements the
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``DependencyScorerI`` interface.
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"""
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self._scorer = dependency_scorer
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self._scorer.train(graphs)
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def initialize_edge_scores(self, graph):
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"""
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Assigns a score to every edge in the ``DependencyGraph`` graph.
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These scores are generated via the parser's scorer which
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was assigned during the training process.
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:type graph: DependencyGraph
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:param graph: A dependency graph to assign scores to.
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"""
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self.scores = self._scorer.score(graph)
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def collapse_nodes(self, new_node, cycle_path, g_graph, b_graph, c_graph):
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"""
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Takes a list of nodes that have been identified to belong to a cycle,
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and collapses them into on larger node. The arcs of all nodes in
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the graph must be updated to account for this.
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:type new_node: Node.
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:param new_node: A Node (Dictionary) to collapse the cycle nodes into.
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:type cycle_path: A list of integers.
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:param cycle_path: A list of node addresses, each of which is in the cycle.
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:type g_graph, b_graph, c_graph: DependencyGraph
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:param g_graph, b_graph, c_graph: Graphs which need to be updated.
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"""
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logger.debug("Collapsing nodes...")
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# Collapse all cycle nodes into v_n+1 in G_Graph
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for cycle_node_index in cycle_path:
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g_graph.remove_by_address(cycle_node_index)
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g_graph.add_node(new_node)
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g_graph.redirect_arcs(cycle_path, new_node["address"])
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def update_edge_scores(self, new_node, cycle_path):
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"""
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Updates the edge scores to reflect a collapse operation into
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new_node.
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:type new_node: A Node.
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:param new_node: The node which cycle nodes are collapsed into.
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:type cycle_path: A list of integers.
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:param cycle_path: A list of node addresses that belong to the cycle.
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"""
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logger.debug("cycle %s", cycle_path)
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cycle_path = self.compute_original_indexes(cycle_path)
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logger.debug("old cycle %s", cycle_path)
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logger.debug("Prior to update: %s", self.scores)
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for i, row in enumerate(self.scores):
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for j, column in enumerate(self.scores[i]):
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logger.debug(self.scores[i][j])
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if j in cycle_path and i not in cycle_path and self.scores[i][j]:
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subtract_val = self.compute_max_subtract_score(j, cycle_path)
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logger.debug("%s - %s", self.scores[i][j], subtract_val)
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new_vals = []
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for cur_val in self.scores[i][j]:
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new_vals.append(cur_val - subtract_val)
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self.scores[i][j] = new_vals
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for i, row in enumerate(self.scores):
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for j, cell in enumerate(self.scores[i]):
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if i in cycle_path and j in cycle_path:
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self.scores[i][j] = []
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logger.debug("After update: %s", self.scores)
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def compute_original_indexes(self, new_indexes):
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"""
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As nodes are collapsed into others, they are replaced
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by the new node in the graph, but it's still necessary
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to keep track of what these original nodes were. This
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takes a list of node addresses and replaces any collapsed
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node addresses with their original addresses.
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:type new_indexes: A list of integers.
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:param new_indexes: A list of node addresses to check for
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subsumed nodes.
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"""
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swapped = True
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while swapped:
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originals = []
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swapped = False
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for new_index in new_indexes:
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if new_index in self.inner_nodes:
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for old_val in self.inner_nodes[new_index]:
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if old_val not in originals:
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originals.append(old_val)
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swapped = True
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else:
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originals.append(new_index)
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new_indexes = originals
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return new_indexes
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def compute_max_subtract_score(self, column_index, cycle_indexes):
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"""
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When updating scores the score of the highest-weighted incoming
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arc is subtracted upon collapse. This returns the correct
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amount to subtract from that edge.
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:type column_index: integer.
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:param column_index: A index representing the column of incoming arcs
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to a particular node being updated
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:type cycle_indexes: A list of integers.
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:param cycle_indexes: Only arcs from cycle nodes are considered. This
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is a list of such nodes addresses.
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"""
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max_score = -100000
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for row_index in cycle_indexes:
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for subtract_val in self.scores[row_index][column_index]:
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if subtract_val > max_score:
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max_score = subtract_val
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return max_score
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def best_incoming_arc(self, node_index):
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"""
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Returns the source of the best incoming arc to the
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node with address: node_index
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:type node_index: integer.
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:param node_index: The address of the 'destination' node,
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the node that is arced to.
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"""
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originals = self.compute_original_indexes([node_index])
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logger.debug("originals: %s", originals)
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max_arc = None
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max_score = None
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for row_index in range(len(self.scores)):
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for col_index in range(len(self.scores[row_index])):
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if col_index in originals and (
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max_score is None or self.scores[row_index][col_index] > max_score
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):
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max_score = self.scores[row_index][col_index]
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max_arc = row_index
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logger.debug("%s, %s", row_index, col_index)
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logger.debug(max_score)
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for key in self.inner_nodes:
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replaced_nodes = self.inner_nodes[key]
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if max_arc in replaced_nodes:
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return key
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return max_arc
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def original_best_arc(self, node_index):
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originals = self.compute_original_indexes([node_index])
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max_arc = None
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max_score = None
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max_orig = None
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for row_index in range(len(self.scores)):
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for col_index in range(len(self.scores[row_index])):
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if col_index in originals and (
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max_score is None or self.scores[row_index][col_index] > max_score
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):
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max_score = self.scores[row_index][col_index]
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max_arc = row_index
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max_orig = col_index
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return [max_arc, max_orig]
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def parse(self, tokens, tags):
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"""
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Parses a list of tokens in accordance to the MST parsing algorithm
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for non-projective dependency parses. Assumes that the tokens to
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be parsed have already been tagged and those tags are provided. Various
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scoring methods can be used by implementing the ``DependencyScorerI``
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interface and passing it to the training algorithm.
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:type tokens: list(str)
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:param tokens: A list of words or punctuation to be parsed.
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:type tags: list(str)
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:param tags: A list of tags corresponding by index to the words in the tokens list.
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:return: An iterator of non-projective parses.
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:rtype: iter(DependencyGraph)
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"""
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self.inner_nodes = {}
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# Initialize g_graph
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g_graph = DependencyGraph()
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for index, token in enumerate(tokens):
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g_graph.nodes[index + 1].update(
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{"word": token, "tag": tags[index], "rel": "NTOP", "address": index + 1}
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)
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# Fully connect non-root nodes in g_graph
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g_graph.connect_graph()
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original_graph = DependencyGraph()
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for index, token in enumerate(tokens):
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original_graph.nodes[index + 1].update(
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{"word": token, "tag": tags[index], "rel": "NTOP", "address": index + 1}
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)
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b_graph = DependencyGraph()
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c_graph = DependencyGraph()
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for index, token in enumerate(tokens):
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c_graph.nodes[index + 1].update(
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{"word": token, "tag": tags[index], "rel": "NTOP", "address": index + 1}
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)
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# Assign initial scores to g_graph edges
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self.initialize_edge_scores(g_graph)
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logger.debug(self.scores)
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# Initialize a list of unvisited vertices (by node address)
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unvisited_vertices = [vertex["address"] for vertex in c_graph.nodes.values()]
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# Iterate over unvisited vertices
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nr_vertices = len(tokens)
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betas = {}
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while unvisited_vertices:
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# Mark current node as visited
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current_vertex = unvisited_vertices.pop(0)
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logger.debug("current_vertex: %s", current_vertex)
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# Get corresponding node n_i to vertex v_i
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current_node = g_graph.get_by_address(current_vertex)
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logger.debug("current_node: %s", current_node)
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# Get best in-edge node b for current node
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best_in_edge = self.best_incoming_arc(current_vertex)
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betas[current_vertex] = self.original_best_arc(current_vertex)
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logger.debug("best in arc: %s --> %s", best_in_edge, current_vertex)
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# b_graph = Union(b_graph, b)
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for new_vertex in [current_vertex, best_in_edge]:
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b_graph.nodes[new_vertex].update(
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{"word": "TEMP", "rel": "NTOP", "address": new_vertex}
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)
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b_graph.add_arc(best_in_edge, current_vertex)
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# Beta(current node) = b - stored for parse recovery
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# If b_graph contains a cycle, collapse it
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cycle_path = b_graph.contains_cycle()
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if cycle_path:
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# Create a new node v_n+1 with address = len(nodes) + 1
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new_node = {"word": "NONE", "rel": "NTOP", "address": nr_vertices + 1}
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# c_graph = Union(c_graph, v_n+1)
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c_graph.add_node(new_node)
|
|
# Collapse all nodes in cycle C into v_n+1
|
|
self.update_edge_scores(new_node, cycle_path)
|
|
self.collapse_nodes(new_node, cycle_path, g_graph, b_graph, c_graph)
|
|
for cycle_index in cycle_path:
|
|
c_graph.add_arc(new_node["address"], cycle_index)
|
|
# self.replaced_by[cycle_index] = new_node['address']
|
|
|
|
self.inner_nodes[new_node["address"]] = cycle_path
|
|
|
|
# Add v_n+1 to list of unvisited vertices
|
|
unvisited_vertices.insert(0, nr_vertices + 1)
|
|
|
|
# increment # of nodes counter
|
|
nr_vertices += 1
|
|
|
|
# Remove cycle nodes from b_graph; B = B - cycle c
|
|
for cycle_node_address in cycle_path:
|
|
b_graph.remove_by_address(cycle_node_address)
|
|
|
|
logger.debug("g_graph: %s", g_graph)
|
|
logger.debug("b_graph: %s", b_graph)
|
|
logger.debug("c_graph: %s", c_graph)
|
|
logger.debug("Betas: %s", betas)
|
|
logger.debug("replaced nodes %s", self.inner_nodes)
|
|
|
|
# Recover parse tree
|
|
logger.debug("Final scores: %s", self.scores)
|
|
|
|
logger.debug("Recovering parse...")
|
|
for i in range(len(tokens) + 1, nr_vertices + 1):
|
|
betas[betas[i][1]] = betas[i]
|
|
|
|
logger.debug("Betas: %s", betas)
|
|
for node in original_graph.nodes.values():
|
|
# TODO: It's dangerous to assume that deps it a dictionary
|
|
# because it's a default dictionary. Ideally, here we should not
|
|
# be concerned how dependencies are stored inside of a dependency
|
|
# graph.
|
|
node["deps"] = {}
|
|
for i in range(1, len(tokens) + 1):
|
|
original_graph.add_arc(betas[i][0], betas[i][1])
|
|
|
|
logger.debug("Done.")
|
|
yield original_graph
|
|
|
|
|
|
#################################################################
|
|
# Rule-based Non-Projective Parser
|
|
#################################################################
|
|
|
|
|
|
class NonprojectiveDependencyParser(object):
|
|
"""
|
|
A non-projective, rule-based, dependency parser. This parser
|
|
will return the set of all possible non-projective parses based on
|
|
the word-to-word relations defined in the parser's dependency
|
|
grammar, and will allow the branches of the parse tree to cross
|
|
in order to capture a variety of linguistic phenomena that a
|
|
projective parser will not.
|
|
"""
|
|
|
|
def __init__(self, dependency_grammar):
|
|
"""
|
|
Creates a new ``NonprojectiveDependencyParser``.
|
|
|
|
:param dependency_grammar: a grammar of word-to-word relations.
|
|
:type dependency_grammar: DependencyGrammar
|
|
"""
|
|
self._grammar = dependency_grammar
|
|
|
|
def parse(self, tokens):
|
|
"""
|
|
Parses the input tokens with respect to the parser's grammar. Parsing
|
|
is accomplished by representing the search-space of possible parses as
|
|
a fully-connected directed graph. Arcs that would lead to ungrammatical
|
|
parses are removed and a lattice is constructed of length n, where n is
|
|
the number of input tokens, to represent all possible grammatical
|
|
traversals. All possible paths through the lattice are then enumerated
|
|
to produce the set of non-projective parses.
|
|
|
|
param tokens: A list of tokens to parse.
|
|
type tokens: list(str)
|
|
return: An iterator of non-projective parses.
|
|
rtype: iter(DependencyGraph)
|
|
"""
|
|
# Create graph representation of tokens
|
|
self._graph = DependencyGraph()
|
|
|
|
for index, token in enumerate(tokens):
|
|
self._graph.nodes[index] = {
|
|
"word": token,
|
|
"deps": [],
|
|
"rel": "NTOP",
|
|
"address": index,
|
|
}
|
|
|
|
for head_node in self._graph.nodes.values():
|
|
deps = []
|
|
for dep_node in self._graph.nodes.values():
|
|
if (
|
|
self._grammar.contains(head_node["word"], dep_node["word"])
|
|
and head_node["word"] != dep_node["word"]
|
|
):
|
|
deps.append(dep_node["address"])
|
|
head_node["deps"] = deps
|
|
|
|
# Create lattice of possible heads
|
|
roots = []
|
|
possible_heads = []
|
|
for i, word in enumerate(tokens):
|
|
heads = []
|
|
for j, head in enumerate(tokens):
|
|
if (i != j) and self._grammar.contains(head, word):
|
|
heads.append(j)
|
|
if len(heads) == 0:
|
|
roots.append(i)
|
|
possible_heads.append(heads)
|
|
|
|
# Set roots to attempt
|
|
if len(roots) < 2:
|
|
if len(roots) == 0:
|
|
for i in range(len(tokens)):
|
|
roots.append(i)
|
|
|
|
# Traverse lattice
|
|
analyses = []
|
|
for root in roots:
|
|
stack = []
|
|
analysis = [[] for i in range(len(possible_heads))]
|
|
i = 0
|
|
forward = True
|
|
while i >= 0:
|
|
if forward:
|
|
if len(possible_heads[i]) == 1:
|
|
analysis[i] = possible_heads[i][0]
|
|
elif len(possible_heads[i]) == 0:
|
|
analysis[i] = -1
|
|
else:
|
|
head = possible_heads[i].pop()
|
|
analysis[i] = head
|
|
stack.append([i, head])
|
|
if not forward:
|
|
index_on_stack = False
|
|
for stack_item in stack:
|
|
if stack_item[0] == i:
|
|
index_on_stack = True
|
|
orig_length = len(possible_heads[i])
|
|
|
|
if index_on_stack and orig_length == 0:
|
|
for j in range(len(stack) - 1, -1, -1):
|
|
stack_item = stack[j]
|
|
if stack_item[0] == i:
|
|
possible_heads[i].append(stack.pop(j)[1])
|
|
|
|
elif index_on_stack and orig_length > 0:
|
|
head = possible_heads[i].pop()
|
|
analysis[i] = head
|
|
stack.append([i, head])
|
|
forward = True
|
|
|
|
if i + 1 == len(possible_heads):
|
|
analyses.append(analysis[:])
|
|
forward = False
|
|
if forward:
|
|
i += 1
|
|
else:
|
|
i -= 1
|
|
|
|
# Filter parses
|
|
# ensure 1 root, every thing has 1 head
|
|
for analysis in analyses:
|
|
if analysis.count(-1) > 1:
|
|
# there are several root elements!
|
|
continue
|
|
|
|
graph = DependencyGraph()
|
|
graph.root = graph.nodes[analysis.index(-1) + 1]
|
|
|
|
for address, (token, head_index) in enumerate(
|
|
zip(tokens, analysis), start=1
|
|
):
|
|
head_address = head_index + 1
|
|
|
|
node = graph.nodes[address]
|
|
node.update({"word": token, "address": address})
|
|
|
|
if head_address == 0:
|
|
rel = "ROOT"
|
|
else:
|
|
rel = ""
|
|
graph.nodes[head_index + 1]["deps"][rel].append(address)
|
|
|
|
# TODO: check for cycles
|
|
yield graph
|
|
|
|
|
|
#################################################################
|
|
# Demos
|
|
#################################################################
|
|
|
|
|
|
def demo():
|
|
# hall_demo()
|
|
nonprojective_conll_parse_demo()
|
|
rule_based_demo()
|
|
|
|
|
|
def hall_demo():
|
|
npp = ProbabilisticNonprojectiveParser()
|
|
npp.train([], DemoScorer())
|
|
for parse_graph in npp.parse(["v1", "v2", "v3"], [None, None, None]):
|
|
print(parse_graph)
|
|
|
|
|
|
def nonprojective_conll_parse_demo():
|
|
from nltk.parse.dependencygraph import conll_data2
|
|
|
|
graphs = [DependencyGraph(entry) for entry in conll_data2.split("\n\n") if entry]
|
|
npp = ProbabilisticNonprojectiveParser()
|
|
npp.train(graphs, NaiveBayesDependencyScorer())
|
|
for parse_graph in npp.parse(
|
|
["Cathy", "zag", "hen", "zwaaien", "."], ["N", "V", "Pron", "Adj", "N", "Punc"]
|
|
):
|
|
print(parse_graph)
|
|
|
|
|
|
def rule_based_demo():
|
|
from nltk.grammar import DependencyGrammar
|
|
|
|
grammar = DependencyGrammar.fromstring(
|
|
"""
|
|
'taught' -> 'play' | 'man'
|
|
'man' -> 'the' | 'in'
|
|
'in' -> 'corner'
|
|
'corner' -> 'the'
|
|
'play' -> 'golf' | 'dachshund' | 'to'
|
|
'dachshund' -> 'his'
|
|
"""
|
|
)
|
|
print(grammar)
|
|
ndp = NonprojectiveDependencyParser(grammar)
|
|
graphs = ndp.parse(
|
|
[
|
|
"the",
|
|
"man",
|
|
"in",
|
|
"the",
|
|
"corner",
|
|
"taught",
|
|
"his",
|
|
"dachshund",
|
|
"to",
|
|
"play",
|
|
"golf",
|
|
]
|
|
)
|
|
print("Graphs:")
|
|
for graph in graphs:
|
|
print(graph)
|
|
|
|
|
|
if __name__ == "__main__":
|
|
demo()
|