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# Natural Language Toolkit: Dependency Grammars # # Copyright (C) 2001-2012 NLTK Project # Author: Jason Narad <jason.narad@gmail.com> # # URL: <http://www.nltk.org/> # For license information, see LICENSE.TXT #
StatisticalDependencyGrammar, parse_dependency_grammar)
################################################################# # Dependency Span #################################################################
""" A contiguous span over some part of the input string representing dependency (head -> modifier) relationships amongst words. An atomic span corresponds to only one word so it isn't a 'span' in the conventional sense, as its _start_index = _end_index = _head_index for concatenation purposes. All other spans are assumed to have arcs between all nodes within the start and end indexes of the span, and one head index corresponding to the head word for the entire span. This is the same as the root node if the dependency structure were depicted as a graph. """
""" :return: An value indexing the head of the entire ``DependencySpan``. :rtype: int """ return self._head_index
""" :return: A concise string representatino of the ``DependencySpan``. :rtype: str. """ return 'Span %d-%d; Head Index: %d' % (self._start_index, self._end_index, self._head_index)
""" :return: A verbose string representation of the ``DependencySpan``. :rtype: str """ str = 'Span %d-%d; Head Index: %d' % (self._start_index, self._end_index, self._head_index) for i in range(len(self._arcs)): str += '\n%d <- %d, %s' % (i, self._arcs[i], self._tags[i]) return str
""" :return: true if this ``DependencySpan`` is equal to ``other``. :rtype: bool """ self._start_index == other._start_index and self._end_index == other._end_index and self._head_index == other._head_index and self._arcs == other._arcs)
""" :return: false if this ``DependencySpan`` is equal to ``other`` :rtype: bool """ return not (self == other)
""" :return: -1 if args are of different class. Otherwise returns the cmp() of the two sets of spans. :rtype: int """ if not isinstance(other, self.__class__): return -1 return cmp((self._start_index, self._start_index, self._head_index), (other._end_index, other._end_index, other._head_index))
""" :return: The hash value of this ``DependencySpan``. """
################################################################# # Chart Cell #################################################################
""" A cell from the parse chart formed when performing the CYK algorithm. Each cell keeps track of its x and y coordinates (though this will probably be discarded), and a list of spans serving as the cell's entries. """ """ :param x: This cell's x coordinate. :type x: int. :param y: This cell's y coordinate. :type y: int. """
""" Appends the given span to the list of spans representing the chart cell's entries.
:param span: The span to add. :type span: DependencySpan """
""" :return: A verbose string representation of this ``ChartCell``. :rtype: str. """ return 'CC[%d,%d]: %s' % (self._x, self._y, self._entries)
""" :return: A concise string representation of this ``ChartCell``. :rtype: str. """ return '%s' % self
################################################################# # Parsing with Dependency Grammars #################################################################
""" A projective, rule-based, dependency parser. A ProjectiveDependencyParser is created with a DependencyGrammar, a set of productions specifying word-to-word dependency relations. The parse() method will then return the set of all parses, in tree representation, for a given input sequence of tokens. Each parse must meet the requirements of the both the grammar and the projectivity constraint which specifies that the branches of the dependency tree are not allowed to cross. Alternatively, this can be understood as stating that each parent node and its children in the parse tree form a continuous substring of the input sequence. """
""" Create a new ProjectiveDependencyParser, from a word-to-word dependency grammar ``DependencyGrammar``.
:param dependency_grammar: A word-to-word relation dependencygrammar. :type dependency_grammar: DependencyGrammar """
""" Performs a projective dependency parse on the list of tokens using a chart-based, span-concatenation algorithm similar to Eisner (1996).
:param tokens: The list of input tokens. :type tokens: list(str) :return: A list of parse trees. :rtype: list(Tree) """ # malt_format = "" # malt_format += '%s\t%s\t%d\t%s\n' % (tokens[i], 'null', parse._arcs[i] + 1, 'null') # if self.meets_arity(dg):
""" Concatenates the two spans in whichever way possible. This includes rightward concatenation (from the leftmost word of the leftmost span to the rightmost word of the rightmost span) and leftward concatenation (vice-versa) between adjacent spans. Unlike Eisner's presentation of span concatenation, these spans do not share or pivot on a particular word/word-index.
:return: A list of new spans formed through concatenation. :rtype: list(DependencySpan) """ print('Error: Mismatched spans - replace this with thrown error') temp_span = span1 span1 = span2 span2 = temp_span # adjacent rightward covered concatenation # print 'Performing rightward cover %d to %d' % (span1._head_index, span2._head_index) # adjacent leftward covered concatenation # print 'performing leftward cover %d to %d' % (span2._head_index, span1._head_index)
################################################################# # Parsing with Probabilistic Dependency Grammars #################################################################
""" A probabilistic, projective dependency parser. This parser returns the most probable projective parse derived from the probabilistic dependency grammar derived from the train() method. The probabilistic model is an implementation of Eisner's (1996) Model C, which conditions on head-word, head-tag, child-word, and child-tag. The decoding uses a bottom-up chart-based span concatenation algorithm that's identical to the one utilized by the rule-based projective parser. """
""" Create a new probabilistic dependency parser. No additional operations are necessary. """ print('')
""" Parses the list of tokens subject to the projectivity constraint and the productions in the parser's grammar. This uses a method similar to the span-concatenation algorithm defined in Eisner (1996). It returns the most probable parse derived from the parser's probabilistic dependency grammar. """ self._tokens = list(tokens) chart = [] for i in range(0, len(self._tokens) + 1): chart.append([]) for j in range(0, len(self._tokens) + 1): chart[i].append(ChartCell(i,j)) if i==j+1: if tokens[i-1] in self._grammar._tags: for tag in self._grammar._tags[tokens[i-1]]: chart[i][j].add(DependencySpan(i-1,i,i-1,[-1], [tag])) else: print('No tag found for input token \'%s\', parse is impossible.' % tokens[i-1]) return [] for i in range(1,len(self._tokens)+1): for j in range(i-2,-1,-1): for k in range(i-1,j,-1): for span1 in chart[k][j]._entries: for span2 in chart[i][k]._entries: for newspan in self.concatenate(span1, span2): chart[i][j].add(newspan) graphs = [] trees = [] max_parse = None max_score = 0 for parse in chart[len(self._tokens)][0]._entries: conll_format = "" malt_format = "" for i in range(len(tokens)): malt_format += '%s\t%s\t%d\t%s\n' % (tokens[i], 'null', parse._arcs[i] + 1, 'null') conll_format += '\t%d\t%s\t%s\t%s\t%s\t%s\t%d\t%s\t%s\t%s\n' % (i+1, tokens[i], tokens[i], parse._tags[i], parse._tags[i], 'null', parse._arcs[i] + 1, 'null', '-', '-') dg = DependencyGraph(conll_format) score = self.compute_prob(dg) if score > max_score: max_parse = dg.tree() max_score = score return [max_parse, max_score]
""" Concatenates the two spans in whichever way possible. This includes rightward concatenation (from the leftmost word of the leftmost span to the rightmost word of the rightmost span) and leftward concatenation (vice-versa) between adjacent spans. Unlike Eisner's presentation of span concatenation, these spans do not share or pivot on a particular word/word-index.
:return: A list of new spans formed through concatenation. :rtype: list(DependencySpan) """ spans = [] if span1._start_index == span2._start_index: print('Error: Mismatched spans - replace this with thrown error') if span1._start_index > span2._start_index: temp_span = span1 span1 = span2 span2 = temp_span # adjacent rightward covered concatenation new_arcs = span1._arcs + span2._arcs new_tags = span1._tags + span2._tags if self._grammar.contains(self._tokens[span1._head_index], self._tokens[span2._head_index]): new_arcs[span2._head_index - span1._start_index] = span1._head_index spans.append(DependencySpan(span1._start_index, span2._end_index, span1._head_index, new_arcs, new_tags)) # adjacent leftward covered concatenation new_arcs = span1._arcs + span2._arcs new_tags = span1._tags + span2._tags if self._grammar.contains(self._tokens[span2._head_index], self._tokens[span1._head_index]): new_arcs[span1._head_index - span1._start_index] = span2._head_index spans.append(DependencySpan(span1._start_index, span2._end_index, span2._head_index, new_arcs, new_tags)) return spans
""" Trains a StatisticalDependencyGrammar based on the list of input DependencyGraphs. This model is an implementation of Eisner's (1996) Model C, which derives its statistics from head-word, head-tag, child-word, and child-tag relationships.
:param graphs: A list of dependency graphs to train from. :type: list(DependencyGraph) """ productions = [] events = {} tags = {} for dg in graphs: for node_index in range(1,len(dg.nodelist)): children = dg.nodelist[node_index]['deps'] nr_left_children = dg.left_children(node_index) nr_right_children = dg.right_children(node_index) nr_children = nr_left_children + nr_right_children for child_index in range(0 - (nr_left_children + 1), nr_right_children + 2): head_word = dg.nodelist[node_index]['word'] head_tag = dg.nodelist[node_index]['tag'] if head_word in tags: tags[head_word].add(head_tag) else: tags[head_word] = set([head_tag]) child = 'STOP' child_tag = 'STOP' prev_word = 'START' prev_tag = 'START' if child_index < 0: array_index = child_index + nr_left_children if array_index >= 0: child = dg.nodelist[children[array_index]]['word'] child_tag = dg.nodelist[children[array_index]]['tag'] if child_index != -1: prev_word = dg.nodelist[children[array_index + 1]]['word'] prev_tag = dg.nodelist[children[array_index + 1]]['tag'] if child != 'STOP': productions.append(DependencyProduction(head_word, [child])) head_event = '(head (%s %s) (mods (%s, %s, %s) left))' % (child, child_tag, prev_tag, head_word, head_tag) mod_event = '(mods (%s, %s, %s) left))' % (prev_tag, head_word, head_tag) if head_event in events: events[head_event] += 1 else: events[head_event] = 1 if mod_event in events: events[mod_event] += 1 else: events[mod_event] = 1 elif child_index > 0: array_index = child_index + nr_left_children - 1 if array_index < nr_children: child = dg.nodelist[children[array_index]]['word'] child_tag = dg.nodelist[children[array_index]]['tag'] if child_index != 1: prev_word = dg.nodelist[children[array_index - 1]]['word'] prev_tag = dg.nodelist[children[array_index - 1]]['tag'] if child != 'STOP': productions.append(DependencyProduction(head_word, [child])) head_event = '(head (%s %s) (mods (%s, %s, %s) right))' % (child, child_tag, prev_tag, head_word, head_tag) mod_event = '(mods (%s, %s, %s) right))' % (prev_tag, head_word, head_tag) if head_event in events: events[head_event] += 1 else: events[head_event] = 1 if mod_event in events: events[mod_event] += 1 else: events[mod_event] = 1 self._grammar = StatisticalDependencyGrammar(productions, events, tags) # print self._grammar
""" Computes the probability of a dependency graph based on the parser's probability model (defined by the parser's statistical dependency grammar).
:param dg: A dependency graph to score. :type dg: DependencyGraph :return: The probability of the dependency graph. :rtype: int """ prob = 1.0 for node_index in range(1,len(dg.nodelist)): children = dg.nodelist[node_index]['deps'] nr_left_children = dg.left_children(node_index) nr_right_children = dg.right_children(node_index) nr_children = nr_left_children + nr_right_children for child_index in range(0 - (nr_left_children + 1), nr_right_children + 2): head_word = dg.nodelist[node_index]['word'] head_tag = dg.nodelist[node_index]['tag'] child = 'STOP' child_tag = 'STOP' prev_word = 'START' prev_tag = 'START' if child_index < 0: array_index = child_index + nr_left_children if array_index >= 0: child = dg.nodelist[children[array_index]]['word'] child_tag = dg.nodelist[children[array_index]]['tag'] if child_index != -1: prev_word = dg.nodelist[children[array_index + 1]]['word'] prev_tag = dg.nodelist[children[array_index + 1]]['tag'] head_event = '(head (%s %s) (mods (%s, %s, %s) left))' % (child, child_tag, prev_tag, head_word, head_tag) mod_event = '(mods (%s, %s, %s) left))' % (prev_tag, head_word, head_tag) h_count = self._grammar._events[head_event] m_count = self._grammar._events[mod_event] prob *= (h_count / m_count) elif child_index > 0: array_index = child_index + nr_left_children - 1 if array_index < nr_children: child = dg.nodelist[children[array_index]]['word'] child_tag = dg.nodelist[children[array_index]]['tag'] if child_index != 1: prev_word = dg.nodelist[children[array_index - 1]]['word'] prev_tag = dg.nodelist[children[array_index - 1]]['tag'] head_event = '(head (%s %s) (mods (%s, %s, %s) right))' % (child, child_tag, prev_tag, head_word, head_tag) mod_event = '(mods (%s, %s, %s) right))' % (prev_tag, head_word, head_tag) h_count = self._grammar._events[head_event] m_count = self._grammar._events[mod_event] prob *= (h_count / m_count) return prob
################################################################# # Demos #################################################################
projective_rule_parse_demo() # arity_parse_demo() projective_prob_parse_demo()
""" A demonstration showing the creation and use of a ``DependencyGrammar`` to perform a projective dependency parse. """ grammar = parse_dependency_grammar(""" 'scratch' -> 'cats' | 'walls' 'walls' -> 'the' 'cats' -> 'the' """) print(grammar) pdp = ProjectiveDependencyParser(grammar) trees = pdp.parse(['the', 'cats', 'scratch', 'the', 'walls']) for tree in trees: print(tree)
""" A demonstration showing the creation of a ``DependencyGrammar`` in which a specific number of modifiers is listed for a given head. This can further constrain the number of possible parses created by a ``ProjectiveDependencyParser``. """ print() print('A grammar with no arity constraints. Each DependencyProduction') print('specifies a relationship between one head word and only one') print('modifier word.') grammar = parse_dependency_grammar(""" 'fell' -> 'price' | 'stock' 'price' -> 'of' | 'the' 'of' -> 'stock' 'stock' -> 'the' """) print(grammar)
print() print('For the sentence \'The price of the stock fell\', this grammar') print('will produce the following three parses:') pdp = ProjectiveDependencyParser(grammar) trees = pdp.parse(['the', 'price', 'of', 'the', 'stock', 'fell']) for tree in trees: print(tree)
print() print('By contrast, the following grammar contains a ') print('DependencyProduction that specifies a relationship') print('between a single head word, \'price\', and two modifier') print('words, \'of\' and \'the\'.') grammar = parse_dependency_grammar(""" 'fell' -> 'price' | 'stock' 'price' -> 'of' 'the' 'of' -> 'stock' 'stock' -> 'the' """) print(grammar)
print() print('This constrains the number of possible parses to just one:') # unimplemented, soon to replace pdp = ProjectiveDependencyParser(grammar) trees = pdp.parse(['the', 'price', 'of', 'the', 'stock', 'fell']) for tree in trees: print(tree)
""" A demo showing the training and use of a projective dependency parser. """ graphs = [DependencyGraph(entry) for entry in conll_data2.split('\n\n') if entry] ppdp = ProbabilisticProjectiveDependencyParser() print('Training Probabilistic Projective Dependency Parser...') ppdp.train(graphs) sent = ['Cathy', 'zag', 'hen', 'wild', 'zwaaien', '.'] print('Parsing \'', " ".join(sent), '\'...') parse = ppdp.parse(sent) print('Parse:') print(parse[0])
demo() |