# Natural Language Toolkit: Dependency Grammars # # Copyright (C) 2001-2009 NLTK Project # Author: Jason Narad # # URL: # For license information, see LICENSE.TXT # import math from nltk import DependencyProduction, DependencyGrammar,\ StatisticalDependencyGrammar, parse_dependency_grammar from dependencygraph import * from pprint import pformat ################################################################# # Dependency Span ################################################################# class DependencySpan(object): """ 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. """ def __init__(self, start_index, end_index, head_index, arcs, tags): self._start_index = start_index self._end_index = end_index self._head_index = head_index self._arcs = arcs self._hash = hash((start_index, end_index, head_index, tuple(arcs))) self._tags = tags def head_index(self): """ @return: An value indexing the head of the entire C{DependencySpan}. @rtype: C{int}. """ return self._head_index def __repr__(self): """ @return: A concise string representatino of the C{DependencySpan}. @rtype: C{string}. """ return 'Span %d-%d; Head Index: %d' % (self._start_index, self._end_index, self._head_index) def __str__(self): """ @return: A verbose string representation of the C{DependencySpan}. @rtype: C{string}. """ 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 def __eq__(self, other): """ @return: true if this C{DependencySpan} is equal to C{other}. @rtype: C{boolean}. """ return (isinstance(other, self.__class__) and 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) def __ne__(self, other): """ @return: false if this C{DependencySpan} is equal to C{other} @rtype: C{boolean} """ return not (self == other) def __cmp__(self, other): """ @return: -1 if args are of different class. Otherwise returns the cmp() of the two sets of spans. @rtype: C{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)) def __hash__(self): """ @return: The hash value of this C{DependencySpan}. """ return self._hash ################################################################# # Chart Cell ################################################################# class ChartCell(object): """ 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. """ def __init__(self, x, y): """ @param x: This cell's x coordinate. @type x: C{int}. @param y: This cell's y coordinate. @type y: C{int}. """ self._x = x self._y = y self._entries = set([]) def add(self, span): """ Appends the given span to the list of spans representing the chart cell's entries. @param span: The span to add. @type span: C{DependencySpan}. """ self._entries.add(span); def __str__(self): """ @return: A verbose string representation of this C{ChartCell}. @rtype: C{string}. """ return 'CC[%d,%d]: %s' % (self._x, self._y, self._entries) def __repr__(self): """ @return: A concise string representation of this C{ChartCell}. @rtype: C{string}. """ return '%s' % self ################################################################# # Parsing with Dependency Grammars ################################################################# class ProjectiveDependencyParser(object): """ 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. """ def __init__(self, dependency_grammar): """ Create a new ProjectiveDependencyParser, from a word-to-word dependency grammar C{DependencyGrammar}. @param dependency_grammar: A word-to-word relation dependencygrammar. @type dependency_grammar: A C{DependencyGrammar}. """ self._grammar = dependency_grammar def parse(self, tokens): """ 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:a C{list} of L{String} @return: A list of parse trees. @rtype: a C{list} of L{tree} """ 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: chart[i][j].add(DependencySpan(i-1,i,i-1,[-1], ['null'])) 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 = [] 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], 'null', 'null', 'null', parse._arcs[i] + 1, 'null', '-', '-') dg = DependencyGraph(conll_format) # if self.meets_arity(dg): graphs.append(dg) trees.append(dg.tree()) return trees def concatenate(self, span1, span2): """ 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: A C{list} of L{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]): # print 'Performing rightward cover %d to %d' % (span1._head_index, 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 if self._grammar.contains(self._tokens[span2._head_index], self._tokens[span1._head_index]): # print 'performing leftward cover %d to %d' % (span2._head_index, 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 ################################################################# # Parsing with Probabilistic Dependency Grammars ################################################################# class ProbabilisticProjectiveDependencyParser(object): """ 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. """ def __init__(self): """ Create a new probabilistic dependency parser. No additional operations are necessary. """ print '' def parse(self, tokens): """ 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 self._grammar._tags.has_key(tokens[i-1]): 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] def concatenate(self, span1, span2): """ 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: A C{list} of L{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 def train(self, graphs): """ 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: A list of C{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 tags.has_key(head_word): 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 events.has_key(head_event): events[head_event] += 1 else: events[head_event] = 1 if events.has_key(mod_event): 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 events.has_key(head_event): events[head_event] += 1 else: events[head_event] = 1 if events.has_key(mod_event): events[mod_event] += 1 else: events[mod_event] = 1 self._grammar = StatisticalDependencyGrammar(productions, events, tags) # print self._grammar def compute_prob(self, dg): """ 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: a C{DependencyGraph} return: The probability of the dependency graph. rtype: A number/double. """ 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 ################################################################# def demo(): projective_rule_parse_demo() # arity_parse_demo() projective_prob_parse_demo() def projective_rule_parse_demo(): """ A demonstration showing the creation and use of a C{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 def arity_parse_demo(): """ A demonstration showing the creation of a C{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 C{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 'Comparatively, the following grammar contains a ' print 'C{DependencyProduction} that specifies a relationship' print 'between the one 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 def projective_prob_parse_demo(): """ 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] if __name__ == '__main__': demo()