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# Natural Language Toolkit: Tree Transformations
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#
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# Copyright (C) 2005-2007 Oregon Graduate Institute
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# Author: Nathan Bodenstab <bodenstab@cslu.ogi.edu>
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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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A collection of methods for tree (grammar) transformations used
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in parsing natural language.
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Although many of these methods are technically grammar transformations
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(ie. Chomsky Norm Form), when working with treebanks it is much more
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natural to visualize these modifications in a tree structure. Hence,
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we will do all transformation directly to the tree itself.
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Transforming the tree directly also allows us to do parent annotation.
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A grammar can then be simply induced from the modified tree.
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The following is a short tutorial on the available transformations.
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1. Chomsky Normal Form (binarization)
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It is well known that any grammar has a Chomsky Normal Form (CNF)
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equivalent grammar where CNF is defined by every production having
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either two non-terminals or one terminal on its right hand side.
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When we have hierarchically structured data (ie. a treebank), it is
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natural to view this in terms of productions where the root of every
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subtree is the head (left hand side) of the production and all of
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its children are the right hand side constituents. In order to
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convert a tree into CNF, we simply need to ensure that every subtree
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has either two subtrees as children (binarization), or one leaf node
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(non-terminal). In order to binarize a subtree with more than two
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children, we must introduce artificial nodes.
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There are two popular methods to convert a tree into CNF: left
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factoring and right factoring. The following example demonstrates
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the difference between them. Example::
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Original Right-Factored Left-Factored
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A A A
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/ | \ / \ / \
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B C D ==> B A|<C-D> OR A|<B-C> D
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/ \ / \
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C D B C
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2. Parent Annotation
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In addition to binarizing the tree, there are two standard
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modifications to node labels we can do in the same traversal: parent
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annotation and Markov order-N smoothing (or sibling smoothing).
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The purpose of parent annotation is to refine the probabilities of
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productions by adding a small amount of context. With this simple
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addition, a CYK (inside-outside, dynamic programming chart parse)
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can improve from 74% to 79% accuracy. A natural generalization from
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parent annotation is to grandparent annotation and beyond. The
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tradeoff becomes accuracy gain vs. computational complexity. We
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must also keep in mind data sparcity issues. Example::
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Original Parent Annotation
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A A^<?>
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/ | \ / \
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B C D ==> B^<A> A|<C-D>^<?> where ? is the
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/ \ parent of A
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C^<A> D^<A>
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3. Markov order-N smoothing
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Markov smoothing combats data sparcity issues as well as decreasing
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computational requirements by limiting the number of children
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included in artificial nodes. In practice, most people use an order
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2 grammar. Example::
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Original No Smoothing Markov order 1 Markov order 2 etc.
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__A__ A A A
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/ /|\ \ / \ / \ / \
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B C D E F ==> B A|<C-D-E-F> ==> B A|<C> ==> B A|<C-D>
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/ \ / \ / \
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C ... C ... C ...
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Annotation decisions can be thought about in the vertical direction
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(parent, grandparent, etc) and the horizontal direction (number of
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siblings to keep). Parameters to the following functions specify
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these values. For more information see:
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Dan Klein and Chris Manning (2003) "Accurate Unlexicalized
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Parsing", ACL-03. http://www.aclweb.org/anthology/P03-1054
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4. Unary Collapsing
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Collapse unary productions (ie. subtrees with a single child) into a
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new non-terminal (Tree node). This is useful when working with
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algorithms that do not allow unary productions, yet you do not wish
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to lose the parent information. Example::
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A
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B ==> A+B
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/ \ / \
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C D C D
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"""
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from nltk.tree import Tree
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def chomsky_normal_form(
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tree, factor="right", horzMarkov=None, vertMarkov=0, childChar="|", parentChar="^"
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):
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# assume all subtrees have homogeneous children
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# assume all terminals have no siblings
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# A semi-hack to have elegant looking code below. As a result,
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# any subtree with a branching factor greater than 999 will be incorrectly truncated.
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if horzMarkov is None:
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horzMarkov = 999
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# Traverse the tree depth-first keeping a list of ancestor nodes to the root.
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# I chose not to use the tree.treepositions() method since it requires
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# two traversals of the tree (one to get the positions, one to iterate
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# over them) and node access time is proportional to the height of the node.
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# This method is 7x faster which helps when parsing 40,000 sentences.
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nodeList = [(tree, [tree.label()])]
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while nodeList != []:
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node, parent = nodeList.pop()
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if isinstance(node, Tree):
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# parent annotation
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parentString = ""
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originalNode = node.label()
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if vertMarkov != 0 and node != tree and isinstance(node[0], Tree):
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parentString = "%s<%s>" % (parentChar, "-".join(parent))
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node.set_label(node.label() + parentString)
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parent = [originalNode] + parent[: vertMarkov - 1]
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# add children to the agenda before we mess with them
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for child in node:
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nodeList.append((child, parent))
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# chomsky normal form factorization
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if len(node) > 2:
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childNodes = [child.label() for child in node]
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nodeCopy = node.copy()
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node[0:] = [] # delete the children
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curNode = node
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numChildren = len(nodeCopy)
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for i in range(1, numChildren - 1):
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if factor == "right":
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newHead = "%s%s<%s>%s" % (
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originalNode,
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childChar,
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"-".join(
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childNodes[i : min([i + horzMarkov, numChildren])]
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),
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parentString,
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) # create new head
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newNode = Tree(newHead, [])
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curNode[0:] = [nodeCopy.pop(0), newNode]
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else:
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newHead = "%s%s<%s>%s" % (
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originalNode,
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childChar,
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"-".join(
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childNodes[max([numChildren - i - horzMarkov, 0]) : -i]
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),
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parentString,
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)
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newNode = Tree(newHead, [])
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curNode[0:] = [newNode, nodeCopy.pop()]
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curNode = newNode
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curNode[0:] = [child for child in nodeCopy]
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def un_chomsky_normal_form(
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tree, expandUnary=True, childChar="|", parentChar="^", unaryChar="+"
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):
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# Traverse the tree-depth first keeping a pointer to the parent for modification purposes.
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nodeList = [(tree, [])]
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while nodeList != []:
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node, parent = nodeList.pop()
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if isinstance(node, Tree):
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# if the node contains the 'childChar' character it means that
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# it is an artificial node and can be removed, although we still need
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# to move its children to its parent
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childIndex = node.label().find(childChar)
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if childIndex != -1:
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nodeIndex = parent.index(node)
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parent.remove(parent[nodeIndex])
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# Generated node was on the left if the nodeIndex is 0 which
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# means the grammar was left factored. We must insert the children
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# at the beginning of the parent's children
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if nodeIndex == 0:
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parent.insert(0, node[0])
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parent.insert(1, node[1])
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else:
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parent.extend([node[0], node[1]])
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# parent is now the current node so the children of parent will be added to the agenda
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node = parent
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else:
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parentIndex = node.label().find(parentChar)
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if parentIndex != -1:
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# strip the node name of the parent annotation
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node.set_label(node.label()[:parentIndex])
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# expand collapsed unary productions
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if expandUnary == True:
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unaryIndex = node.label().find(unaryChar)
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if unaryIndex != -1:
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newNode = Tree(
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node.label()[unaryIndex + 1 :], [i for i in node]
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)
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node.set_label(node.label()[:unaryIndex])
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node[0:] = [newNode]
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for child in node:
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nodeList.append((child, node))
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def collapse_unary(tree, collapsePOS=False, collapseRoot=False, joinChar="+"):
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"""
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Collapse subtrees with a single child (ie. unary productions)
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into a new non-terminal (Tree node) joined by 'joinChar'.
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This is useful when working with algorithms that do not allow
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unary productions, and completely removing the unary productions
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would require loss of useful information. The Tree is modified
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directly (since it is passed by reference) and no value is returned.
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:param tree: The Tree to be collapsed
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:type tree: Tree
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:param collapsePOS: 'False' (default) will not collapse the parent of leaf nodes (ie.
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Part-of-Speech tags) since they are always unary productions
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:type collapsePOS: bool
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:param collapseRoot: 'False' (default) will not modify the root production
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if it is unary. For the Penn WSJ treebank corpus, this corresponds
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to the TOP -> productions.
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:type collapseRoot: bool
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:param joinChar: A string used to connect collapsed node values (default = "+")
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:type joinChar: str
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"""
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if collapseRoot == False and isinstance(tree, Tree) and len(tree) == 1:
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nodeList = [tree[0]]
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else:
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nodeList = [tree]
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# depth-first traversal of tree
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while nodeList != []:
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node = nodeList.pop()
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if isinstance(node, Tree):
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if (
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len(node) == 1
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and isinstance(node[0], Tree)
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and (collapsePOS == True or isinstance(node[0, 0], Tree))
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):
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node.set_label(node.label() + joinChar + node[0].label())
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node[0:] = [child for child in node[0]]
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# since we assigned the child's children to the current node,
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# evaluate the current node again
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nodeList.append(node)
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else:
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for child in node:
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nodeList.append(child)
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#################################################################
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# Demonstration
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#################################################################
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def demo():
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"""
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A demonstration showing how each tree transform can be used.
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"""
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from nltk.draw.tree import draw_trees
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from nltk import tree, treetransforms
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from copy import deepcopy
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# original tree from WSJ bracketed text
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sentence = """(TOP
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(S
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(S
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(VP
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(VBN Turned)
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(ADVP (RB loose))
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(PP
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(IN in)
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(NP
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(NP (NNP Shane) (NNP Longman) (POS 's))
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(NN trading)
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(NN room)))))
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(, ,)
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(NP (DT the) (NN yuppie) (NNS dealers))
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(VP (AUX do) (NP (NP (RB little)) (ADJP (RB right))))
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(. .)))"""
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t = tree.Tree.fromstring(sentence, remove_empty_top_bracketing=True)
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# collapse subtrees with only one child
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collapsedTree = deepcopy(t)
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treetransforms.collapse_unary(collapsedTree)
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# convert the tree to CNF
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cnfTree = deepcopy(collapsedTree)
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treetransforms.chomsky_normal_form(cnfTree)
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# convert the tree to CNF with parent annotation (one level) and horizontal smoothing of order two
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parentTree = deepcopy(collapsedTree)
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treetransforms.chomsky_normal_form(parentTree, horzMarkov=2, vertMarkov=1)
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# convert the tree back to its original form (used to make CYK results comparable)
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original = deepcopy(parentTree)
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treetransforms.un_chomsky_normal_form(original)
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# convert tree back to bracketed text
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sentence2 = original.pprint()
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print(sentence)
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print(sentence2)
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print("Sentences the same? ", sentence == sentence2)
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draw_trees(t, collapsedTree, cnfTree, parentTree, original)
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if __name__ == "__main__":
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demo()
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__all__ = ["chomsky_normal_form", "un_chomsky_normal_form", "collapse_unary"]
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