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Chinese Whispers an Efficient Graph Clustering Algorithm and its Application to Natural Language Processing Problems. Chris Biemann University of Leipzig, NLP-Dept. Leipzig, Germany June 9, 2006 TextGraphs 06, NYC, USA. Outline. Introduction to Graph Clustering Chinese Whispers Algorithm
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Chinese Whispers an Efficient Graph Clustering Algorithm and its Application to Natural Language Processing Problems Chris BiemannUniversity of Leipzig, NLP-Dept.Leipzig, Germany June 9, 2006 TextGraphs 06, NYC, USA
Outline • Introduction to Graph Clustering • Chinese Whispers Algorithm • Experiments with Synthetic Data • Application of CW to • Language Seperation • POS clustering • Word Sense Induction • Extensions
Graph Clustering • Find groups of nodes in undirected, weighted graphs • Hierarchical Clustering vs. Flat Partitioning 3 3 3 3 4 4 3
? Desired outcomes ? • Colors symbolise partitions 3 3 3 3 4 4 3
Chinese Whispers Algorithm D L2 B L4 5 8 A L1 deg=1 deg=2 E L3 3 C L3 6 deg=4 deg=3 deg=5 Algorithm: initialize: forall vi in V: class(vi)=i; while changes: forall v in V, randomized order: class(v)=highest ranked class in neighborhood of v; • Nodes have a class and communicate it to their adjacent nodes • A node adopts one of the the majority class in its neighbourhood • Nodes are processed in random order for some iterations
Properties of CW PRO: • Efficiency: CW is time-linear in the number of edges. This is bound by n² with n= number of nodes, but in real world data, graphs are much sparser • Parameter-free: this includes number of clusters CON: • Non-deterministic: due to random order processing and possible ties w.r.t. the majority. • Does not converge: See tie example: However, the CONs are not severe for real world data... Formally hard to analyse: perform experiments
Experiment: Bi-partite cliques, unweighted • Intuition: Bi-partite cliques should be split into two cliques • CW can split bi-partite cliques into two parts or leave them as a whole. • Measure, how often CW succeeds: the larger the graph, the saver the split -> CW meant for large graphs
Co-occurrences: A source for Graphs • The entirety of all significant co-occurrences is a co-occurrence graph G(V,E) withV: Vertices = WordsE: Edges (v1, v2, s) with v1, v2 words, s significance value. • Co-occurrence graph is • weighted by significance (here: log-likelihood) • undirected • Small-world-property
Application: Language Seperation • Cluster the co-occurrence graph of a multilingual corpus • Use words of the same class in a language identifier as lexicon • Almost perfect performance
Application: Acquisition of POS-classes • Distributional similarity: Words that co-occur significantly with the same neighbours should be of the same POS • Clustering the second-order NB-co-occurrence graph of the BNC (excluding the top 2000 frequent words)
Results: POS-clusters • In total: 282 clusters, of which 26 with more than 100 members. Syntacto-semantic motivation. Purity: 88%
Application: Word Sense Induction • Co-occurrence graphs of ambigous words can be partitioned [Dorow & Widdows 03]: Leave out focus word • Clusters contain context words for disambiguation
Unsupervised WSI Evaluation Framework Evaluation: For unambiguos words, merge their co-occurrence graphs and try to split them into previous parts • retrieval precision (rP): similarity of the found sense with the gold standard sense • retrieval recall (rR): amount of words that have been correctly assigned to the gold standard sense • precision (P): fraction of correctly found disambiguations • recall (R): fraction of correctly found senses 45 test words of different POS and frequency bands.
Results: WSI • No parameter for expected number of clusters • CW scores compareable to an algorithm especially designed for WSI
Conclusion • Very effective graph partitioning algorithm for weighted, undirected graphs • Possible to process really large graphs • Fuzzy partitioning and hierachichal clustering possible • Especially suited for small world graphs (sparse adjacency matrix) • Useful in NLP applications such as Language Seperation, POS clustering, Word Sense Induction Download a GUI implementation in Java of Chinese Whispers (Open Source) at http://wortschatz.informatik.uni-leipzig.de/~cbiemann/software/CW.html
Questions ? THANK YOU
Experiment: Convergence • Weighted graphs converge much faster (less ties) • For weighted graphs, 15 iterations were enough to partition the 1.7M nodes / 56M edges co-occurrence graph of our main German corpus • Larger graphs result in less uncertainity
Experiment: Small World Mixtures • CW can seperate well if merge rate is not too high • Different sizes of original SWs do not impose a problem
Experiment: Small World Mixtures • CW can seperate well if merge rate is not too high • Different sizes of original SWs do not impose a problem
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