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1 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

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2 Outline Introduction to Graph Clustering Chinese Whispers Algorithm Experiments with Synthetic Data Application of CW to –Language Seperation –POS clustering –Word Sense Induction Extensions

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3 Graph Clustering Find groups of nodes in undirected, weighted graphs Hierarchical Clustering vs. Flat Partitioning

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4 ? Desired outcomes ? Colors symbolise partitions

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5 Chinese Whispers Algorithm 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 Algorithm: initialize: forall v i in V: class(v i )=i; while changes: forall v in V, randomized order: class(v)=highest ranked class in neighborhood of v; A L1 D L2 E L3 B L4 C L deg=1 deg=2 deg=3 deg=5 deg=4

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6 Example: CW-Partitioning in two steps

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7 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

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8 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

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9 Co-occurrences: A source for Graphs The entirety of all significant co-occurrences is a co-occurrence graph G(V,E) with V: Vertices = Words E: 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

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10 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

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11 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)

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12 Results: POS-clusters In total: 282 clusters, of which 26 with more than 100 members. Syntacto-semantic motivation. Purity: 88%

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13 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

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14 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.

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15 Results: WSI No parameter for expected number of clusters CW scores compareable to an algorithm especially designed for WSI

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20 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

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21 Questions ? THANK YOU

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22 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

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23 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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24 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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25 Usages of hip FIGHT: The punching hip, be it the leading hip of a front punch or the trailing hip of a reverse punch, must swivel forwards, so that your centre-line directly faces the opponent. MUSIC: This hybrid mix of reggae and hip hop follows acid jazz, Belgian New Beat and acid swing the wholly forgettable contribution of Jive Bunny as the sound to set disco feet tapping. DANCER: Sitting back and taking it all in is another former hip hop dancer, Moet Lo, who lost his Wall Street messenger job when his firm discovered his penchant for the five-finger discount at Polo stores HOORAY: Ho, hey, ho hi, ho, hey, ho, hip hop hooray, funky, get down, a-boogie, get down. MEDICINE: We treated orthopaedic screening as a distinct category because some neonatal deformations (such as congenital dislocation of the hip ) represent only a predisposition to congenital abnormality, and surgery is avoided by conservative treatment. BODYPART-INJURY: I had a hip replacement operation on my left side, after which I immediately broke my right leg. BODYPART-CLOTHING: At his hip he wore a pistol in an ancient leather holster.

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