Chris Biemann University of Leipzig, NLP-Dept. Leipzig, Germany 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 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 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 A L1 D L2 E L3 B L4 C 5 8 6 3 deg=1 deg=2 deg=3 deg=5 deg=4

Example: CW-Partitioning in two steps

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) 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

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

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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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