6533b826fe1ef96bd1283cc1
RESEARCH PRODUCT
A fast and recursive algorithm for clustering large datasets with k-medians
Hervé CardotJean-marie MonnezPeggy Cénacsubject
Statistics and ProbabilityClustering high-dimensional dataFOS: Computer and information sciencesMathematical optimizationhigh dimensional dataMachine Learning (stat.ML)02 engineering and technologyStochastic approximation01 natural sciencesStatistics - Computation010104 statistics & probabilityk-medoidsStatistics - Machine Learning[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]stochastic approximation0202 electrical engineering electronic engineering information engineeringComputational statisticsrecursive estimatorsAlmost surely[ MATH.MATH-ST ] Mathematics [math]/Statistics [math.ST]0101 mathematicsCluster analysisComputation (stat.CO)Mathematicsaveragingk-medoidsRobbins MonroApplied MathematicsEstimator[STAT.TH]Statistics [stat]/Statistics Theory [stat.TH]stochastic gradient[ STAT.TH ] Statistics [stat]/Statistics Theory [stat.TH]MedoidComputational MathematicsComputational Theory and Mathematicsonline clustering020201 artificial intelligence & image processingpartitioning around medoidsAlgorithmdescription
Clustering with fast algorithms large samples of high dimensional data is an important challenge in computational statistics. Borrowing ideas from MacQueen (1967) who introduced a sequential version of the $k$-means algorithm, a new class of recursive stochastic gradient algorithms designed for the $k$-medians loss criterion is proposed. By their recursive nature, these algorithms are very fast and are well adapted to deal with large samples of data that are allowed to arrive sequentially. It is proved that the stochastic gradient algorithm converges almost surely to the set of stationary points of the underlying loss criterion. A particular attention is paid to the averaged versions, which are known to have better performances, and a data-driven procedure that allows automatic selection of the value of the descent step is proposed. The performance of the averaged sequential estimator is compared on a simulation study, both in terms of computation speed and accuracy of the estimations, with more classical partitioning techniques such as $k$-means, trimmed $k$-means and PAM (partitioning around medoids). Finally, this new online clustering technique is illustrated on determining television audience profiles with a sample of more than 5000 individual television audiences measured every minute over a period of 24 hours.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-01-01 |