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ODAC

The Online Divisive-Agglomerative Clustering (ODAC)1 aims at continuously maintaining a hierarchical cluster structure from evolving time series data streams.

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ODAC continuosly monitors the evolution of clusters' diameters and split or merge them by gathering more data or reacting to concept drift. Such changes are supported by a confidence level that comes from the Hoeffding bound. ODAC relies on keeping the linear correlation between series to evaluate whether or not the time series hierarchy has changed.

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The distance between time-series a and b is given by rnomc(a, b) = sqrt((1 - corr(a, b)) / 2), where corr(a, b) is the Pearson Correlation coefficient.

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In the following topics, ε stands for the Hoeffding bound and considers clusters cj with descendants ck and cs.

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The Merge Operator

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The Splitting Criteria guarantees that cluster's diameters monotonically decrease.

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Splitting Criteria

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Consider:

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Then:

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The distance between time-series a and b is given by rnomc(a, b) = sqrt((1 - corr(a, b)) / 2), where corr(a, b) is the Pearson Correlation coefficient. If the cluster has only one time-series, the diameter is given by the time-series variance. The cluster's diameter is given by the largest distance between the cluster's time-series.

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ODAC continuously monitors the evolution of diameters, only of the leaves, and splits or merges them by gathering more data or reacting to concept drift - a confidence level from the Hoeffding bound supports such changes.

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So, the split operator, where the Hoeffding bound is applied, occurs when the difference between the largest distance (diameter) and the second largest difference is greater than a constant. Furthermore, the merge operator checks if one of the cluster's children has a diameter bigger than their parent - applying the Hoeffding bound again.

Parameters