Combining multiple weak clusterings
A data set can be clustered in many ways depending on the clustering algorithm employed, parameter settings used and other factors. Can multiple clusterings be combined so that the final partitioning of data provides better clustering? The answer depends on the quality of clusterings to be combined as well as the properties of the fusion method. First, we introduce a unified representation for multiple clusterings and formulate the corresponding categorical clustering problem. As a result, we show that the consensus function is related to the classical intra-class variance criterion using the generalized mutual information definition. Second, we show the efficacy of combining partitions generated by weak clustering algorithms that use data projections and random data splits. A simple explanatory model is offered for the behavior of combinations of such weak clustering components. We analyze the combination accuracy as a function of parameters controlling the power and resolution of component partitions as well as the learning dynamics vs. the number of clusterings involved. Finally, some empirical studies compare the effectiveness of several consensus functions.