Many algorithms designed to accelerate the Fuzzy c-Means (FCM) clustering algorithm randomly sample the data. Typically, no statistical method is used to estimate the subsample size, despite the impact subsample sizes have on speed and quality. This paper introduces two new accelerated algorithms, GOFCM and MSERFCM, that use a statistical method to estimate the subsample size. GOFCM, a variant of SPFCM, also leverages progressive sampling. MSERFCM, a variant of rseFCM, gains a speedup from improved initialization. A general, novel stopping criterion for accelerated clustering is introduced. The new algorithms are compared to FCM and four accelerated variants of FCM. GOFCM's speedup was 4-47 times that of FCM and faster than SPFCM on each of the six datasets used in experiments. For five of the datasets, partitions were within 1% of those of FCM. MSERFCM's speedup was 5-26 times that of FCM and produced partitions within 3% of those of FCM on all datasets. A unique dataset, consisting of plankton images, exposed the strengths and weaknesses of many of the algorithms tested. It is shown that the new stopping criterion is effective in speeding up algorithms such as SPFCM and the final partitions are very close to those of FCM.

Fuzzy c-means (FCM) is a well-known algorithm for clustering data, but for large datasets termination takes significant time. As a result, a number of scalable algorithms based on FCM have been developed. In this paper, four scalable variants of FCM are compared to the base algorithm. Runtime and three quality metrics are calculated. Experimental results using five data sets are analyzed. We show that the scalable algorithms are consistent with regard to speedup, but less consistent when quality is considered. The three quality measures are shown to have little correlation and vary in magnitude across datasets. Selection of a scalable algorithm must consider a tradeoff between the quality of results and speed. Of the variants, single pass FCM (SPFCM) is fastest with good fidelity to FCM, and extensible fast FCM (eFFCM) is almost as fast as SPFCM (as implemented) with very good fidelity to FCM. Random FCM is the fastest overall and often close in quality to FCM. The results showed that scalable algorithms occasionally produce better optimized results than FCM.

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