Incremental Kernel Fuzzy c-Means

The size of everyday data sets is outpacing the capability of computational hardware to analyze these data sets. Social networking and mobile computing alone are producing data sets that are growing by terabytes every day. Because these data often cannot be loaded into a computer’s working memory, most literal algorithms (algorithms that require access to the full data set) cannot be used. One type of pattern recognition and data mining method that is used to analyze databases is clustering; thus, clustering algorithms that can be used on large data sets are important and useful. We focus on a specific type of clustering: kernelized fuzzy c-means (KFCM). The literal KFCM algorithm has a memory requirement of O(n), where n is the number objects in the data set. Thus, even data sets that have nearly 1,000,000 objects require terabytes of working memory—infeasible for most computers. One way to attack this problem is by using incremental algorithms; these algorithms sequentially process chunks or samples of the data, combining the results from each chunk. Here we propose three new incremental KFCM algorithms: rseKFCM, spKFCM, and oKFCM. We assess the performance of these algorithms by, first, comparing their clustering results to that of the literal KFCM and, second, by showing that these algorithms can produce reasonable partitions of large data sets. In summary, the rseKFCM is the most efficient of the three, exhibiting significant speedup at low sampling rates. The oKFCM algorithm seems to produce the most accurate approximation of KFCM, but at a cost of low efficiency. Our recommendation is to use rseKFCM at the highest sample rate allowable for your computational and problem needs.