A novel string grammar fuzzy C-medians

One of the popular classification problems is the syntactic pattern recognition. A syntactic pattern can be described using string grammar. The string grammar hard C-means is one of the classification algorithms in syntactic pattern recognition. However, it has been proved that fuzzy clustering is better than hard clustering. Hence, in this paper we develop a string grammar fuzzy C-medians algorithm. In particular, the string grammar fuzzy C-medians algorithm is a counterpart of fuzzy C-medians in which a fuzzy median approach is applied for finding fuzzy median string as the center of string data. However, the fuzzy median string may not provide a good clustering result. We then modified a method to compute fuzzy median string with the edition operations (insertion, deletion, and substitution) over each symbol of the string. The fuzzy C-medians with regular fuzzy median and the one with the modified fuzzy median are implemented on 3 real data sets, i.e., Copenhagen chromosomes data set, MNIST database of handwritten digits, and USPS database of handwritten digits. We also compare the results with those from the string grammar hard C-means. The results show that the string grammar fuzzy C-medians is better than the string grammar hard C-means.