Internal Validity Index for Fuzzy Clustering Based on Relative Uncertainty

Unsupervised clustering and clustering validity are used as essential instruments of data analytics. Despite clustering being realized under uncertainty, validity indices do not deliver any quantitative evaluation of the uncertainties in the suggested partitionings. Also, validity measures may be biased towards the underlying clustering method. Moreover, neglecting a confidence requirement may result in over-partitioning. In the absence of an error estimate or a confidence parameter, probable clustering errors are forwarded to the later stages of the system. Whereas, having an uncertainty margin of the projected labeling can be very fruitful for many applications such as machine learning. Herein, the validity issue was approached through estimation of the uncertainty and a novel low complexity index proposed for fuzzy clustering. It involves only uni-dimensional membership weights, regardless of the data dimension, stipulates no specific distribution, and is independent of the underlying similarity measure. Inclusive tests and comparisons returned that it can reliably estimate the optimum number of partitions under different data distributions, besides behaving more robust to over partitioning. Also, in the comparative correlation analysis between true clustering error rates and some known internal validity indices, the suggested index exhibited the highest strong correlations. This relationship has been also proven stable through additional statistical acceptance tests. Thus the provided relative uncertainty measure can be used as a probable error estimate in the clustering as well. Besides, it is the only method known that can exclusively identify data points in dubiety and is adjustable according to the required confidence level.