An investigation on scaling parameter and distance metrics in semi-supervised Fuzzy c-means

The scaling parameter α helps maintain a balance between supervised and unsupervised learning in semi-supervised Fuzzy c-Means (ssFCM). In this study, we investigated the effects of different α values, 0.1, 0.5, 1 and 10 in Pedrycz and Waletsky’s ssFCM with various amounts of labelled data, 10%, 20%, 30%, 40%, 50% and 60% and three distance metrics, Euclidean, Mahalanobis and kernel-based on the Nottingham Tenovus Breast Cancer dataset and five popular UCI datasets. Higher α values were found to produced better accuracy using Euclidean distance on four datasets out of the six datasets. For Mahalanobis distance, increasing α to improve accuracy is effective up to α = 1 and not at α = 10 in three out of six dataseets. For kernel-based distance, accuracy tend to decrease with increasing α value, which has been observed in four out of six datasets. Such trends in the effects of α values on the classification results using different distance metrics and datasets can be established to form a guide in the selection of α. Care should be taken in selection of α value as they are dependant on the distance metric, particularly the Mahalanobis and kernelbased distance metrics, and the dataset used.