Abstract
In this study, kernel interval-valued Fuzzy C-Means clustering (KIFCM) and multiple kernel interval-valued Fuzzy C-Means clustering (MKIFCM) are proposed. The KIFCM algorithm is built on a basis of the kernel learning method and the interval-valued fuzzy sets with intent to overcome some drawbacks existing in the “conventional” Fuzzy C-Means (FCM) algorithm. The development of the method is motivated by two factors. First, uncertainty is inherent in clustering problems due to some information deficiency, which might be incomplete, imprecise, fragmentary, not fully reliable, vague, contradictory, etc. With this regard, interval-valued fuzzy sets exhibit advantages when handling such aspects of uncertainty. Second, kernel methods form a new class of pattern analysis algorithms which can cope with general types of data and detect general types of relations (geometric properties) by embedding input data in a vector space based on the inner products and looking for linear relations in the space. However, as the clustering problems may involve various input features exhibiting different impacts on the obtained results, we introduce a new MKIFCM algorithm, which uses a combination of different kernels (giving rise to a concept of a composite kernel). The composite kernel was built by mapping each input feature onto individual kernel space and linearly combining these kernels with the optimized weights of the corresponding kernel. The experiments were completed for several well-known datasets, land cover classification from multi-spectral satellite image and Multiplex Fluorescent In Situ Hybridization (MFISH) classification problem. The obtained results demonstrate the advantages of the proposed algorithms.