Random Feature Based Attribute-weighed Kernel Fuzzy Clustering for Non-linear Data

Traditional kernel clustering methods are useful in dealing with non-linear data, but the high-dimensional kernel space obtained by kernel mapping is an abstract concept, which is difficult to be determined. The kernel mapping between raw data space and kernel space needs high computational complexity which is burdensome for hardware. At the same time, due to the unknown nature of kernel space, traditional kernel clustering methods cannot process data with the consideration of different importance among dimensions, i.e., discover the hidden feature subset of high-dimensional sparse data. To overcome these limitations, we put forward a novel random Fourier feature based attribute-weighed kernel fuzzy c-means clustering algorithm (RFF-WKFCM). This method employs RFF map to generate low-rank random features, and performs fuzzy c-means clustering with attribute weight entropy regularization in this feature space, which greatly reduces the computational complexity. What is more, the adoption of the maximum entropy technique ensures the optimal distribution of attribute weights, which stimulate important dimensions play a greater role in the clustering process. The proposed method shows good performance on the experiments of ring data set compared with other fuzzy clutering methods.