Approximate empirical kernel map-based iterative extreme learning machine for clustering

Maximum margin clustering (MMC) is a recent approach of applying margin maximization in supervised learning to unsupervised learning, aiming to partition the data into clusters with high discrimination. Recently, extreme learning machine (ELM) has been applied to MMC (called iterative ELM clustering or ELMCIter) which maximizes the data discrimination by iteratively training a weighted extreme learning machine (W-ELM). In this way, ELMC(Iter)achieves a substantial reduction in training time and provides a unified model for both binary and multi-class clusterings. However, there exist two issues in ELMCIter: (1) random feature mappings adopted in ELMC(Iter)are unable to well obtain high-quality discriminative features for clustering and (2) a large model is usually required in ELMC(Iter)because its performance is affected by the number of hidden nodes, and training such model becomes relatively slow. In this paper, the hidden layer in ELMC(Iter)is encoded by an approximate empirical kernel map (AEKM) rather than the random feature mappings, in order to solve these two issues. AEKM is generated from low-rank approximation of the kernel matrix, derived from the input data through a kernel function. Our proposed method is called iterative AEKM for clustering (AEKMC(Iter)), whose contributions are: (1) AEKM can extract discriminative and robust features from the kernel matrix so that better performance is always achieved in AEKMC(Iter)and (2) AEKMC(Iter)produces an extremely small number of hidden nodes for low memory consumption and fast training. Detailed experiments verified the effectiveness and efficiency of our approach. As an illustration, on the MNIST10 dataset, our approach AEKMC(Iter)improves the clustering accuracy over ELMC(Iter)up to 5%, while significantly reducing the training time and the memory consumption (i.e., the number of hidden nodes) up to 1/7 and 1/20, respectively.