Unsupervised kernel parameter estimation by constrained nonlinear optimization for clustering nonlinear biological data

Data on a wide-range of bio-chemical phenomena is often highly non-linear. Due to this characteristic, data analysis tasks, such as clustering can become non-trivial. In recent years, the use of kernel-based algorithms has gained popularity for data analysis and clustering to ameliorate the above challenges. In this paper, we propose a novel approach for kernel parameter estimation using constrained nonlinear programming and conditionally positive definite kernels. The central idea is to maximize the trace of the kernel matrix, which maximizes the variance in the feature space. Therefore, the parameter estimation process does not involve any user intervention or prior understanding of the data and the parameters are learned only from data. The results from the proposed method significantly improve upon results obtained with other leading non-linear analysis techniques.