Kernel and Range Approach to Analytic Network Learning

The problem of machine learning has been traditionally formulated as an optimization task where an error metric is minimized. In terms of solving the system of linear equations, an approximation is often sought-after according to a least error metric because it is difficult to have an exact match between the sample size and the number of model parameters. Such an approximation to the least error metric, particularly in the squared error form, can be determined analytically either in the primal solution space or in the dual solution space depending on the rank property of the covariance matrix. This optimization approach has been a popular choice due to its simplicity and tractability in analysis and implementation. The approach is predominant in engineering applications as evident from its pervasive adoption in statistical and shallow network learning.