Minimal Learning Machine: Theoretical Results and Clustering-Based Reference Point Selection
This work provides foundational theoretical support and practical improvements for the MLM, a nonlinear supervised learning method, though it is incremental in nature.
The paper addresses theoretical gaps in the Minimal Learning Machine (MLM) by proving its interpolation and universal approximation capabilities, and proposes clustering-based methods for selecting reference points that outperform random selection, especially with few reference points.
The Minimal Learning Machine (MLM) is a nonlinear supervised approach based on learning a linear mapping between distance matrices computed in the input and output data spaces, where distances are calculated using a subset of points called reference points. Its simple formulation has attracted several recent works on extensions and applications. In this paper, we aim to address some open questions related to the MLM. First, we detail theoretical aspects that assure the interpolation and universal approximation capabilities of the MLM, which were previously only empirically verified. Second, we identify the task of selecting reference points as having major importance for the MLM's generalization capability. Several clustering-based methods for reference point selection in regression scenarios are then proposed and analyzed. Based on an extensive empirical evaluation, we conclude that the evaluated methods are both scalable and useful. Specifically, for a small number of reference points, the clustering-based methods outperformed the standard random selection of the original MLM formulation.