Parametric kernels for structured data analysis

Structured representation of input physical patterns as a set of local features has been useful for a veriety of robotics and human computer interaction (HCI) applications. It enables a stable understanding of the variable inputs. However, this representation does not fit the conventional machine learning algorithms and distance metrics because they assume vector inputs. To learn from input patterns with variable structure is thus challenging. To address this problem, I propose a general and systematic method to design distance metrics between structured inputs that can be used in conventional learning algorithms. Based on the observation of the stability in the geometric distributions of local features over the physical patterns across similar inputs, this is done combining the local similarities and the conformity of the geometric relationship between local features. The produced distance metrics, called “parametric kernels”, are positive semi-definite and require almost linear time to compute. To demonstrate the general applicability and the efficacy of this approach, I designed and applied parametric kernels to handwritten character recognition, on-line face recognition, and object detection from laser range finder sensor data. Parametric kernels achieve recognition rates competitive to state-of-the-art approaches in these tasks.