NHDC and PHDC: Non-propagating and Propagating Heat Diffusion Classifiers

By imitating the way that heat flows in a medium with a geometric structure, we propose two novel classification algorithms, Non-propagating Heat Diffusion Classifier (NHDC) and Propagating Heat Diffusion Classifier (PHDC). In NHDC, an unlabelled data is classified into the class that diffuses the most heat to the unlabelled data after one local diffusion from time 0 to a small time period, while in PHDC, an unlabelled data is classified into the class that diffuses the most heat to the unlabelled data in the propagating effect of the heat flow from time 0 to time t, which means that in PHDC, the heat diffuses infinitely many times from time 0 and each time period is infinitely small. In other words, we measure the similarity between an unlabelled data and a class by the heat amount that the unlabelled data receives from the set of labelled data in the class, and then classify the unlabelled data into the class with the most similarity. Unlike the traditional method, in which the heat kernel is applied to a kernel-based classifier we employ the heat kernel to construct the classifier directly; moreover, instead of imitating the way that the heat flows along a linear or nonlinear manifold, we let the heat flow along a graph formed by the k-nearest neighbors. An important and special feature in both NHDC and PHDC is that the kernel is not symmetric. We show theoretically that PWA (Parzen Window Approach when the window function is a multivariate normal kernel) and KNN are actually special cases of NHDC model, and that PHDC has the ability to approximate NHDC. Experiments show that NHDC performs better than PWA and KNN in prediction accuracy, and that PHDC performs better than NHDC.