Heterogeneous datasets representation and learning using diffusion maps and Laplacian pyramids

The diffusion maps together with the geometric harmonics provide a method for describing the geometry of high dimensional data and for extending these descriptions to new data points and to functions, which are defined on the data. This method suffers from two limitations. First, even though real-life data is often heterogeneous , the assumption in diffusion maps is that the attributes of the processed dataset are comparable. Second, application of the geometric harmonics requires careful setting for the correct extension scale and condition number. In this paper, we propose a method for representing and learning heterogeneous datasets by using diffusion maps for unifying and embedding heterogeneous dataset and by replacing the geometric harmonics with the Laplacian pyramid extension. Experimental results on three benchmark datasets demonstrate how the learning process becomes straightforward when the constructed representation smoothly parameterizes the task-related function.