Multiscale Dimensionality Reduction Based on Diffusion Wavelets

Many machine learning data sets are embedded in high-dimensional spaces, and require some type of dimensionality reduction to visualize or analyze the data. In this paper, we propose a novel framework for multiscale dimensionality reduction based on diffusion wavelets. Our approach is completely data driven, computationally efficient, and able to directly process non-symmetric neighborhood relationships without ad-hoc symmetrization. The superior performance of our approach is illustrated using several synthetic and real-world data sets.