Projection and visualization based on synchronization of coupled oscillators

This work introduces a tool for mapping high dimensional data to a low-dimensional space by combining concepts from clustering and synchronization of pulse-coupled oscillators. Each data point is represented by an integrate-and-fire oscillator which is characterized by a phase variable. Using an appropriate coupling function, we show that the relative values of the phases evolve to reflect the proximity of the data in the original space. As a result, the oscillators phases could be used as a 1-D representation of the original space. To generate a 2-D phase space, we apply the synchronization procedure twice with different resolution parameters or different distance measures. The proposed approach is used to visualize the classical Iris data and two collection of images.