Diffusion Equation Based Subspace Extraction of Image Data for Fast K-Means

The past decade has undergone an explosion of image data collection from various sensors. The extreme increase of high dimensional data poses significant challenges for processing vast amounts of new data. Since most of the important and useful features are contained in low dimensional subspaces of the high dimensional data, subspace clustering techniques have been extensively developed to process these high dimensional data. In this paper, a diffusion equation evolution approach is proposed to extract subspaces from high dimensional image sensor data. Iterative exponential filtering is introduced to implement this diffusion equation evolution. Theoretical analysis and simulation tests show that the computational cost of the proposed method is independent of the number of neighboring points and much lower than the traditional methods. As an application, the proposed method is applied to K-Means implementation for image data. Test results show that the proposed method is over 20 times faster in computing time and over 20% higher in clustering performance than the traditional Floyd implementation.