Competitive Learning Based on Kernel Functions and Quadtree for Image Segmentation

This paper proposes an online competitive learning algorithm, briefly denoted as KACL (Kernel Averaging Competitive Learning), using kernel functions and quadtree structure for clustering analysis and remotely sensed image segmentation. Initially, KACL constructs a quadtree with a pre-specified scale from online input data and then locates all clusters by moving or self-splitting the nodes of the quadtree. The complexity of the quadtree is decided by the distribution of data. In the learning rule of KACL, we use the local means of vectors but not single vector so as to avoid the movement of learning prototypes among different clusters. We give the mathematical properties of KACL and present the proof of its convergence. KACL avoids the dead node problem and presetting of the number of clusters. Two experiments are separately carried out on Gaussian mixture data sets and remote sensing images and the results have shown good performance.