Kernel Matrix Based Incremental Learning Isomap Algorithm

The Isomap algorithm operates in batch mode, meaning that all data should to be available when training is done. However, in many scenarios the data come sequentially and the effect of the data is accumulated. When new data is added, it takes a long time to update the geodesic distance matrix including all data points. In order to improve the computing speed, a kernel based incremental learning Isomap algorithm (ILIsomap) is proposed. The geodesic distance matrix can be interpreted as a kernel matrix, and then ILIsomap exploits a constant-shifting method to guarantee that the geodesic distance matrix satisfy the Mercer kernel. ILIsomap only needs to calculate the geodesic distance between new data and the original data, making it possible to project test data points onto low-dimensional manifold embedding using a kernel trick as in kernel PCA. Experimental results on Swiss data sets, Helix data sets, and multi-posture face data set demonstrate that ILIsomap reduces the computational complexity, making it possible to quickly visualize low-dimensional manifolds embedding in high-dimensional space.