Kernel approximately harmonic projection

Dimensionality reduction is an important preprocessing procedure in computer vision, pattern recognition, information retrieval, and data mining. In this paper we present a kernel method based on approximately harmonic projection (AHP), a recently proposed linear manifold learning method that has an excellent performance in clustering. The kernel matrix implicitly maps the data into a reproducing kernel Hilbert space (RKHS) and makes the structure of data more distinct, which distributes on nonlinear manifold. It retains and extends the advantages of its linear version and keeps the sensitive to the connected components. This makes the method particularly suitable for unsupervised clustering. Besides, this method can cover various classes of nonlinearities with different kernels. We experiment the new method on several well-known data sets to demonstrate its effectiveness. The results show that the new algorithm performs a good job and outperforms other classic algorithms on those data sets.