Graph Laplacian Kernels for Object Classification from a Single Example

Classification with only one labeled example per class is a challenging problem in machine learning and pattern recognition. While there have been some attempts to address this problem in the context of specific applications, very little work has been done so far on the problem under more general object classification settings. In this paper, we propose a graph-based approach to the problem. Based on a robust path-based similarity measure proposed recently, we construct a weighted graph using the robust path-based similarities as edge weights. A kernel matrix, called graph Laplacian kernel, is then defined based on the graph Laplacian. With the kernel matrix, in principle any kernel-based classifier can be used for classification. In particular, we demonstrate the use of a kernel nearest neighbor classifier on some synthetic data and real-world image sets, showing that our method can successfully solve some difficult classification tasks with only very few labeled examples.