  In this abstract paper, we introduce a new kernel learning method by a
nonparametric density estimator. The estimator consists of a group of
k-centroids clusterings. Each clustering randomly selects data points with
randomly selected features as its centroids, and learns a one-hot encoder by
one-nearest-neighbor optimization. The estimator generates a sparse
representation for each data point. Then, we construct a nonlinear kernel
matrix from the sparse representation of data. One major advantage of the
proposed kernel method is that it is relatively insensitive to its free
parameters, and therefore, it can produce reasonable results without parameter
tuning. Another advantage is that it is simple. We conjecture that the proposed
method can find its applications in many learning tasks or methods where sparse
representation or kernel matrix is explored. In this preliminary study, we have
applied the kernel matrix to spectral clustering. Our experimental results
demonstrate that the kernel generated by the proposed method outperforms the
well-tuned Gaussian RBF kernel. This abstract paper is used to protect the
idea, full versions will be updated later.
