  Multilayer bootstrap network builds a gradually narrowed multilayer nonlinear
network from bottom up for unsupervised nonlinear dimensionality reduction.
Each layer of the network is a nonparametric density estimator. It 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. Geometrically, the nonparametric
density estimator at each layer projects the input data space to a
uniformly-distributed discrete feature space, where the similarity of two data
points in the discrete feature space is measured by the number of the nearest
centroids they share in common. The multilayer network gradually reduces the
nonlinear variations of data from bottom up by building a vast number of
hierarchical trees implicitly on the original data space. Theoretically, the
estimation error caused by the nonparametric density estimator is proportional
to the correlation between the clusterings, both of which are reduced by the
randomization steps.
