Multilayer bootstrap networks
This addresses dimensionality reduction for data analysis, but appears incremental as it builds on existing clustering and bootstrap methods.
The paper tackles unsupervised nonlinear dimensionality reduction by constructing a multilayer bootstrap network that uses nonparametric density estimators to project data into uniformly-distributed discrete feature spaces, gradually reducing nonlinear variations from bottom up. Theoretically, it shows that estimation error is proportional to clustering correlation, which is reduced through randomization.
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.