  In (\cite{zhang2014nonlinear,zhang2014nonlinear2}), we have viewed machine
learning as a coding and dimensionality reduction problem, and further proposed
a simple unsupervised dimensionality reduction method, entitled deep
distributed random samplings (DDRS). In this paper, we further extend it to
supervised learning incrementally. The key idea here is to incorporate label
information into the coding process by reformulating that each center in DDRS
has multiple output units indicating which class the center belongs to. The
supervised learning method seems somewhat similar with random forests
(\cite{breiman2001random}), here we emphasize their differences as follows. (i)
Each layer of our method considers the relationship between part of the data
points in training data with all training data points, while random forests
focus on building each decision tree on only part of training data points
independently. (ii) Our method builds gradually-narrowed network by sampling
less and less data points, while random forests builds gradually-narrowed
network by merging subclasses. (iii) Our method is trained more straightforward
from bottom layer to top layer, while random forests build each tree from top
layer to bottom layer by splitting. (iv) Our method encodes output targets
implicitly in sparse codes, while random forests encode output targets by
remembering the class attributes of the activated nodes. Therefore, our method
is a simpler, more straightforward, and maybe a better alternative choice,
though both methods use two very basic elements---randomization and nearest
neighbor optimization---as the core. This preprint is used to protect the
incremental idea from (\cite{zhang2014nonlinear,zhang2014nonlinear2}). Full
empirical evaluation will be announced carefully later.
