  Inspired by the feedforward multilayer perceptron (FF-MLP), decision tree
(DT) and extreme learning machine (ELM), a new classification model, called the
subspace learning machine (SLM), is proposed in this work. SLM first identifies
a discriminant subspace, $S^0$, by examining the discriminant power of each
input feature. Then, it uses probabilistic projections of features in $S^0$ to
yield 1D subspaces and finds the optimal partition for each of them. This is
equivalent to partitioning $S^0$ with hyperplanes. A criterion is developed to
choose the best $q$ partitions that yield $2q$ partitioned subspaces among
them. We assign $S^0$ to the root node of a decision tree and the intersections
of $2q$ subspaces to its child nodes of depth one. The partitioning process is
recursively applied at each child node to build an SLM tree. When the samples
at a child node are sufficiently pure, the partitioning process stops and each
leaf node makes a prediction. The idea can be generalized to regression,
leading to the subspace learning regressor (SLR). Furthermore, ensembles of
SLM/SLR trees can yield a stronger predictor. Extensive experiments are
conducted for performance benchmarking among SLM/SLR trees, ensembles and
classical classifiers/regressors.
