  A new machine learning methodology, called successive subspace learning
(SSL), is introduced in this work. SSL contains four key ingredients: 1)
successive near-to-far neighborhood expansion; 2) unsupervised dimension
reduction via subspace approximation; 3) supervised dimension reduction via
label-assisted regression (LAG); and 4) feature concatenation and decision
making. An image-based object classification method, called PixelHop, is
proposed to illustrate the SSL design. It is shown by experimental results that
the PixelHop method outperforms the classic CNN model of similar model
complexity in three benchmarking datasets (MNIST, Fashion MNIST and CIFAR-10).
Although SSL and deep learning (DL) have some high-level concept in common,
they are fundamentally different in model formulation, the training process and
training complexity. Extensive discussion on the comparison of SSL and DL is
made to provide further insights into the potential of SSL.
