  The design of robust learning systems that offer stable performance under a
wide range of supervision degrees is investigated in this work. We choose the
image classification problem as an illustrative example and focus on the design
of modularized systems that consist of three learning modules: representation
learning, feature learning and decision learning. We discuss ways to adjust
each module so that the design is robust with respect to different training
sample numbers. Based on these ideas, we propose two families of learning
systems. One adopts the classical histogram of oriented gradients (HOG)
features while the other uses successive-subspace-learning (SSL) features. We
test their performance against LeNet-5, which is an end-to-end optimized neural
network, for MNIST and Fashion-MNIST datasets. The number of training samples
per image class goes from the extremely weak supervision condition (i.e., 1
labeled sample per class) to the strong supervision condition (i.e., 4096
labeled sample per class) with gradual transition in between (i.e., $2^n$,
$n=0, 1, \cdots, 12$). Experimental results show that the two families of
modularized learning systems have more robust performance than LeNet-5. They
both outperform LeNet-5 by a large margin for small $n$ and have performance
comparable with that of LeNet-5 for large $n$.
