  A framework is presented for unsupervised learning of representations based
on infomax principle for large-scale neural populations. We use an asymptotic
approximation to the Shannon's mutual information for a large neural population
to demonstrate that a good initial approximation to the global
information-theoretic optimum can be obtained by a hierarchical infomax method.
Starting from the initial solution, an efficient algorithm based on gradient
descent of the final objective function is proposed to learn representations
from the input datasets, and the method works for complete, overcomplete, and
undercomplete bases. As confirmed by numerical experiments, our method is
robust and highly efficient for extracting salient features from input
datasets. Compared with the main existing methods, our algorithm has a distinct
advantage in both the training speed and the robustness of unsupervised
representation learning. Furthermore, the proposed method is easily extended to
the supervised or unsupervised model for training deep structure networks.
