  Feature selection reduces the dimensionality of data by identifying a subset
of the most informative features. In this paper, we propose an innovative
framework for unsupervised feature selection, called fractal autoencoders
(FAE). It trains a neural network to pinpoint informative features for global
exploring of representability and for local excavating of diversity.
Architecturally, FAE extends autoencoders by adding a one-to-one scoring layer
and a small sub-neural network for feature selection in an unsupervised
fashion. With such a concise architecture, FAE achieves state-of-the-art
performances; extensive experimental results on fourteen datasets, including
very high-dimensional data, have demonstrated the superiority of FAE over
existing contemporary methods for unsupervised feature selection. In
particular, FAE exhibits substantial advantages on gene expression data
exploration, reducing measurement cost by about $15$\% over the widely used
L1000 landmark genes. Further, we show that the FAE framework is easily
extensible with an application.
