  Feature selection is a dimensionality reduction technique that selects a
subset of representative features from high dimensional data by eliminating
irrelevant and redundant features. Recently, feature selection combined with
sparse learning has attracted significant attention due to its outstanding
performance compared with traditional feature selection methods that ignores
correlation between features. These works first map data onto a low-dimensional
subspace and then select features by posing a sparsity constraint on the
transformation matrix. However, they are restricted by design to linear data
transformation, a potential drawback given that the underlying correlation
structures of data are often non-linear. To leverage a more sophisticated
embedding, we propose an autoencoder-based unsupervised feature selection
approach that leverages a single-layer autoencoder for a joint framework of
feature selection and manifold learning. More specifically, we enforce column
sparsity on the weight matrix connecting the input layer and the hidden layer,
as in previous work. Additionally, we include spectral graph analysis on the
projected data into the learning process to achieve local data geometry
preservation from the original data space to the low-dimensional feature space.
Extensive experiments are conducted on image, audio, text, and biological data.
The promising experimental results validate the superiority of the proposed
method.
