  Sparse coding aims to model data vectors as sparse linear combinations of
basis elements, but a majority of related studies are restricted to continuous
data without spatial or temporal structure. A new model-based sparse coding
(MSC) method is proposed to provide an effective and flexible framework for
learning features from different data types: continuous, discrete, or
categorical, and modeling different types of correlations: spatial or temporal.
The specification of the sparsity level and how to adapt the estimation method
to large-scale studies are also addressed. A fast EM algorithm is proposed for
estimation, and its superior performance is demonstrated in simulation and
multiple real applications such as image denoising, brain connectivity study,
and spatial transcriptomic imaging.
