  Hierarchical feature learning based on convolutional neural networks (CNN)
has recently shown significant potential in various computer vision tasks.
While allowing high-quality discriminative feature learning, the downside of
CNNs is the lack of explicit structure in features, which often leads to
overfitting, absence of reconstruction from partial observations and limited
generative abilities. Explicit structure is inherent in hierarchical
compositional models, however, these lack the ability to optimize a
well-defined cost function. We propose a novel analytic model of a basic unit
in a layered hierarchical model with both explicit compositional structure and
a well-defined discriminative cost function. Our experiments on two datasets
show that the proposed compositional model performs on a par with standard CNNs
on discriminative tasks, while, due to explicit modeling of the structure in
the feature units, affording a straight-forward visualization of parts and
faster inference due to separability of the units. Actions
