  Kernel pruning methods have been proposed to speed up, simplify, and improve
explanation of convolutional neural network (CNN) models. However, the
effectiveness of a simplified model is often below the original one. In this
letter, we present new methods based on objective and subjective relevance
criteria for kernel elimination in a layer-by-layer fashion. During the
process, a CNN model is retrained only when the current layer is entirely
simplified, by adjusting the weights from the next layer to the first one and
preserving weights of subsequent layers not involved in the process. We call
this strategy \emph{progressive retraining}, differently from kernel pruning
methods that usually retrain the entire model after each simplification action
-- e.g., the elimination of one or a few kernels. Our subjective relevance
criterion exploits the ability of humans in recognizing visual patterns and
improves the designer's understanding of the simplification process. The
combination of suitable relevance criteria and progressive retraining shows
that our methods can increase effectiveness with considerable model
simplification. We also demonstrate that our methods can provide better results
than two popular ones and another one from the state-of-the-art using four
challenging image datasets.
