Convolutional Dictionary Learning through Tensor Factorization
This work addresses convolutional models in domains with shift invariances, offering an incremental improvement for machine learning applications like signal processing.
The paper tackled the problem of parameter estimation in convolutional dictionary learning by developing a novel tensor decomposition algorithm based on alternating least squares with efficient projections onto stacked circulant matrices, resulting in faster and more accurate convergence to the dictionary compared to existing methods.
Tensor methods have emerged as a powerful paradigm for consistent learning of many latent variable models such as topic models, independent component analysis and dictionary learning. Model parameters are estimated via CP decomposition of the observed higher order input moments. However, in many domains, additional invariances such as shift invariances exist, enforced via models such as convolutional dictionary learning. In this paper, we develop novel tensor decomposition algorithms for parameter estimation of convolutional models. Our algorithm is based on the popular alternating least squares method, but with efficient projections onto the space of stacked circulant matrices. Our method is embarrassingly parallel and consists of simple operations such as fast Fourier transforms and matrix multiplications. Our algorithm converges to the dictionary much faster and more accurately compared to the alternating minimization over filters and activation maps.