Multivariate Convolutional Sparse Coding with Low Rank Tensor
This work addresses efficient signal encoding for multivariate data analysis, representing an incremental advancement in sparse coding methods.
The paper tackles the problem of multivariate convolutional sparse coding by introducing a tensor-based model that enforces both sparsity and low-rankness in activations, using CP decomposition for more efficient encoding in high-dimensional settings. The result is improved performance demonstrated through extensive experiments.
This paper introduces a new multivariate convolutional sparse coding based on tensor algebra with a general model enforcing both element-wise sparsity and low-rankness of the activations tensors. By using the CP decomposition, this model achieves a significantly more efficient encoding of the multivariate signal-particularly in the high order/ dimension setting-resulting in better performance. We prove that our model is closely related to the Kruskal tensor regression problem, offering interesting theoretical guarantees to our setting. Furthermore, we provide an efficient optimization algorithm based on alternating optimization to solve this model. Finally, we evaluate our algorithm with a large range of experiments, highlighting its advantages and limitations.