Online multidimensional dictionary learning
This work provides an incremental improvement for handling large-scale tensor data analysis in signal processing and machine learning domains.
The authors tackled the problem of dictionary learning for multidimensional tensor data by proposing an online method using the t-product framework with an accelerated ISTA algorithm enhanced by Anderson acceleration. Their approach significantly improved signal reconstruction results and outperformed existing acceleration techniques in applications like data completion.
Dictionary learning is a widely used technique in signal processing and machine learning that aims to represent data as a linear combination of a few elements from an overcomplete dictionary. In this work, we propose a generalization of the dictionary learning technique using the t-product framework, enabling efficient handling of multidimensional tensor data. We address the dictionary learning problem through online methods suitable for tensor structures. To effectively address the sparsity problem, we utilize an accelerated Iterative Shrinkage-Thresholding Algorithm (ISTA) enhanced with an extrapolation technique known as Anderson acceleration. This approach significantly improves signal reconstruction results. Extensive experiments prove that our proposed method outperforms existing acceleration techniques, particularly in applications such as data completion. These results suggest that our approach can be highly beneficial for large-scale tensor data analysis in various domains.