Efficient Nonnegative Tensor Factorization via Saturating Coordinate Descent
This work addresses a bottleneck in processing multi-dimensional sparse data for applications like web-based systems, though it appears incremental as it builds on existing NTF methods.
The paper tackles the problem of Nonnegative Tensor Factorization (NTF) algorithms being inefficient for tensors with varying size, density, and rank, and proposes a novel algorithm using element selection based on Lipschitz continuity and saturation points, which is shown to be scalable compared to state-of-the-art methods.
With the advancements in computing technology and web-based applications, data is increasingly generated in multi-dimensional form. This data is usually sparse due to the presence of a large number of users and fewer user interactions. To deal with this, the Nonnegative Tensor Factorization (NTF) based methods have been widely used. However existing factorization algorithms are not suitable to process in all three conditions of size, density, and rank of the tensor. Consequently, their applicability becomes limited. In this paper, we propose a novel fast and efficient NTF algorithm using the element selection approach. We calculate the element importance using Lipschitz continuity and propose a saturation point based element selection method that chooses a set of elements column-wise for updating to solve the optimization problem. Empirical analysis reveals that the proposed algorithm is scalable in terms of tensor size, density, and rank in comparison to the relevant state-of-the-art algorithms.