Fast Hypergraph Regularized Nonnegative Tensor Ring Factorization Based on Low-Rank Approximation
This work addresses feature extraction in tensor data for applications like clustering, but it is incremental as it builds on existing nonnegative tensor ring methods by adding hypergraph regularization and optimization.
The paper tackled the problem of representing high-dimensional tensor data with complex manifold structures by introducing hypergraph regularization into nonnegative tensor ring factorization to better capture higher-dimensional similarities, and developed a low-rank approximation method to reduce computational complexity. The results showed that the proposed methods achieved higher clustering performance compared to state-of-the-art algorithms, with the accelerated version reducing running time without accuracy loss.
For the high dimensional data representation, nonnegative tensor ring (NTR) decomposition equipped with manifold learning has become a promising model to exploit the multi-dimensional structure and extract the feature from tensor data. However, the existing methods such as graph regularized tensor ring decomposition (GNTR) only models the pair-wise similarities of objects. For tensor data with complex manifold structure, the graph can not exactly construct similarity relationships. In this paper, in order to effectively utilize the higher-dimensional and complicated similarities among objects, we introduce hypergraph to the framework of NTR to further enhance the feature extraction, upon which a hypergraph regularized nonnegative tensor ring decomposition (HGNTR) method is developed. To reduce the computational complexity and suppress the noise, we apply the low-rank approximation trick to accelerate HGNTR (called LraHGNTR). Our experimental results show that compared with other state-of-the-art algorithms, the proposed HGNTR and LraHGNTR can achieve higher performance in clustering tasks, in addition, LraHGNTR can greatly reduce running time without decreasing accuracy.