Advances in Tensor-Based Methods

The field of tensor-based methods is rapidly advancing, with a focus on developing innovative techniques for tensor decomposition, denoising, and approximation. Recent research has led to the proposal of novel methods, such as auto tensor singular value thresholding and tensor sketch, which have shown to outperform existing techniques in terms of accuracy and computational efficiency. Additionally, there has been significant progress in the development of algorithms for canonical polyadic decomposition over finite fields, which has important implications for fast matrix multiplication. The field is also seeing advancements in the application of tensor-based methods to real-world problems, such as medical imaging and data compression. Notable papers in this area include those that propose efficient algorithms for tensor denoising and approximation, such as Auto Tensor Singular Value Thresholding, and those that develop new methods for canonical polyadic decomposition, such as New results in canonical polyadic decomposition over finite fields. These papers demonstrate the potential of tensor-based methods to advance the field and have significant practical applications.

Sources

Designing 3D Anisotropic Frame Fields with Odeco Tensors

Auto Tensor Singular Value Thresholding: A Non-Iterative and Rank-Free Framework for Tensor Denoising

On the permanent of random tensors

Tensor Sketch: Fast and Scalable Polynomial Kernel Approximation

Clustering-based Low-Rank Matrix Approximation: An Adaptive Theoretical Analysis with Application to Data Compression

On Unbiased Low-Rank Approximation with Minimum Distortion

New results in canonical polyadic decomposition over finite fields

The finiteness conjecture for $3 \times 3$ binary matrices

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