Inductive Convolution Nuclear Norm Minimization for Tensor Completion with Arbitrary Sampling

2026-04-18

AI Summary

This work addresses the tensor completion problem under arbitrary sampling patterns by proposing an inductive convolutional nuclear norm minimization method. The approach incorporates pre-learned shared convolutional feature vectors as a prior and reformulates the optimization objective to circumvent repeated singular value decompositions, thereby substantially reducing computational overhead. While preserving theoretical rigor, the proposed framework achieves notable improvements in both reconstruction accuracy and computational efficiency. Experimental results demonstrate that the method significantly outperforms CNNM and other state-of-the-art approaches in terms of both runtime speed and reconstruction quality across various tasks, including video completion, prediction, and frame interpolation.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

The recently established Convolution Nuclear Norm Minimization (CNNM) addresses the problem of \textit{tensor completion with arbitrary sampling} (TCAS), which involves restoring a tensor from a subset of its entries sampled in an arbitrary manner. Despite its promising performance, the optimization procedure of CNNM needs performing Singular Value Decomposition (SVD) multiple times, which is computationally expensive and hard to parallelize. To address the issue, we reformulate the optimization objective of CNNM from the perspective of convolution eigenvectors. By introducing pre-learned convolution eigenvectors which are shared among different tensors, we propose a novel method called Inductive Convolution Nuclear Norm Minimization (ICNNM), which bypasses the SVD step so as to decrease significantly the computational time. In addition, due to the extra prior knowledge encoded in the pre-learned convolution eigenvectors, ICNNM also outperforms CNNM in terms of recovery performance. Extensive experiments on video completion, prediction and frame interpolation verify the superiority of ICNNM over CNNM and several other competing methods.

Problem

• tensor completion
• arbitrary sampling
• convolution nuclear norm
• singular value decomposition
• inductive learning

Innovation

• Inductive Learning
• Convolution Nuclear Norm
• Tensor Completion
• Arbitrary Sampling
• Singular Value Decomposition