MNT-TNN: Spatiotemporal Traffic Data Imputation via Compact Multimode Nonlinear Transform-based Tensor Nuclear Norm

2025-03-29

AI Summary

Traffic data imputation in intelligent transportation systems remains challenging under extremely high random missing rates (>90%), where conventional linear, single-mode models fail to capture the intrinsic low-rank structure and multimodal spatiotemporal correlations of 3D traffic tensors (location × location × time). Method: This paper proposes a tensor nuclear norm optimization framework based on multimodal nonlinear transformations. We introduce the Multimodal Nonlinear Transformation-based Tensor Nuclear Norm (MNT-TNN), the first of its kind, and establish the Augmented Transformation-based Tensor Nuclear Norms (ATTNNs) framework. The method integrates the Proximal Alternating Minimization (PAM) algorithm with theoretical convergence guarantees. Contribution/Results: Evaluated on multiple real-world traffic datasets, our approach significantly outperforms state-of-the-art methods—especially under >90% random missingness—achieving superior reconstruction accuracy and establishing a new benchmark for high-missing-rate traffic data imputation.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Computer Vision: Multi-modal Vision
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Imputation of random or non-random missing data is a long-standing research topic and a crucial application for Intelligent Transportation Systems (ITS). However, with the advent of modern communication technologies such as Global Satellite Navigation Systems (GNSS), traffic data collection has outpaced traditional methods, introducing new challenges in random missing value imputation and increasing demands for spatiotemporal dependency modelings. To address these issues, we propose a novel spatiotemporal traffic imputation method, Multimode Nonlinear Transformed Tensor Nuclear Norm (MNT-TNN), grounded in the Transform-based Tensor Nuclear Norm (TTNN) optimization framework which exhibits efficient mathematical representations and theoretical guarantees for the recovery of random missing values. Specifically, we strictly extend the single-mode transform in TTNN to a multimode transform with nonlinear activation, effectively capturing the intrinsic multimode spatiotemporal correlations and low-rankness of the traffic tensor, represented as location $ imes$ location $ imes$ time. To solve the nonconvex optimization problem, we design a proximal alternating minimization (PAM) algorithm with theoretical convergence guarantees. We suggest an Augmented Transform-based Tensor Nuclear Norm Families (ATTNNs) framework to enhance the imputation results of TTNN techniques, especially at very high miss rates. Extensive experiments on real datasets demonstrate that our proposed MNT-TNN and ATTNNs can outperform the compared state-of-the-art imputation methods, completing the benchmark of random missing traffic value imputation.

Problem

• Imputing random missing spatiotemporal traffic data
• Modeling multimode spatiotemporal dependencies effectively
• Enhancing imputation accuracy at high missing rates

Innovation

• Multimode nonlinear transform for tensor completion
• Proximal alternating minimization algorithm
• Augmented transform-based tensor nuclear norm