Core Tensor Research Articles

Unsupervised Hyperspectral and Multispectral Image Blind Fusion Based on Deep Tucker Decomposition Network With Spatial-Spectral Manifold Learning.

Hyperspectral image (HSI) and multispectral image (MSI) fusion aims to generate high spectral and spatial resolution hyperspectral image (HR-HSI) by fusing high-resolution multispectral image (HR-MSI) and low-resolution hyperspectral image (LR-HSI). However, existing fusion methods encounter challenges such as unknown degradation parameters, and incomplete exploitation of the correlation between high-dimensional structures and deep image features. To overcome these issues, in this article, an unsupervised blind fusion method for LR-HSI and HR-MSI based on Tucker decomposition and spatial-spectral manifold learning (DTDNML) is proposed. We design a novel deep Tucker decomposition network that maps LR-HSI and HR-MSI into a consistent feature space, achieving reconstruction through decoders with shared parameters. To better exploit and fuse spatial-spectral features in the data, we design a core tensor fusion network (CTFN) that incorporates a spatial-spectral attention mechanism for aligning and fusing features at different scales. Furthermore, to enhance the capacity to capture global information, a Laplacian-based spatial-spectral manifold constraint is introduced in shared-decoders. Sufficient experiments have validated that this method enhances the accuracy and efficiency of hyperspectral and multispectral fusion on different remote sensing datasets. The source code is available at https://github.com/Shawn-H-Wang/DTDNML.

A fast Lanczos-based hierarchical algorithm for tensor ring decomposition

Tensor ring (TR) decomposition has made remarkable achievements in numerous high-order data processing tasks. However, the current alternating least squares (ALS)- and singular value decomposition (SVD)-based algorithms for TR decomposition, i.e., TR-ALS and TR-SVD, especially the former, are computationally expensive, making them unfriendly for large-scale data processing. This paper adopts three strategies to propose a novel fast TR decomposition algorithm: (1) Use a more efficient Lanczos bidiagonalization algorithm than SVD to generate the TR core tensors. (2) Exploit the hierarchical strategy to generate the TR core tensors in parallel. (3) Employ new reshaping and unfolding operations to reduce the dimensionality of the data used to generate TR core tensors. By incorporating these three strategies, we propose the TR-HLanczos algorithm for fast TR decomposition. This algorithm seamlessly produces the TR core tensors through the Lanczos bidiagonalization algorithm in a hierarchical manner. The effectiveness of the proposed TR-HLanczos algorithm is demonstrated through experimental results on both highly oscillatory functions and real-world datasets. For instance, when dealing with data of size 505, TR-HLanczos is nearly 561 times and 18 times faster than algorithms based on ALS and SVD, respectively.

A novel data-driven 3D site characterisation method: Tucker decomposition-Bayesian compressive sensing and benchmarking study

ABSTRACT Site characterisation plays a pivotal role in geotechnical design and analysis. With advancements in machine learning and other digital technologies, data-driven site characterisation (DDSC) has garnered substantial interest in data-centric geotechnics. This paper proposes a novel and competitive 3D DDSC method, called Tucker decomposition-Bayesian compressive sensing (TD-BCS), which employs Tucker decomposition to factorise a 3D high-order tensor into a low-rank core tensor along with three associated factor matrices. The method comprises three key components: (1) 3D sparse representation using Tucker decomposition and discrete cosine transform; (2) Bayesian compressive sensing, and its algorithm implementation; and (3) Determination of three effective factor matrices. The proposed TD-BCS method is evaluated through its application to two benchmark examples, involving virtual ground and actual ground scenario based on real CPT data. And the benchmarking results demonstrate that the method not only yields accurate estimates with quantified uncertainty from sparse measurements but also exhibits high computational efficiency compared to other DDSC methods. Indeed, the TD-BCS method can be effectively applied to other 3D geotechnical engineering cases, and its framework is readily extendable to higher dimensions.

Judgment Prediction Based on Tensor Decomposition With Optimized Neural Networks.

In the field of smart justice, handling legal cases through artificial intelligence technology is a research hotspot. Traditional judgment prediction methods are mainly based on feature models and classification algorithms. The former is difficult to describe cases from multiple angles and capture the correlation information between different case modules, while requires a wealth of legal expertise and manual labeling. The latter is unable to accurately extract the most useful information from case documents and produce fine-grained predictions. This article proposes a judgment prediction method based on tensor decomposition with optimized neural networks, which consists of OTenr, GTend, and RnEla. OTenr represents cases as normalized tensors. GTend decomposes normalized tensors into core tensors using the guidance tensor. RnEla intervenes in a case modeling process in GTend by optimizing the guidance tensor, so that core tensors represent tensor structural and elemental information, which is most conducive to improving the accuracy of judgment prediction. RnEla consists of the similarity correlation Bi-LSTM and optimized Elastic-Net regression. RnEla takes the similarity between cases as an important factor for judgment prediction. Experimental results on real legal case dataset show that the accuracy of our method is higher than that of the previous judgment prediction methods.

Cyclic tensor singular value decomposition with applications in low-rank high-order tensor recovery

The rapid advancements in emerging technologies have increased the demand for recovery tasks involving high-dimensional data with complex structures. Effectively utilizing tensor decomposition techniques to capture the low-rank structure of such data is crucial. Recently, the high-order t-SVD has demonstrated strong adaptability. However, this decomposition approach can only capture the low-rank correlation of two modes along other modes individually, while disregarding the structural correlation between different modes. In this paper, we propose a novel cyclic tensor singular value decomposition (CTSVD) method that effectively characterizes the low-rank structures of high-order tensors along all modes. Specifically, our method decomposes an order-N tensor into N factor tensors and one core tensor, connecting them using a defined mode-k tensor-tensor product (t-product). Building upon this, we establish the corresponding tensor rank and its convex relaxation. To address the issue of dimensional imbalance between adjacent modes in high-dimensional data, we propose and integrate a square reshaping strategy into the recovery models for tensor completion (TC) and tensor principal component analysis (TRPCA) tasks. Effective alternating direction method of multipliers (ADMM)-based algorithms are designed to these tasks. Extensive experiments on both synthetic and real data demonstrate that our methods outperform state-of-the-art approaches.

Efficient enhancement of low-rank tensor completion via thin QR decomposition.

Low-rank tensor completion (LRTC), which aims to complete missing entries from tensors with partially observed terms by utilizing the low-rank structure of tensors, has been widely used in various real-world issues. The core tensor nuclear norm minimization (CTNM) method based on Tucker decomposition is one of common LRTC methods. However, the CTNM methods based on Tucker decomposition often have a large computing cost due to the fact that the general factor matrix solving technique involves multiple singular value decompositions (SVDs) in each loop. To address this problem, this article enhances the method and proposes an effective CTNM method based on thin QR decomposition (CTNM-QR) with lower computing complexity. The proposed method extends the CTNM by introducing tensor versions of the auxiliary variables instead of matrices, while using the thin QR decomposition to solve the factor matrix rather than the SVD, which can save the computational complexity and improve the tensor completion accuracy. In addition, the CTNM-QR method's convergence and complexity are analyzed further. Numerous experiments in synthetic data, real color images, and brain MRI data at different missing rates demonstrate that the proposed method not only outperforms in terms of completion accuracy and visualization, but also conducts more efficiently than most state-of-the-art LRTC methods.

CuFastTucker: A Novel Sparse FastTucker Decomposition For HHLST on Multi-GPUs

High-order, high-dimension, and large-scale sparse tensors (HHLST) have found their origin in various real industrial applications, such as social networks, recommender systems, bioinformatics, and traffic information. To handle these complex tensors, sparse tensor decomposition techniques are employed to project the HHLST into a low-rank space. In this paper, we propose a novel sparse tensor decomposition model called Sparse FastTucker Decomposition (SFTD), which is a variant of Sparse Tucker Decomposition (STD). The SFTD utilizes Kruskal approximation for the core tensor, and we present a theorem that reduces the exponential space and computational overhead to a polynomial one. Additionally, we reduce the space overhead of intermediate parameters in the algorithmic process by sampling the intermediate matrix. Furthermore, this method guarantees convergence. To enhance the speed of SFTD, we leverage the compactness of matrix multiplication and parallel access through a stochastic strategy, resulting in GPU-accelerated cuFastTucker. Moreover, we propose a data division and communication strategy for cuFastTucker to accommodate data on Multi-GPU setups. Our proposed cuFastTucker demonstrates faster calculation and convergence speeds, as well as significantly lower space and computational overhead compared to state-of-the-art (SOTA) algorithms such as P-Tucker, Vest, GTA, Bigtensor and SGD_Tucker.

Towards Super Compressed Neural Networks for Object Identification: Quantized Low-Rank Tensor Decomposition with Self-Attention

Deep convolutional neural networks have a large number of parameters and require a significant number of floating-point operations during computation, which limits their deployment in situations where the storage space is limited and computational resources are insufficient, such as in mobile phones and small robots. Many network compression methods have been proposed to address the aforementioned issues, including pruning, low-rank decomposition, quantization, etc. However, these methods typically fail to achieve a significant compression ratio in terms of the parameter count. Even when high compression rates are achieved, the network’s performance is often significantly deteriorated, making it difficult to perform tasks effectively. In this study, we propose a more compact representation for neural networks, named Quantized Low-Rank Tensor Decomposition (QLTD), to super compress deep convolutional neural networks. Firstly, we employed low-rank Tucker decomposition to compress the pre-trained weights. Subsequently, to further exploit redundancies within the core tensor and factor matrices obtained through Tucker decomposition, we employed vector quantization to partition and cluster the weights. Simultaneously, we introduced a self-attention module for each core tensor and factor matrix to enhance the training responsiveness in critical regions. The object identification results in the CIFAR10 experiment showed that QLTD achieved a compression ratio of 35.43×, with less than 1% loss in accuracy and a compression ratio of 90.61×, with less than a 2% loss in accuracy. QLTD was able to achieve a significant compression ratio in terms of the parameter count and realize a good balance between compressing parameters and maintaining identification accuracy.

Underdetermined blind source separation based on third‐order cumulant and tensor compression

AbstractA method for Underdetermined Blind Source Separation is proposed using third‐order cumulants and tensor compression. To effectively suppress symmetrical distributed noise, the third‐order cumulant is considered. Additionally, the complexity of high‐dimensional tensors can be reduced through high order singular value decomposition (HOSVD) for compression purposes. The method begins by calculating the third‐order cumulant tensor for whitening signals at different time delays, and then stacks several cumulants into a fourth‐order tensor. The HOSVD decomposition is applied to the fourth‐order tensor, compressing the high‐dimensional tensor into a low‐dimensional core tensor. Next, the core tensor is further decomposed using the canonical polyadic decomposition, and the resulting factor matrices are fused to obtain an estimation of the mixed matrix. Finally, leveraging the signal independence, a matrix diagonalisation method is employed to recover the source signals. Theoretical analysis and simulation results demonstrate that the proposed method effectively suppresses the influence of Gaussian noise, reduces computational complexity, and saves computational time. Moreover, compared with five representative approaches, the proposed method achieves superior separation results. Specifically, for the 3 × 4 mixed model with a signal‐to‐noise ratio of 20 dB, the average relative error of speech signal and radio signal are −11.02 and −6.8 dB respectively.

Temporal pattern-aware QoS prediction by Biased Non-negative Tucker Factorization of tensors

Dynamic quality of service (QoS) data contain rich temporal patterns of user-service interactions, which are vital for better understanding user behaviors and service conditions. Canonical polyadic (CP)-based latent factorization model has proven to be capable of capturing such patterns. However, it models the relations among latent features of user, service and time in a rigid and unnatural way, causing its failures in capturing the complex patterns when the target QoS data become massive. To address that issue, this paper proposes a Biased Non-negative Tucker Factorization of 3D tensors (BNTucF) model with the four-fold ideas: (1) utilizing a core tensor for modeling the complex interactions among latent features; (2) incorporating linear biases into the model for accurate descriptions on QoS fluctuation; (3) constraining the model to be non-negative for describing QoS non-negativity; (4) deducing a single latent factor-dependent, multiplicative updating scheme for training the model in an efficient density-oriented way. Empirical studies demonstrate that the proposed BNTucF can learn complex dynamic user-service interaction patterns more accurately, hence achieving accurate predictions on missing QoS data.

CuFasterTucker: A Stochastic Optimization Strategy for Parallel Sparse FastTucker Decomposition on GPU Platform

The amount of scientific data is currently growing at an unprecedented pace, with tensors being a common form of data that display high-order, high-dimensional, and sparse features. While tensor-based analysis methods are effective, the vast increase in data size has made processing the original tensor infeasible. Tensor decomposition offers a solution by decomposing the tensor into multiple low-rank matrices or tensors that can be efficiently utilized by tensor-based analysis methods. One such algorithm is the Tucker decomposition, which decomposes an N -order tensor into N low-rank factor matrices and a low-rank core tensor. However, many Tucker decomposition techniques generate large intermediate variables and require significant computational resources, rendering them inadequate for processing high-order and high-dimensional tensors. This paper introduces FasterTucker decomposition, a novel approach to tensor decomposition that builds on the FastTucker decomposition, a variant of the Tucker decomposition. We propose an efficient parallel FasterTucker decomposition algorithm, called cuFasterTucker, designed to run on a GPU platform. Our algorithm has low storage and computational requirements and provides an effective solution for high-order and high-dimensional sparse tensor decomposition. Compared to state-of-the-art algorithms, our approach achieves a speedup of approximately 7 to 23 times.

Semi-parametric tensor factor analysis by iteratively projected singular value decomposition

Abstract This paper introduces a general framework of Semi-parametric TEnsor Factor Analysis (STEFA) that focuses on the methodology and theory of low-rank tensor decomposition with auxiliary covariates. Semi-parametric TEnsor Factor Analysis models extend tensor factor models by incorporating auxiliary covariates in the loading matrices. We propose an algorithm of iteratively projected singular value decomposition (IP-SVD) for the semi-parametric estimation. It iteratively projects tensor data onto the linear space spanned by the basis functions of covariates and applies singular value decomposition on matricized tensors over each mode. We establish the convergence rates of the loading matrices and the core tensor factor. The theoretical results only require a sub-exponential noise distribution, which is weaker than the assumption of sub-Gaussian tail of noise in the literature. Compared with the Tucker decomposition, IP-SVD yields more accurate estimators with a faster convergence rate. Besides estimation, we propose several prediction methods with new covariates based on the STEFA model. On both synthetic and real tensor data, we demonstrate the efficacy of the STEFA model and the IP-SVD algorithm on both the estimation and prediction tasks.

MvTuckER: Multi-view knowledge graphs representation learning based on tensor tucker model

Recently, more and more multi-view knowledge graphs with various important attributes are being constructed and applied, such as temporal information, geolocation, commonsense knowledge, multi-language and multi-modal. Knowledge graphs (KGs) have been widely applied in question answering systems, drug discovery, information retrieval, and so on. Knowledge graph representation learning (KGRL) is emerging as the most effective approach to tasks such as knowledge graph completion, entity alignment, knowledge reasoning and knowledge query. However, most previous work on KGs and KGRL are mainly designed for traditional KGs and only consider single-view, and the KGRL methods for special multi-view KGs faces the challenges of lacking a unified framework, insufficient interactive information and underutilizing important attributes. To bridge this gap, in this paper, we proposes a multi-view knowledge graphs (e.g., temporal KGs) representation learning method based on tensor tucker model (MvTuckER), which models the multi-view KGs from tuples to a nth-order binary tensor, and adopts the tensor n-mode product to capture complete interaction between and within different views. We also introduce low-rank and sparse approximations of core tensors to balance expressivity and complexity of MvTuckER. Moreover, we theoretically illustrate that our model is fully expressive for modeling multi-view KGs, discuss the working mechanism of MvTuckER from the perspective of logical operation, and explain how to migrate and extend our method to other types of views. We conducted extensive experiments on three multi-view knowledge graphs, and obtain 4.7%, 2.7%, and 5.3% effective improvement in Hit@1 respectively, which proves that the proposed MvTuckER can achieve state-of-the-art performance.

Neural Network Compression Based on Tensor Ring Decomposition.

Deep neural networks (DNNs) have made great breakthroughs and seen applications in many domains. However, the incomparable accuracy of DNNs is achieved with the cost of considerable memory consumption and high computational complexity, which restricts their deployment on conventional desktops and portable devices. To address this issue, low-rank factorization, which decomposes the neural network parameters into smaller sized matrices or tensors, has emerged as a promising technique for network compression. In this article, we propose leveraging the emerging tensor ring (TR) factorization to compress the neural network. We investigate the impact of both parameter tensor reshaping and TR decomposition (TRD) on the total number of compressed parameters. To achieve the maximal parameter compression, we propose an algorithm based on prime factorization that simultaneously identifies the optimal tensor reshaping and TRD. In addition, we discover that different execution orders of the core tensors result in varying computational complexities. To identify the optimal execution order, we construct a novel tree structure. Based on this structure, we propose a top-to-bottom splitting algorithm to schedule the execution of core tensors, thereby minimizing computational complexity. We have performed extensive experiments using three kinds of neural networks with three different datasets. The experimental results demonstrate that, compared with the three state-of-the-art algorithms for low-rank factorization, our algorithm can achieve better performance with much lower memory consumption and lower computational complexity.

Bayesian tensor-on-tensor regression with efficient computation.

We propose a Bayesian tensor-on-tensor regression approach to predict a multidimensional array (tensor) of arbitrary dimensions from another tensor of arbitrary dimensions, building upon the Tucker decomposition of the regression coefficient tensor. Traditional tensor regression methods making use of the Tucker decomposition either assume the dimension of the core tensor to be known or estimate it via cross-validation or some model selection criteria. However, no existing method can simultaneously estimate the model dimension (the dimension of the core tensor) and other model parameters. To fill this gap, we develop an efficient Markov Chain Monte Carlo (MCMC) algorithm to estimate both the model dimension and parameters for posterior inference. Besides the MCMC sampler, we also develop an ultra-fast optimization-based computing algorithm wherein the maximum a posteriori estimators for parameters are computed, and the model dimension is optimized via a simulated annealing algorithm. The proposed Bayesian framework provides a natural way for uncertainty quantification. Through extensive simulation studies, we evaluate the proposed Bayesian tensor-on-tensor regression model and show its superior performance compared to alternative methods. We also demonstrate its practical effectiveness by applying it to two real-world datasets, including facial imaging data and 3D motion data.

Deep Factor Learning for Accurate Brain Neuroimaging Data Analysis on Discrimination for Structural MRI and Functional MRI.

Analysis of neuroimaging data (e.g., Magnetic Resonance Imaging, structural and functional MRI) plays an important role in monitoring brain dynamics and probing brain structures. Neuroimaging data are multi-featured and non-linear by nature, and it is a natural way to organise these data as tensors prior to performing automated analyses such as discrimination of neurological disorders like Parkinson's Disease (PD) and Attention Deficit and Hyperactivity Disorder (ADHD). However, the existing approaches are often subject to performance bottlenecks (e.g., conventional feature extraction and deep learning based feature construction), as these can lose the structural information that correlates multiple data dimensions or/and demands excessive empirical and application-specific settings. This study proposes a Deep Factor Learning model on a Hilbert Basis tensor (namely, HB-DFL) to automatically derive latent low-dimensional and concise factors of tensors. This is achieved through the application of multiple Convolutional Neural Networks (CNNs) in a non-linear manner along all possible dimensions with no assumed a priori knowledge. HB-DFL leverages the Hilbert basis tensor to enhance the stability of the solution by regularizing the core tensor to allow any component in a certain domain to interact with any component in the other dimensions. The final multi-domain features are handled through another multi-branch CNN to achieve reliable classification, exemplified here using MRI discrimination as a typical case. A case study of MRI discrimination has been performed on public MRI datasets for discrimination of PD and ADHD. Results indicate that 1) HB-DFL outperforms the counterparts in terms of FIT, mSIR and stability (mSC and umSC) of factor learning; 2) HB-DFL identifies PD and ADHD with an accuracy significantly higher than state-of-the-art methods do. Overall, HB-DFL has significant potentials for neuroimaging data analysis applications with its stability of automatic construction of structural features.

Non-negative Tucker decomposition with graph regularization and smooth constraint for clustering

Non-negative Tucker decomposition (NTD) and its graph regularized extensions are the most popular techniques for representing high-dimensional non-negative data, which are typically found in a low-dimensional sub-manifold of ambient space, from a geometric perspective. Therefore, the performance of the graph-based NTD methods relies heavily on the low-dimensional representation of the original data. However, most existing approaches treat the last factor matrix in NTD as a low-dimensional representation of the original data. This treatment leads to the loss of the original data’s multi-linear structure in the low-dimensional subspace. To remedy this defect, we propose a novel graph regularized Lp smooth NTD (GSNTD) method for high-dimensional data representation by incorporating graph regularization and an Lp smoothing constraint into NTD. The new graph regularization term constructed by the product of the core tensor and the last factor matrix in NTD, and it is used to uncover hidden semantics while maintaining the intrinsic multi-linear geometric structure of the data. The addition of the Lp smoothing constraint to NTD may produce a more accurate and smoother solution to the optimization problem. The update rules and the convergence of the GSNTD method are proposed. In addition, a randomized variant of the GSNTD algorithm based on fiber sampling is proposed. Finally, the experimental results on four standard image databases show that the proposed method and its randomized variant have better performance than some other state-of-the-art graph-based regularization methods for image clustering.

Hybrid model of tensor sparse representation and total variation regularization for image denoising

The method based on non-local self-similarity patches has been widely applied in image denoising. For a given image patch, there are similar image patches at neighbor windows in the image. Traditionally, similar patches are vectorized and then rearranged into a matrix, which should have a low rank. Hence the denoising problem can be reformulated into a low rank recovery problem. However, the vectorization process can disrupt the spatial relationships among the patches. To improve this drawback, we rearrange the similar patches into a tensor to keep the spatial relationships. When the higher-order singular value decomposition (HOSVD) is applied to this tensor, the resulting core tensor should be sparse. In this paper, the sparse property of the core tensor is utilized to characterize similar patches, and then an optimization model is derived. Since the commonly used l0 norm regularization is NP-hard, we adopt the MCP function to constrain the sparse property of the core tensor. In addition, a total variation (TV) regularization term for the tensor is added to the model to preserve structural information in the image such as edges. Using the dual form to represent the total variation regularization and transforming the original problem into a saddle point problem, the primal–dual algorithm is applied to overcome the non-differentiability of the TV regularization. Finally, experimental results demonstrate that compared to existing denoising methods, the method proposed can better preserve details and structural information in the image.

Heterogeneous Regularization-Based Tensor Subspace Clustering for Hyperspectral Band Selection.

Band selection (BS) reduces effectively the spectral dimension of a hyperspectral image (HSI) by selecting relatively few representative bands, which allows efficient processing in subsequent tasks. Existing unsupervised BS methods based on subspace clustering are built on matrix-based models, where each band is reshaped as a vector. They encode the correlation of data only in the spectral mode (dimension) and neglect strong correlations between different modes, i.e., spatial modes and spectral mode. Another issue is that the subspace representation of bands is performed in the raw data space, where the dimension is often excessively high, resulting in a less efficient and less robust performance. To address these issues, in this article, we propose a tensor-based subspace clustering model for hyperspectral BS. Our model is developed on the well-known Tucker decomposition. The three factor matrices and a core tensor in our model encode jointly the multimode correlations of HSI, avoiding effectively to destroy the tensor structure and information loss. In addition, we propose well-motivated heterogeneous regularizations (HRs) on the factor matrices by taking into account the important local and global properties of HSI along three dimensions, which facilitates the learning of the intrinsic cluster structure of bands in the low-dimensional subspaces. Instead of learning the correlations of bands in the original domain, a common way for the matrix-based models, our model learns naturally the band correlations in a low-dimensional latent feature space, which is derived by the projections of two factor matrices associated with spatial dimensions, leading to a computationally efficient model. More importantly, the latent feature space is learned in a unified framework. We also develop an efficient algorithm to solve the resulting model. Experimental results on benchmark datasets demonstrate that our model yields improved performance compared to the state-of-the-art.

Fast autoregressive tensor decomposition for online real-time traffic flow prediction

Online real-time traffic flow prediction typically offers better real-time performance than offline prediction. However, existing studies rarely discussed online real-time traffic flow prediction and the balance between prediction accuracy and computational costs. Training and predicting traffic flow data with complex patterns by artificial intelligence models is usually time-consuming. Some high-accuracy statistical learning methods also reach a performance bottleneck in terms of computational speed. Therefore, a Fast Autoregressive Tensor Decomposition (FATD) algorithm is proposed for online real-time traffic flow prediction. First, the historical tensor data is decomposed by Tucker Decomposition into factor matrices and easy-to-compute core tensors, and these core tensors are modeled by Tensor Seasonal Autoregressive Integrated Moving Average (Tensor SARIMA). Second, a future core tensor is predicted by Tensor SARIMA. By the Inverse Tucker Decomposition, the traffic flow data to be predicted is recovered. The experimental results show that the FATD algorithm can reduce the computational cost while maintaining high accuracy. Compared with baselines, the FATD algorithm reduces MAE, RMSE, and the computational cost by approximately 35.04%, 26.86%, and 99.28% on average, respectively.