Abstract Recommendation systems have been effectively utilized in various fields, but their internal decision-making methods are still largely unknown. This opaque decision-making method can greatly affect users’ trust in the recommendation system. Therefore, finding a way to explain the reasons for model decisions has become an urgent task. Previous studies often used LSTM and other models to generate recommendation explanations and explain the reasons for recommendations in text form. However, traditional methods cannot effectively use the ID information of users and items, and the text generated is highly repetitive. To solve this problem, this paper uses the method of prompt learning combined with a graph encoder to design a recommendation explanation generation model. In order to narrow the semantic gap between the ID information of users and items and natural language and capture high-level interaction information, this paper designs a graph encoder based on user similarity to learn the interactive semantic information of user and item IDs, and to construct a continuous prompt. Then, the discrete prompt composed of discrete features of users and items is combined with the continuous prompt to construct a hybrid prompt to input into the pre-trained model to generate the recommended explanation. This paper experiments on three publicly available datasets and compares them with several state-of-the-art methods to demonstrate the personalization and text quality of the generated explanations.

Accurate traffic flow prediction is of great importance in Intelligent Transportation System (ITS) for improving traffic efficiency, reducing congestion and so on. However, due to the complex spatial and temporal dependencies, achieving the accurate prediction is challenging. Traditional attention-based networks for traffic flow prediction typically use sine and cosine functions to do position encoding, which fail to capture the spatial and temporal dependencies and do not contain the graph structure information. In this paper, we propose a novel model named Spatial-Temporal Graph ATtention networks (STGAT), which leverages structure-aware self-attention mechanism to predict future traffic flow. The model introduces temporal multi-head self-attention modules, and designs spatial multi-head graph self-attention modules with structure-aware graph filters to extract more temporal and spatial information. Besides, our model adopts temporal and spatial position embedding layers to capture the spatial-temporal dependencies in traffic flow data. Experimental results show that STGAT shows better prediction performance than the state-of-art models on three real-world datasets PEMS04, PEMS07 and PEMS08. For example, we observe up to 10.38% improvement in terms of Mean Absolute Percentage Error (MAPE) compared with the well-known model ASTGNN.

The rank- ($L, L, 1,1$) block term decomposition (BTD) with spatial orthonormality (BTD-O) applied to 4-way multi-subject fMRI data achieves good performance due to preserving higher spatial structure and reducing crosstalk between components. However, the high rank$L$value (e.g., 35) of BTD-O for fMRI data leads to high computation complexity. Moreover, multi-subject fMRI data contains high noise nature. Although an accelerated BTD-O (accBTD-O) was proposed, it showed similar performance to BTD-O. Inspired by the compression, smoothing, and spatial structure invariance features of the pooling scheme, we respectively propose weighted spatial 3D and 2D pooling preprocessing for BTD-O of fMRI data. These two methods give higher weight to meaningful in-brain voxels and reduce the size and noise of fMRI data. Specifically, weighted spatial 3D pooling compresses weighted 3D brain images of a 5-way fMRI tensor, then transforms pooled 5-way fMRI tensor into a 4-way fMRI tensor. In contrast, for weighted spatial 2D pooling, the 5-way weighted fMRI data is first transformed into a 4-way tensor, and then 2D brain images of 4-way fMRI tensor are compressed by 2D pooling. The pooled 4-way fMRI tensor is separated by BTD-O to extract shared spatial maps, shared time courses, and subject intensities. Results of simulated and experimental fMRI data analyses both demonstrate that these two proposed methods achieve obviously better task-related component than compared methods. Moreover, the proposed 3D pooling is about 2.243 times faster than accBTD-O.

Independence and sparsity are proved to be two basic features for spatial activations of functional magnetic resonance imaging (fMRI) data, and have shown efficiency in analysis of magnitude-only fMRI data. Since complex-valued fMRI data contains additional brain activity information beyond magnitude-only fMRI data, we propose to incorporate sparsity constraint into complex independent vector analysis (IVA) to take advantages of the two features in analyzing multi-subject complex-valued fMRI data. Specifically, we propose to improve a complex-valued IVA algorithm named AFIVA (adaptive fixed-point IVA) to add a phase sparsity constraint on spatial maps. Based on the cost function of AFIVA, we further implement the phase sparsity constraint using smoothed Lo norm, and utilize noncircularity of spatial maps as well in the second update of phase sparsity to extract meaningful activations. The results from experimental complex-valued fMRI datasets show that the proposed method yields higher accuracy than AFIV A in terms of true positive rates, confirming the advantage of sparsity in de-noising the independent spatial maps.

The decomposition of multi-subject fMRI data using rank-(L,L,1,1) block term decomposition (BTD) can preserve higher-way data structure and is more robust to noise effects by decomposing shared spatial maps (SMs) into a product of two rank-L loading matrices. However, since the number of whole-brain voxels is very large and rank L is larger than 1, the rank-(L,L,1,1) BTD requires high computation and memory. Therefore, we propose an accelerated rank-(L,L,1,1) BTD algorithm based upon the method of alternating least squares (ALS). We speed up updates of loading matrices by reducing fMRI data into subspaces, and add an orthonormality constraint on shared SMs to improve the performance. Moreover, we evaluate the rank-L effect on the proposed method for actual task-related fMRI data. The proposed method shows better performance when L=35. Meanwhile, experimental comparison results verify that the proposed method largely reduced (17.36 times) computation time compared to ALS while also providing satisfying separation performance.

Tucker decomposition can provide an intuitive summary to understand brain function by decomposing multi-subject fMRI data into a core tensor and multiple factor matrices, and was mostly used to extract functional connectivity patterns across time/subjects using orthogonality constraints. However, these algorithms are unsuitable for extracting common spatial and temporal patterns across subjects due to distinct characteristics such as high-level noise. Motivated by a successful application of Tucker decomposition to image denoising and the intrinsic sparsity of spatial activations in fMRI, we propose a low-rank Tucker-2 model with spatial sparsity constraint to analyze multi-subject fMRI data. More precisely, we propose to impose a sparsity constraint on spatial maps by using an$ \ell _{p} $norm (${0}< {p}\le {1}$), in addition to adding low-rank constraints on factor matrices via the Frobenius norm. We solve the constrained Tucker-2 model using alternating direction method of multipliers, and propose to update both sparsity and low-rank constrained spatial maps using half quadratic splitting. Moreover, we extract new spatial and temporal features in addition to subject-specific intensities from the core tensor, and use these features to classify multiple subjects. The results from both simulated and experimental fMRI data verify the improvement of the proposed method, compared with four related algorithms including robust Kronecker component analysis, Tucker decomposition with orthogonality constraints, canonical polyadic decomposition, and block term decomposition in extracting common spatial and temporal components across subjects. The spatial and temporal features extracted from the core tensor show promise for characterizing subjects within the same group of patients or healthy controls as well.

Tucker decomposition (TKD) has been utilized to identify functional connectivity patterns using processed fMRI data, but seldom focuses on originally acquired fMRI data. This study proposes to decompose multi-subject fMRI data in a natural three-way of voxel × time × subject via TKD. Different from existing tensor decomposition algorithms such as canonical polyadic decomposition (CPD) for extracting shared spatial maps (SMs), we propose to extract both shared and individual SMs by exploring spatial-temporal-subject relationship contained in the core tensor. We test the proposed method using multi-subject resting-state fMRI data with comparison to CPD for evaluating shared SMs and independent vector analysis (IVA) for assessing individual SMs under different model orders. The results show that the proposed method yields better and more robust shared SMs than CPD and more consistent individual SMs than IVA, indicating the potential of TKD in providing group and individual brain networks in a high-dimensional coupling way.

Canonical polyadic decomposition (CPD) of multi-subject complex-valued fMRI data can be used to provide spatially and temporally shared components among groups with both magnitude and phase information. However, the CPD model is not well formulated due to the large subject variability in the spatial and temporal modalities, as well as the high noise level in complexvalued fMRI data. Considering that the shift-invariant CPD can model temporal variability across subjects, we propose to further impose a phase sparsity constraint on the shared spatial maps to denoise the complex-valued components and to model the inter-subject spatial variability as well. More precisely, subject-specific time delays are first estimated for the complex-valued shared time courses in the framework of real-valued shift-invariant CPD. Source phase sparsity is then imposed on the complex-valued shared spatial maps. A smoothed ℓ0norm is specifically used to reduce voxels with large phase values after phase de-ambiguity based on the small phase characteristic of BOLD-related voxels. The results from both the simulated and experimental fMRI data demonstrate improvements of the proposed method over three complex-valued algorithms, namely, tensor-based spatial ICA, shift-invariant CPD and CPD without spatiotemporal constraints. When comparing with a real-valued algorithm combining shiftinvariant CPD and ICA, the proposed method detects 178.7% more contiguous task-related activations.

Magnitude-only resting-state fMRI data have been largely investigated via independent component analysis (ICA) for exacting spatial maps (SMs) and time courses. However, the native complex-valued fMRI data have rarely been studied. Motivated by the significant improvements achieved by ICA of complex-valued task fMRI data than magnitude-only task fMRI data, we present an efficient method for de-noising SM estimates which makes full use of complex-valued resting-state fMRI data. Our two main contributions include: (1) The first application of a post-ICA phase de-noising method, originally proposed for task fMRI data, to resting-state data, which recognizes voxels within a specific phase range as desired voxels. (2) A new phase range detection strategy for a specific SM component based on correlation with its reference. We continuously change the phase range within a larger range, and compute a set of correlation coefficients between each de-noised SM and its reference. The phase range with the maximal correlation determines the final selection. The detected results by the proposed approach confirm the correctness of the post-ICA phase de-noising method in the analysis of resting-state complex-valued fMRI data.

Independent vector analysis (IVA) has exhibited great potential for the group analysis of magnitude-only fMRI data, but has rarely been applied to native complex-valued fMRI data. We propose an adaptive fixed-point IVA algorithm by taking into account the extremely noisy nature, large variability of the source component vector (SCV) distribution, and non-circularity of the complex-valued fMRI data. The multivariate generalized Gaussian distribution (MGGD) is exploited to match the SCV distribution based on nonlinearity, the shape parameter of MGGD is estimated using maximum likelihood estimation, and the nonlinearity is updated in the dominant SCV subspace to achieve denoising goal. In addition, the pseudo-covariance matrix is incorporated into the algorithm to represent the non-circularity. Experimental results from simulated and actual fMRI data demonstrate significant improvements of our algorithm over a complex-valued IVA-G algorithm and several circular and noncircular fixed-point IVA variants.