Coupled Tensor-Tensor Completion Method with Applications in Drug Repurposing

Many biomedical challenges can be posed as tensor completion problems where the observed entries of a multidimensional array (a tensor) are used to impute the missing values. In such settings, incorporating side information about the modes of the tensor, such as gene-gene similarity, can significantly enhance the solutions of the completion problem. Most existing tensor completion methods can only incorporate side information in the form of matrices. In this study, we introduce a novel framework to incorporate side information in the form of tensors. Our new approach, called Coupled Tensor-Tensor Completion (CTTC), leverages the hidden connections among multimodal tensors to improve tensor completion performance. In addition to practical utility, CTTC has theoretical foundations in distance metric learning and group theory. We derive an alternating algorithm to solve the CTTC optimization problem and establish its convergence to a stationary point. Finally, we show that CTTC outperforms state-of-the-art tensor completion methods at predicting drug effects. Results: Compared with other tensor completion methods, including HaLRTC, CTRC, Cell, and NTDDR, CTTC demonstrates superior run-time and RSE tensor completion accuracy on two benchmark datasets, DTD and LINCS.

Robust Low-Tubal-Rank Tensor Completion under Cross-Concentrated Sampling

Tensor cross-concentrated sampling (t-CCS) bridges entrywise sampling and t-CUR slice-wise sampling by observing entries only within selected horizontal and lateral slices. Existing t-CCS completion methods, however, assume that the observations are free of gross corruption. In this work, we study robust recovery of a third-order low-tubal-rank tensor from partial t-CCS observations contaminated by sparse, arbitrarily large outliers. We propose Robust Iterative t-CUR (R-ItCUR), a tensor-native algorithm that partitions the sampled tensor cross into two exterior blocks and an intersection block, applies adaptive blockwise Welsch correction for outlier suppression, and updates the low-rank component through projected blockwise gradient descent. By operating directly on the sampled cross, R-ItCUR avoids reconstructing the full tensor throughout the iterations, resulting in substantial memory and computational savings. Experiments on synthetic tensors, cardiac MRI data, and three-dimensional seismic data demonstrate accurate recovery and strong robustness to sparse gross corruptions. The results further highlight the importance of explicitly exploiting the cross-concentrated sampling structure in robust tensor completion.

Exponential-Family Tensor Completion via Nonconvex Dual Total-Variation Regularization

With the emergence of various tensor data, tensor completion from partial measurements has attracted widespread attention in data science and signal processing. Total Variation (TV) has been widely used as an effective regularization technique for tensor completion; however, theoretical studies on TV regularization in this context remain limited. In this work, we present a rigorous theoretical analysis of TV regularization for tensor completion. Specifically, we consider tensor completion under exponential-family noise, which generalizes the standard settings such as Gaussian and Poisson tensor completion. To handle exponential-family tensor completion, we propose a family of dual-TV (DTV) regularizers based on the transformed L1 function, which simultaneously capture sparsity and low-rank structures in the gradient tensor. Moreover, we establish the theoretical upper bounds on the recovery error of the proposed estimator. In certain cases, these upper bounds can attain the convergence order of $\mathcal{O}\big( n_3 r_t\big(\max_{k} s_k^2\big) \log\big((n_1+n_2)n_3\big) /n \big)$, and the minimax lower bound analysis is further presented to show that the upper-bounds can approach the lower bound with the gap of order $\mathcal{O}(\max_k s_k^2/max(n_1, n_2))$ up to a logarithmic factor. Finally, multiple groups of experiments on synthetic, image and video tensor data sets are conducted to support our theoretical results and demonstrate the effectiveness of our method.

Dual-Attention Convolution Experts for Sparse Tensor Completion

Tensor factorization (TF) has been widely adopted for high-dimensional sparse data completion tasks. Despite significant progress, neural TF methods often struggle to capture complex cross-mode interactions and remain vulnerable to (extreme) data sparsity. To address these challenges, we propose a novel neural tensor factorization approach, termed Dual-Attention Convolution Expert Networks with Group-Level Contrastive Learning (DCGC). For the first problem, DCGC generates diverse non-linear alignment patterns of latent factors via a multi-channel convolution network, and leverages the gated dual-attention mechanism to drive the model to focus on more important output channels (i.e., convolution experts) and the aligned features. Furthermore, DCGC introduces a group-level contrastive learning strategy that aggregates positive samples with identical feedback levels while separating negative samples across different levels. This strategy injects high-quality self-supervised signals to mitigate data sparsity. Extensive experiments conducted on five datasets demonstrate that our DCGC outperforms the state-of-the-art methods in sparse tensor completion for traffic and recommendation applications. Code to reproduce the experimental results in the paper is available at https://github.com/ku1z/DCGC.

Low-Rank Tensor Completion Based on Fractional Regularization with Ky Fan p-k Norm

This paper addresses low-rank tensor completion (LRTC) by proposing a novel nonconvex surrogate, namely the ratio of the tensor nuclear norm to the tensor Ky Fan p-k norm (TNPK), to accurately approximate the tensor tubal rank. The TNPK possesses appealing properties, including scale invariance, parameter flexibility, and the existence of closed-form solutions under specific choices of p and k. With specific parameter settings of p and k, it reduces to the ratio of the tensor nuclear norm to the tensor Ky Fan k norm (TNK) or the ratio of the tensor nuclear norm to the tensor Frobenius norm (TNF). We construct a LRTC model and, under the tensor null space property (NSP), prove that low-rank tensors are local minimizers of the proposed model. Moreover, we derive the proximal operator of the Ky Fan p-k inverse-norm and further develop an efficient alternating direction method of multipliers (ADMM) algorithm with guaranteed subsequential convergence under mild conditions. Extensive experiments on synthetic and real-world datasets validate the superior performance of our method against state-of-the-art competitors.

Robust Neural Tucker Factorization with Bias Correction and Adaptive Initialization

High-dimensional incomplete (HDI) tensors are widely used in traffic and climate applications, but sparse observations make accurate completion difficult. The intrinsic non-linear dynamics and non-stationary variations across distinct multi-modal fields severely hinder the efficacy of conventional linear reconstruction frameworks. Neural Tucker factorization provides an effective framework for modeling high-order interactions among tensor modes. By parameterizing underlying structural characteristics into continuous latent spaces, neural representations circumvent the rigid low-rank constraints of classical algebra. However, its performance can still be affected by implementation-level choices, especially parameter initialization and the bias configuration of the final output mapping. Suboptimal initializations frequently lead to variance explosion across the cubically expanded interaction spaces, driving the subsequent non-linear activation boundaries into severe gradient saturation zones, while the omission of a dedicated translation parameter forces interaction weights to implicitly absorb global statistical deviations. This paper proposes a simple yet effective neural Tucker factorization model with Kaiming initialization and bias correction (KaBiN) for HDI tensor completion. The proposed model utilizes Kaiming uniform initialization for the embedding and Tucker linear parameters, and adopts a simple bias correction in output mapping. By elegantly decoupling global mean shifts from local structural representations, the framework provides a highly stable and well-conditioned optimization landscape. Experiments on three real-world HDI tensor datasets show that KaBiN achieves better performance than the original NeuTucF, while introducing minimal computational overhead.