Overview
This study introduces a novel framework, Coupled Tensor-Tensor Completion (CTTC), designed to address tensor completion problems by incorporating side information in the form of tensors. Biomedical challenges, including drug repurposing, often involve multidimensional arrays (tensors) where observed entries are utilized to impute missing values. Existing tensor completion methods typically integrate side information as matrices. CTTC distinguishes itself by leveraging hidden connections among multimodal tensors to improve completion performance, specifically outperforming state-of-the-art methods in predicting drug effects.
Research Context
Many biomedical challenges are conceptualized as tensor completion problems. In these scenarios, the objective is to impute missing values within a multidimensional array by utilizing its observed entries. The incorporation of side information pertaining to the tensor's modes, such as gene-gene similarity, has been identified as a significant factor in enhancing the quality of solutions for these completion problems. Prior methodologies for tensor completion predominantly accommodate such side information when it is presented in a matrix format.
Approach
The CTTC framework was developed to integrate side information provided in a tensor format. This approach is founded on the principle of leveraging latent connections present within multimodal tensors. The theoretical underpinnings of CTTC are rooted in distance metric learning and group theory. To implement this framework, an alternating algorithm was derived to solve the associated optimization problem. This algorithm's convergence to a stationary point was established. The performance of CTTC was evaluated by comparing it against established tensor completion methods on benchmark datasets relevant to drug effect prediction.
Findings
CTTC demonstrated superior performance in predicting drug effects when compared with other tensor completion methods, specifically HaLRTC, CTRC, Cell, and NTDDR. This superiority was observed in both runtime efficiency and RSE (Root-Squared Error) tensor completion accuracy. The evaluation utilized two benchmark datasets: DTD and LINCS.
Potential Applications
The method's application in predicting drug effects suggests utility in drug repurposing. The capability to address biomedical challenges posed as tensor completion problems implies broader applicability where imputing missing values in multidimensional biomedical data is critical.