Tensor factorization for missing data imputation in medical questionnaires

Abstract

This paper presents innovative collaborative filtering techniques to complete missing data in repeated medical questionnaires. The proposed techniques are based on the canonical polyadic (CP) decomposition (a.k.a. PARAFAC). Besides the standard CP decomposition, also a normalized decomposition is utilized. As an illustration, systemic lupus erythematosus-specific quality-of-life questionnaire is considered. Measures such as normalized root mean square error, bias and variance are used to assess the performance of the proposed tensor-based methods in comparison with other widely used approaches, such as mean substitution, regression imputations and k-nearest neighbor estimation. The numerical results demonstrate that the proposed methods provide significant improvement in comparison to popular methods. The best results are obtained for the normalized decomposition.