Tensor Completion through Total Variationwith Initialization from Weighted HOSVD

In our paper, we have studied the tensor completion problem when the sampling pattern is deterministic. We first propose a simple but efficient weighted HOSVD algorithm for recovery from noisy observations. Then we use the weighted HOSVD result as an initialization for the total variation. We have proved the accuracy of the weighted HOSVD algorithm from theoretical and numerical perspectives. In the numerical simulation parts, we also showed that by using the proposed initialization, the total variation algorithm can efficiently fill the missing data for images and videos.Comment: 8 pages, 6 figures, ITA 202

Semi-supervised Learning with Missing Values Imputation

Incomplete instances with various missing attributes in many real-world applications have brought challenges to the classification tasks. Missing values imputation methods are often employed to replace the missing values with substitute values. However, this process often separates the imputation and classification, which may lead to inferior performance since label information are often ignored during imputation. Moreover, traditional methods may rely on improper assumptions to initialize the missing values, whereas the unreliability of such initialization might lead to inferior performance. To address these problems, a novel semi-supervised conditional normalizing flow (SSCFlow) is proposed in this paper. SSCFlow explicitly utilizes the label information to facilitate the imputation and classification simultaneously by estimating the conditional distribution of incomplete instances with a novel semi-supervised normalizing flow. Moreover, SSCFlow treats the initialized missing values as corrupted initial imputation and iteratively reconstructs their latent representations with an overcomplete denoising autoencoder to approximate their true conditional distribution. Experiments on real-world datasets demonstrate the robustness and effectiveness of the proposed algorithm