Beyond Low Rank: A Graph-Based Propagation Approach to Tensor Completion for Multi-Acquisition Scenarios

Tensor completion refers to the problem of recovering the missing, corrupted or unobserved entries in data represented by tensors. In this paper, we tackle the tensor completion problem in the scenario in which multiple tensor acquisitions are available and do so without placing constraints on the underlying tensor's rank. Whereas previous tensor completion work primarily focuses on low-rank completion methods, we propose a novel graph-based diffusion approach to the problem. Referred to as GraphProp, the method propagates observed entries around a graph-based representation of the tensor in order to recover the missing entries. A series of experiments have been performed to validate the presented approach, including a synthetically-generated tensor recovery experiment which shows that the method can be used to recover both low and high rank tensor entries. The successful tensor completion capabilities of the approach are also demonstrated on a real-world completion problem from the field of multispectral remote sensing completion. Using data acquired from the Landsat 7 platform, we synthetically obscure image sections in order to simulate the scenario in which image acquisitions overlap only partially. In these tests, we benchmark against alternative tensor completion approaches as well as existing graph signal recovery methods, demonstrating the superior reconstruction performance of our method versus the state of the art.

Enhancing ensemble learning and transfer learning in multimodal data analysis by adaptive dimensionality reduction

Modern data analytics take advantage of ensemble learning and transfer learning approaches to tackle some of the most relevant issues in data analysis, such as lack of labeled data to use to train the analysis models, sparsity of the information, and unbalanced distributions of the records. Nonetheless, when applied to multimodal datasets (i.e., datasets acquired by means of multiple sensing techniques or strategies), the state-of-theart methods for ensemble learning and transfer learning might show some limitations. In fact, in multimodal data analysis, not all observations would show the same level of reliability or information quality, nor an homogeneous distribution of errors and uncertainties. This condition might undermine the classic assumptions ensemble learning and transfer learning methods rely on. In this work, we propose an adaptive approach for dimensionality reduction to overcome this issue. By means of a graph theory-based approach, the most relevant features across variable size subsets of the considered datasets are identified. This information is then used to set-up ensemble learning and transfer learning architectures. We test our approach on multimodal datasets acquired in diverse research fields (remote sensing, brain-computer interfaces, photovoltaic energy). Experimental results show the validity and the robustness of our approach, able to outperform state-of-the-art techniques.