Structured Tensor Approximation under Kronecker Graph and Its Application on Hydrological Data
Grant-in-Aid for Early-Career Scientists
Basic Section 61030:Intelligent informatics-related
|Institute of Physical and Chemical Research
Li Chao 国立研究開発法人理化学研究所, 革新知能統合研究センター, 研究員 (10869837)
|Project Period (FY)
2020-04-01 – 2022-03-31
Completed (Fiscal Year 2021)
|Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2021: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2020: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
|tensor network / Tensor network / Machine learning / time series forecasting / Tensor Learning / complex graph
|Outline of Research at the Start
Tensor decomposition (TD) is becoming a promising tool in various fields. However, how to exploit the inherent graphical structure of the data is not widely explored. To this end, we plan to develop new TD methods based on the Kronecker structure of the large-scale complex graph. In addition, we will generalize the existing theoretical studies such that the new theory can guide us to analyse the performance of the methods. Finally, we will apply the new methods to the task of hydrological data restoration, which is of importance for the subsequent prediction and analysis tasks.
|Outline of Final Research Achievements
Tensor models have been widely applied to resolving extremely high-dimensional tasks in various fields. However, there remain many unexplored problems for tensors, particularly for tensor network structure search (TN-SS) and the analysis of the tensor learning dynamics (TLD). In this project, we conduct a thorough investigation of the preceding issues. For TN-SS, we found that the optimal tensor network structure can be obtained by sampling-based algorithms, for which we propose two efficient sampling schemes with theoretical analysis of the search space. For analyzing TLD in time series forecasting, our study reveals the relationship between the models’ memory mechanism and the tensor orders. We also propose a new forecasting method called the fractional tensor recurrent unit (fTRU), which can maximize the benefit of the long-memory effect by tensors. Extensive experimental results on real-world data demonstrate the usefulness of the methods studied in the project.
|Academic Significance and Societal Importance of the Research Achievements
Tensor is a promising framework, which tightly bonds many scientific fields for the human society. The results of the project reveal how the tensor structures impact its behavior in machine learning and practically provides methods to maximize the performance in real-world applications.
Report (3 results)
Research Products (17 results)