Collaborative Research: High-Dimensional Tensor Learning under Labeled-Data Scarcity

University Of Notre Dame, Notre Dame IN

Investigators

Abstract

This project harnesses the power of multi-dimensional tensor data to improve predictive accuracy and insights across crucial scientific and societal sectors through the development of advanced tensor classification techniques. Specifically, these techniques will facilitate early Alzheimer's diagnosis via sophisticated fMRI tensor analysis and improve the detection of anomalies in complex financial transactions. Despite the richness of tensor data, a significant barrier exists due to the scarcity of labeled instances, which are essential for effective statistical learning. These labels are often costly and labor-intensive to produce, particularly given the complex nature of tensor data. To address this challenge, the methods developed in the project will be optimized to perform robustly even with limited labeled data. By improving diagnostic tools and financial monitoring systems through enhanced tensor classification techniques, the project will support national health, economic security, and overall societal well-being. Moreover, it will promote interdisciplinary collaboration and educational growth, enhancing diversity in STEM fields and broadening participation across scientific and technological sectors. This initiative will not only drive scientific innovation but also serve national interests by improving public health, economic stability, and educating future scientists. This project will create computationally efficient and statistically optimal methods for tensor classification amidst the challenge of the scarcity of labeled data. The approach encompasses three innovative strategies: (i) employing low-rank discriminant tensors for high-dimensional tensor classification, (ii) utilizing abundant unlabeled tensor data for semi-supervised tensor learning, and (iii) adjusting for distributional differences between labeled and unlabeled data. The research team brings a strong theoretical foundation in tensor classification, supported by preliminary studies and experimental results. Collaborations with experts in biology, medical science, economics, computer science, and social science will facilitate the application of these new methods to a variety of pressing issues in these fields. This integrated approach is expected to yield significant advancements in tensor-based data analysis techniques, enhancing the capabilities and understanding across multiple disciplines. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.