7 papers
Manifold Fitting: A Review of Methods and Applications
Zhigang Yao, Jiaji Su
With data growing in scale and complexity, traditional linear dimension reduction techniques are becoming inadequate in some settings. Manifold fitting offers an important alternat…
Routine Blood Biomarkers Reveal a Preclinical Continuum of Multiple Myeloma Risk
Bingjie Li, Jiadai Xu, Yiqing Sun +4
Multiple myeloma (MM) is preceded by a long preclinical phase spanning decades, yet scalable, non-specialist tools to identify individuals at elevated risk before end-organ damage…
Estimation of Riemannian Quantities from Noisy Data via Density Derivatives
Junhao Chen, Ruowei Li, Zhigang Yao
We study the recovery of geometric structure from data generated by convolving the uniform measure on a smooth compact submanifold with ambient Gaussian nois…
Principal Decomposition with Nested Submanifolds
Jiaji Su, Zhigang Yao
Over the past decades, the increasing dimensionality of data has increased the need for effective data decomposition methods. Existing approaches, however, often rely on linear mod…
Beyond Missing Data: Questionnaire Uncertainty Responses as Early Digital Biomarkers of Cognitive Decline and Neurodegenerative Diseases
Yukun Lu, Bingjie Li, Zhigang Yao
Identifying preclinical biomarkers of neurodegenerative diseases remains a major challenge in aging research. In this study, we demonstrate that frequent "Don't know/can't remember…
Distinguishing Calabi-Yau Topology using Machine Learning
Yang-Hui He, Zhi-Gang Yao, Shing-Tung Yau
While the earliest applications of AI methodologies to pure mathematics and theoretical physics began with the study of Hodge numbers of Calabi-Yau manifolds, the topology type of…