9 papers
Local Manifold Attention for Recovery and Generation of Rare 3D Human Poses
Feiyue Pan, Zhigang Yao
A rare 3D human pose in a motion sequence may reflect either a genuine movement or an estimation error, making correction difficult when reference databases contain few comparable…
Manifold Fitting by Successive Tangent-Space Projection
Yuqing Xia, Bingjie Li, Zhigang Yao
Manifold fitting seeks to recover the geometric structure underlying noisy ambient observations. We propose Successive Tangent Space Projection (STSP), an iterative manifold-fittin…
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…
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…
Beyond Missing Data: Questionnaire Response Uncertainty as an Early Digital Sign of Dementia-Related Vulnerability
Yukun Lu, Bingjie Li, Zhigang Yao +1
Explicit "Do not know" responses are treated as missing data, although their accumulation may encode uncertainty. We analysed 502,234 UK Biobank participants to test associations b…
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…
Enhanced High-Dimensional Data Visualization through Adaptive Multi-Scale Manifold Embedding
Tianhao Ni, Bingjie Li, Zhigang Yao
To address the dual challenges of the curse of dimensionality and the difficulty in separating intra-cluster and inter-cluster structures in high-dimensional manifold embedding, we…
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…
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…