CAREER: Advancing Shape Learning for Biosciences

直接从图像数据中了解生物结构(蛋白质、细胞、器官)的健康和病理形状对于理解它们在活体中的作用至关重要。它对人类健康和社会的影响范围从我们对癌症的理解到神经退行性疾病的诊断。这份职业建议书将评估和开发可靠的形状分析方法，这些方法可以利用最近的生物成像数据爆炸，促进我们对生命基本规则的理解，并使数据驱动的生物医学取得突破。与研究活动紧密结合，教育和推广的目标是通过面向高中生的新颖艺术科学表演、用于形状分析的几何机器学习的开创性课程、研究生培训和面向广大受众的免费社区推广讲座，吸引不同的受众参与形状分析和生物科学。尽管形状分析领域取得了令人印象深刻的进展，但由于计算和统计方面的障碍，它被阻止部署到生物科学中。这带来了与结果解释相关的挑战，不一致的分析有可能将科学结论推向错误的方向--对于一个最终研究人类健康的学科来说，这是一个严重的缺陷。在数学中，(生物)形状可以表示为关键点的形状、曲线的形状或曲面的形状。关联的形状数据空间表示了非欧氏流形的常见抽象几何结构。这个项目将利用这些共性来建立一个一致的数值框架，以系统地和详尽地评估机器学习算法在形状空间上可能存在的不一致。特别是，它将提供对非欧氏流形上的测地线和多项式回归模型的深入研究。这些发现将被用于一项先导性研究，该研究将可靠地提取活体迁移细胞形态动力学的生物学相关参数。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Understanding the healthy and pathological shapes of biological structures (proteins, cells, organs) directly from image data is critical to understand their roles in living organisms. The impact for human health and society range from our understanding of cancers to the diagnosis of neurodegenerative diseases. This CAREER proposal will evaluate and develop reliable shape analysis methods that can harness the recent bio-imaging data explosion, advance our understanding of the fundamental rules of life, and enable breakthroughs in data-driven biomedicine. Tightly integrated with the research activities, the education and outreach objective is to engage diverse audiences in shape analysis and bioscience through novel art-science performances for high-school students, pioneering courses on geometric machine learning for shape analysis, training of graduate students, and free community outreach lectures for the wide audience.Despite impressive advances in the field of shape analysis, its deployment to biosciences is prohibited by computational and statistical hurdles. This yields challenges related to the interpretation of results, where inconsistent analyses bear the danger of driving scientific conclusions in the wrong direction —a serious drawback for a discipline that ultimately researches human health. In mathematics, (biological) shapes can be represented as shapes of key points, shapes of curves, or shapes of surfaces. The associated shape data spaces present common abstract geometric structures of non-Euclidean manifolds. This project will utilize these commonalities to establish a consistent numerical framework to systematically and exhaustively evaluate the possible inconsistencies of machine learning algorithms on shape spaces. In particular, it will provide a deep dive into the geodesic and polynomial regression models on non-Euclidean manifolds. The findings will be leveraged into a pilot study that will reliably extract biologically relevant parameters on the morphodynamics of cells migrating in vivo.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.