流形上的空间模式分析及其在大脑发育研究中的应用

In this project, we propose a highly innovative interdisciplinary project on developing a novel computational framework for analyzing spatial patterns in manifold structures. Our work is motivated by a high-impact brain development study. In mammalian brains, neurons form various structures such columns, horizontal arrays, nuclei and strata. Understanding the formation of such structures from neural stem cells is critical in elucidating brain development process and functions as well as potential causes for neurological diseases. While currently a large amount of brain imaging data on the distribution of stem cells and neurons, there is a lack of computational framework for effectively characterizing such spatial patterns. Our project is designed to bridge this gap. Specifically, we will achieve our goal with three Sub-projects: .•.Sub-project 1: Develop spatial statistics for characterizing clustering of point processes in manifold..•.Sub-project 2: Detect point distribution patterns in manifold-like structures using sparse representation approach..•.Sub-project 3: Apply the spatial pattern discovery algorithms developed and implemented in Sub-projects 1 and 2 to multiple sets of mouse brain study data to identify patterns of neural stem cell development..The developed methods and algorithms will be tested extensively on both synthetic data and large brain imaging datasets with both statistical and knowledge-based measures to evaluate their accuracy and effectiveness. .Overall, our proposed project integrates machine learning, spatial statistics and brain science. The outcome will include a series of novel machine learning algorithms on discovering low-dimensional structures on manifolds and the application of these algorithms on real large brain study data will lead to high impact discoveries in brain development. Furthermore, this computational framework will contribute to many other fields such as machine learning, spatial statistics, computer vision, and pattern recognition as well as application areas such as biology, ecology, and geography.

哺乳动物的大脑神经元，会形成柱状、水平阵列、核和层等各种模式的空间结构。了解神经干细胞的这种结构的形成对阐明大脑发育过程和功能以及神经系统疾病的潜在原因是至关重要的。而目前有大量的干细胞和神经元的脑成像数据，但缺少有效的分析空间模式的计算框架。本课题中，我们创新的提出开发一种新的计算框架，来分析流形结构的空间模式，具体包括开发分析流形点聚类过程的空间统计，利用稀疏子空间聚类方法在类似流形的结构上检测点分布的模式，并将上述算法应用在老鼠大脑研究数据上识别神经干细胞发育的模式。开发的方法和算法将在合成数据和大脑成像数据集上用基于统计和知识的度量来评价算法的准确性和有效性。本课题融合了机器学习、空间统计和脑科学的研究，成果包括一系列创新的用于检测流形上的低维结构机器学习算法，并促进大脑发育研究的重大发现。此外该计算框架同样适用于生物、生态、地理等很多应用领域。

大脑是人体最复杂最神秘的器官。大脑的结构组织决定了其功能的水平，包括高级的认知过程，如感知、记忆、学习和决策等。先前的研究已经表明大脑中的神经元在结构上会形成一些特定的空间模式，如层、核或者功能性的柱状结构等。了解这些模式的发育和形成的机制对阐明大脑功能和辨别神经和发育方面疾病的潜在原因是至关重要的。目前有大量的干细胞和神经元的脑成像数据，但缺少有效的分析空间模式的计算框架 。针对这种情况，本课题中，我们开发了一种新的计算框架，来分析流形结构的空间模式，具体包括开发分析流形点聚类过程的空间统计，利用稀疏子空间聚类方法在类似流形的结构上检测点分布的模式。上述算法已经应用在老鼠大脑研究数据上识别神经干细胞发育的模式，相关论文已经发表在Nature Neuroscience, Neuron, Nature Communications等高影响因子的知名期刊上。本课题融合了机器学习、空间统计和脑科学的研究，通过对大脑模式的空间结构的分析研究，有助于促进大脑发育研究的重大发现。该计算框架同样适用于生物、生态、地理等其他应用领域。