Cluster Analysis for High-Dimensional and Multi-Source Data

高维多源数据聚类分析

• 批准号: 2013905
• 负责人: Jia Li
• 金额: $ 22.5万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-08-01 至 2023-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2013905&HistoricalAwards=false
• 关键词: Cluster; Analysis; Dimensional; Multi; Source

Rapid technology advances in devices and computer systems continue to grow our capacity to collect and store data. Clustering is often the first stage analysis performed to discover patterns, gain insights, and extract knowledge from massive amount of data routinely faced in science, engineering, and commercial domains. For instance, in biomedical studies, clustering is used to reveal pathological subgroups and help researchers form new hypothesis for in-depth investigation. It is thus imperative to develop new clustering methods to meet the ever-increasing challenges of data with high complexity, huge volume, and from distributed sources. In this project, novel statistical and optimization-based approaches and software packages will be developed to address these challenges. Graduate students will be trained to conduct research at the forefront of machine learning. The research results will be used to enrich courses and outreach educational materials in data science. A prominent statistical paradigm for clustering is based on mixture models, which is objective, parsimonious, not biased for known clusters, and has a probabilistic framework that can be extended and interpreted in standard ways. For high-dimensional large-scale data, existing mixture-model based methods have fundamental limitations. Furthermore, a big data environment can require the integration of clustering results at distributed sites, a problem called multi-source clustering. This research will advance cluster analysis from multiple aspects. First, hidden Markov model on variable blocks (HMM-VB), a special Gaussian mixture model (GMM), is developed to tackle high dimensionality. The estimation of HMM-VB will be enhanced by computationally efficient methods to identify the latent variable block structure and by mixture factor analyzers. Second, leveraging the latent states of HMM-VB, a new variable selection approach will be developed for clustering high-dimensional data. Third, the emerging topic of multi-source clustering will be studied. New methods based on optimal transport and Wasserstein barycenter will be developed for aggregating clustering results from multiple sources. Applications in biomedical areas will be pursued.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.

设备和计算机系统技术的快速进步不断增强我们收集和存储数据的能力。聚类通常是为发现模式、获得见解并从科学、工程和商业领域中经常面临的大量数据中提取知识而执行的第一阶段分析。例如，在生物医学研究中，聚类用于揭示病理亚组并帮助研究人员形成新的假设以进行深入研究。 因此，迫切需要开发新的聚类方法来应对高复杂性、海量、分布式数据日益增长的挑战。在该项目中，将开发新的基于统计和优化的方法和软件包来应对这些挑战。研究生将接受培训以在机器学习的前沿进行研究。研究结果将用于丰富数据科学的课程和推广教育材料。聚类的一个突出的统计范式是基于混合模型，它是客观的、简约的、不偏向于已知的聚类，并且具有可以以标准方式扩展和解释的概率框架。对于高维大规模数据，现有的基于混合模型的方法具有根本的局限性。此外，大数据环境可能需要集成分布式站点的聚类结果，这个问题称为多源聚类。本研究将从多个方面推进聚类分析。首先，开发了可变块隐马尔可夫模型（HMM-VB），这是一种特殊的高斯混合模型（GMM），用于解决高维问题。 HMM-VB 的估计将通过计算有效的方法来识别潜在变量块结构和混合因子分析器来增强。其次，利用 HMM-VB 的潜在状态，将开发一种新的变量选择方法来聚类高维数据。第三，将研究多源聚类这一新兴课题。将开发基于最优传输和 Wasserstein 重心的新方法，用于聚合来自多个来源的聚类结果。将寻求生物医学领域的应用。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Multisource Single-Cell Data Integration by MAW Barycenter for Gaussian Mixture Models

MAW Barycenter 用于高斯混合模型的多源单细胞数据集成

• DOI: 10.1111/biom.13630
• 发表时间: 2022
• 期刊: Biometrics
• 影响因子: 1.9
• 作者: Lin, Lin;Shi, Wei;Ye, Jianbo;Li, Jia
• 通讯作者: Li, Jia

Optimal Transport With Relaxed Marginal Constraints

放宽边际约束的最佳运输

• DOI: 10.1109/access.2021.3072613
• 发表时间: 2021
• 期刊: IEEE Access
• 影响因子: 3.9
• 作者: Li, Jia;Lin, Lin
• 通讯作者: Lin, Lin

VtNet: A neural network with variable importance assessment

• DOI: 10.1002/sta4.325
• 发表时间: 2020-10
• 期刊: Stat
• 影响因子: 1.7
• 作者: Lixiang Zhang;Lin Lin-Lin;Jia Li

Robust deep neural network surrogate models with uncertainty quantification via adversarial training

• DOI: 10.1002/sam.11610
• 发表时间: 2023-01
• 期刊: Statistical Analysis and Data Mining: The ASA Data Science Journal
• 作者: Lixiang Zhang;Jia Li

Mixture of Linear Models Co-supervised by Deep Neural Networks

• DOI: 10.1080/10618600.2022.2107533
• 发表时间: 2021-08
• 期刊: Journal of Computational and Graphical Statistics
• 影响因子: 2.4
• 作者: Beomseok Seo;Lin Lin-Lin;Jia Li