Cluster Analysis for High-Dimensional and Multi-Source Data

设备和计算机系统的快速技术进步继续提高我们收集和存储数据的能力。聚类通常是第一阶段的分析，用于发现模式，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。例如，在生物医学研究中，聚类用于揭示病理亚组，帮助研究人员形成新的假设进行深入研究。 因此，迫切需要开发新的聚类方法，以满足日益增长的挑战，数据具有高复杂性，巨大的体积，并从分布式源。在本项目中，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，在机器学习的最前沿进行研究。研究成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例是基于混合模型，它是客观的，简约的，不偏向于已知的集群，并有一个概率框架，可以扩展和解释标准的方式。对于高维大规模数据，现有的基于混合模型的方法有根本的局限性。此外，大数据环境可能需要在分布式站点集成聚类结果，这是一个称为多源聚类的问题。本研究将从多个方面推进聚类分析。首先，可变块隐马尔可夫模型（HMM-VB），一种特殊的高斯混合模型（GMM），被开发用于解决高维问题。HMM-VB的估计将通过计算高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，一个新的变量选择方法将被开发用于聚类高维数据。第三，将研究新出现的多源聚类问题。基于最优运输和Wasserstein重心的新方法将被开发用于聚合来自多个源的聚类结果。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.