RUI: A Family of Versatile Mixture Models for Analyzing Mixed-Type Data with Asymmetry, Outliers, and Missing Values

RUI：一系列多功能混合模型，用于分析具有不对称性、离群值和缺失值的混合类型数据

• 批准号: 2209974
• 负责人: Cristina Tortora
• 金额: $ 15万
• 依托单位: San Jose State University Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-07-15 至 2025-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2209974&HistoricalAwards=false
• 关键词: RUI; Family; Versatile; Mixture; Models

Cluster analysis aims to discover patterns and homogeneity in the data. It reveals subgroups in a population of study, and it has applications in many fields. For example, in psychology, the clusters can be groups of patients that can benefit from a specific set of treatments. To apply cluster analysis to a data set, the data need to have some characteristics; for example, some techniques require the data to be continuous, and oftentimes they need pre-treatments. This project will develop a series of new clustering techniques that are suitable for challenging data sets without pre-treatments, such as those with high dimension, missing values, non-continuous variables, or with outliers. Novel statistical approaches and software packages will be produced and made available to general users. Undergraduate students will be directly involved in the research project, and together with graduate students, they will be trained to conduct research in data analysis. Many more students will be involved through class projects and the research outcomes will enrich the content of some of the offered courses. A widely used approach for cluster analysis is model-based clustering. It assumes that a population is a mixture of subpopulations, each of which can be represented by a density function. A variety of clustering methods and algorithms exist; however, they still have a series of limitations. Outliers and missing data can impact the clustering results, the high number of parameters makes the techniques not usable on high-dimensional data sets. Moreover, many algorithms assume continuous data; and they are not readily adaptable to handle discrete, binary, categorical, or a mixture of continuous and categorical data types. This is a major limitation because, in many fields such as medicine, biology, marketing, and many others, the data have all those characteristics. In this project, new clustering techniques based on non-Gaussian model-based clustering will be developed that will circumvent existing limitations on cluster shape, outliers, missing data, dimension, and data type of current methods. The novel methods will improve the flexibility in detecting skewed clusters and in obtaining robustness when dealing with outliers and missing data. Implicit and explicit dimension reduction techniques will be used for dimension reduction and latent class models will be adopted to deal with mixed-type data. The project will include a study on the indices to select the number of clusters and a thorough comparison with existing methods on real and simulated data will be undertaken, giving the users a guideline on which model to use based on the goal and challenges in their data.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.

聚类分析的目的是发现数据中的模式和同质性。它揭示了研究群体中的亚群，在许多领域都有应用。例如，在心理学中，集群可以是可以从一组特定治疗中受益的患者群体。要将聚类分析应用于数据集，数据需要具有一些特征;例如，某些技术要求数据是连续的，并且通常需要预处理。该项目将开发一系列新的聚类技术，适用于未经预处理的具有挑战性的数据集，例如高维，缺失值，非连续变量或离群值。将制作新的统计方法和软件包，并提供给一般用户。本科生将直接参与研究项目，并与研究生一起，他们将接受培训，进行数据分析研究。更多的学生将参与课堂项目，研究成果将丰富一些课程的内容。一种广泛使用的聚类分析方法是基于模型的聚类。它假设一个种群是一个子种群的混合体，每个子种群都可以用一个密度函数来表示。存在各种聚类方法和算法;然而，它们仍然具有一系列局限性。异常值和缺失数据会影响聚类结果，大量的参数使得该技术不能用于高维数据集。此外，许多算法假设连续数据;并且它们不容易适应于处理离散、二进制、分类或连续和分类数据类型的混合。这是一个主要的限制，因为在许多领域，如医学，生物学，市场营销和许多其他领域，数据具有所有这些特征。在这个项目中，将开发基于非高斯模型的聚类的新聚类技术，该技术将规避当前方法在聚类形状、离群值、缺失数据、维度和数据类型上的现有限制。新的方法将提高灵活性，在检测倾斜的集群，并在处理离群值和缺失数据时获得鲁棒性。将使用隐式和显式降维技术进行降维，并采用潜在类模型来处理混合类型数据。该项目将包括一项关于选择聚类数目的指数的研究，并将对真实的和模拟数据的现有方法进行彻底的比较，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进行评估，被认为值得支持的搜索.