CIF: Small: Info-Clustering: An Information-Theoretic Framework for Data Clustering

聚类是指将相似的对象分组在一起，同时将不相似的对象分开的过程。这个简单的想法在不同的科学研究领域有着广泛的应用。从数学的角度来看，聚类问题是非常独特的，因为它试图发现未知的数据模式，而没有明确的基础知识。而不是跳到一个特定的算法或数据集（这是在文献中的常见做法），这项研究的目的是奠定一个严格的理论基础，在此基础上，许多有意义的和实际的实现可以随后开发。这项研究是伴随着调查员的持续努力，在课程开发，涉及本科生和研究生的研究，并扩大妇女和代表性不足的少数民族在engineering.To实现上述目标的参与，调查员计划采取信息论的观点的数据聚类问题，通过建模每个对象被聚类为一条信息。这种信息论观点的一个关键优势是，现在多个对象之间的相似性可以通过共享信息的数量来自然地测量。这正是信息论在70多年积极研究的积累下最有用的地方。本研究的主要议程是了解：1）什么聚类算法可以从所提出的信息聚类框架，利用大量的文献多元依赖建模，包括图形模型和参数家庭; 2）是否可以利用所提出的信息聚类框架，以取得一些进展的长期开放的问题，子集特征选择在统计和机器学习。

Clustering refers to a procedure that groups similar objects together while separating dissimilar ones apart. This simple idea has a wide range of applications in different areas of scientific research. From the mathematical viewpoint, the problem of clustering is quite unique in that it attempts to discover unknown patterns of data without a clear knowledge of the ground truth. Instead of jumping to a specific algorithm or a dataset (which is a common practice in the literature), this research aims to lay a rigorous theoretical ground, upon which many meaningful and practical implementations can be developed subsequently. This research is accompanied by the investigator's continuing effort in curriculum development, involving undergraduate and graduate students in research, and broadening the participation of women and underrepresented minorities in engineering.To achieve the aforementioned goal, the investigator plans to take an information-theoretic view of the data clustering problem by modeling each object to be clustered as a piece of information. A key advantage of this information-theoretic view is that now the similarity among multiple objects can be naturally measured by the amount of shared information. This is precisely where information theory, with the accumulation of over 70 years of active research, can be most useful. The main agendas of this research are to understand: 1) what clustering algorithms can be derived from the proposed info-clustering framework by leveraging the large body of literature on multivariate dependency modeling including graphical models and parameter families; 2) whether the proposed info-clustering framework can be leveraged to make some progress on the long-standing open problem of subset feature selection in statistics and machine learning.