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，同时将不同的对象分开的过程。这个简单的想法在不同的科学研究领域有着广泛的应用。从数学的观点来看，聚类问题是非常独特的，因为它试图在不清楚基本事实的情况下发现未知的数据模式。本研究的目的不是跳到特定的算法或数据集(这是文献中的常见做法)，而是奠定严格的理论基础，在此基础上可以开发许多有意义和实用的实现。这项研究伴随着调查者在课程开发方面的持续努力，让本科生和研究生参与研究，并扩大女性和未被充分代表的少数群体参与工程。为了实现上述目标，调查者计划从信息论的角度看待数据聚集问题，将每个对象建模为一条信息。这种信息论观点的一个关键优势是，现在可以通过共享信息量来自然地衡量多个对象之间的相似性。这正是经过70多年积极研究积累的信息论最有用的地方。本研究的主要目的是了解：1)利用包括图形模型和参数家族在内的多变量相关性建模的大量文献，可以从所提出的信息聚类框架中得到什么聚类算法；2)所提出的信息聚类框架是否可以用于解决统计学和机器学习中长期悬而未决的子集特征选择问题。

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.