Matrix Algorithms for Data Clustering and Nonlinear Dimension Reduction

本研究旨在探讨数据矩阵同时聚类的统计和计算方法及其扩展，以使用谱技术处理数据超立方体。它使用聚类分析技术，这是从大数据集中提取信息的方法。许多现有方法依赖于使用所有属性对数据对象进行聚类以进行相似性度量。但是，数据对象的自然分组通常不涉及所有属性。例如，在基因表达分析中，对于DNA芯片在各种条件下（组织类型、个体、外部刺激等）产生的数据，生物学上相关的基因不太可能在所有条件下都表现相似，也不可能在相关的一组条件下涉及所有基因。这个项目的重点是开发聚类算法，例如，可以找到在不同条件下行为相似的基因子集。该技术是基于谱方法的数据矩阵的同时聚类。所开发的结果、算法和技术将在生物信息学和文本分析应用中得到应用。研究的重点是识别数据矩阵中可以通过数据矩阵的谱信息恢复的聚类模式的类别。该研究探索了表征理想分组模式的各种目标函数，并开发了基于光谱信息的聚类隶属分配算法。该方法正在被扩展到多路数据超立方体的情况下，并探索聚类和降维的联系。

This research is to investigate statistical and computational methods for simultaneous clustering of data matrices and their extensions to handle data hypercubes using spectral techniques. It uses techniques of cluster analysis, which is method of extracting information from large data sets. Many existing methods rely on clustering the data objects using all the attributes for similarity measurement. However, often the natural groupings of the data objects do not involve all attributes. For example, in gene expression analysis, for data generated by DNA chips under various conditions (tissue types, individuals, external stimuli etc.), it is unlikely that biologically related genes will behave similarly across all conditions, nor related set of conditions will involve all the genes. The focus of this project is to develop clustering algorithms that can, for example, find subsets of genes that behave similarly across subsets of conditions. The techniques are based on spectral methods for simultaneous clustering of data matrices. The results, algorithms, and techniques developed will have applications in bioinformatics and text analysis applications.The focus of the research is on identifying classes of cluster patterns in a data matrix that can be recovered by the spectral information of the data matrix. The research explores various objective functions that characterize desirable grouping patterns, and develops algorithms for cluster membership assignment from the spectral information. The methodology is being extended to the case of multi-way data hypercubes and to exploring connection of clustering and dimension reduction.