Dimensionality reduction: methodology and applications

本研究的重点是复杂数据集的简单表示。感兴趣的三个具体问题是数据挖掘，找到实现特定结果的一系列行动(规划)，以及维护一个人的位置表示(本地化)。这项工作适用于许多领域，其中有意义的信息必须从非常大的和多变量的序列数据集中提取。在这些领域，在数据点采取的行动(例如，患者进行治疗)会对随后的观察产生直接影响。目标是找到一种表示法，其中的动作对应于简单的数学变换，如平移和旋转。

This research focuses on simple representations of complex data sets. Three specific problems of interest are data mining, finding a sequence of actions to achieve a particular outcome (planning), and maintaining a representation of one's location (localization). This work is applicable to numerous areas in which meaningful information must be extracted from extremely large and multivariate sequential data sets. In these domains, action taken at a data point (e.g. taking a treatment by a patient) has immediate effect on consequent observations. The goal is to find a representation in which the actions correspond to simple mathematical transformations such as translation and rotation.