Dimensionality reduction: methodology and applications

这项研究的重点是复杂数据集的简单表示。三个具体的问题是数据挖掘，找到一系列的行动，以实现一个特定的结果（规划），并保持一个代表性的一个人的位置（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提取。在这些领域中，在数据点采取的行动（例如，患者接受治疗）对后续观察具有直接影响。我们的目标是找到一种表示，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.