Reasoning about perceptual systems

知识发现和数据挖掘的大多数方法都假设观察到的数据之外的参数，例如 先验概率、置信函数或统计分布，其来源并不总是清楚或合理的。另一方面，有定性或“非侵入性”的时间/空间数据分析方法（如粗糙集或概念格），只考虑给定的数据，没有严格的额外模型假设。使用更少的模型假设可以提高通用性、更广泛的适用性、更少的脱离背景，并减少成本和时间。 我的研究的主要目的是调查的代数和逻辑方面的定性推理 方法，并通过统计和信息理论工具补充这种推理，使其能够 作为时间/空间数据分析的可靠工具。我将集中在一个特定的应用领域，即定性的时间和空间推理，目的是描述感知系统的行为。使用最优粗糙四叉树（ORQT）作为基本表示-以及ORQT在时间和空间上的多个实例-可以确定复杂的时间/空间特征，以仅假设一些结构机制来“动态”设置对象定义。使用这个基本框架，我的目标是描述不变的属性，如“对象”，“接触”，“接近”或“时间接触”在一个严格的逻辑/代数数据模型。

Most methods of knowledge-discovery and data mining assume parameters outside the observed data such as prior probabilities, belief functions or statistical distributions, the origin of which is not always clear or justifiable. On the other hand, there are qualitative or "non-invasive" methods of temporal/spatial data analysis (such as rough sets or concept lattices) that take into account only the given data without stringent additional model assumptions. Using fewer model assumptions results in more generality, wider applicability, less de-contextualization, and reduced costs and time. The main aim of my research is the investigation of the algebraic and logical aspects of qualitative reasoning methods and to supplement such reasoning by statistical and information theoretic tools that enable it to function as a reliable tool of temporal/spatial data analysis. I will concentrate on a specific application area, namely, qualitative temporal und spatial reasoning with the aim to describe the behavior of perceptual systems. Using optimal Rough-Quadtrees (ORQT) as the basic representation - and multiple instances of ORQTs in time and space - it is possible to determine complex temporal/spatial features to set up an object definition "on the fly" assuming a few structural mechanisms only. Using this basic framework I will aim to describe invariant properties like ''objects'', ''contact'', ''approaching'' or ''time-to-contact'' in terms of a rigid logical/algebraical data model.