Data Mining Methods Based on Closed Sets for Data Which Are Combination of Discrete and Continuous Attributes

本研究项目旨在为离散数据和连续数据的知识发现算法奠定基础。基础的关键概念是闭合集合。对于既具有离散属性又具有连续属性的数据，我们提出了一种半监督算法。我们将闭集方法应用于经济学中离散数据和连续数据的组合。我们还提出了离散数据之间的新距离、连续数据的新伪距离和孤立点的诊断方法。我们还将二进制编码应用到图像检索中。作为理论结果，我们发展了一种基于格雷码的计算学习理论，这是一种代数闭集的计算学习理论，是一种快速更新由快速闭集形成的格的方法。

This research project is aiming at foundations of knowledge discovery algorithms for both discrete data and continuous data. The key concept of the foundations is closed set. We developed a semi-supervised algorithm for data which have both discrete attributes and continuous attributes. We applied the closed set method to combination of discrete data and continuous data from economics. We also developed new distances between discrete data, a new pseud-distance for continuous data, and a method diagnosis of outliers. We also applied binary coding to image retrieval. As theoretical results, we developed a computational learning theory based on Gray code, a computational learning theory of algebraic closed sets, a fast method of updating the lattice formed by fast closed sets.