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

本研究计画针对离散资料与连续资料之知识发现演算法之基础。基础的关键概念是闭集。我们开发了一个半监督算法的数据，同时具有离散属性和连续属性。将闭集方法应用于经济学中离散数据和连续数据的组合。 我们还开发了离散数据之间的新距离，连续数据的新伪距离，以及异常值的诊断方法。 我们还将二进制编码应用于图像检索。作为理论成果，我们发展了基于Gray码的计算学习理论，代数闭集的计算学习理论，快速更新由快速闭集构成的格的方法。

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.