基于矩阵模型的高维聚类边界模式发现

流形学习关注于寻找合适的嵌入方式将高维空间映射至低维空间，但映射子空间依然可能具有较高的维度，难以解决高维空间的数据挖掘任务.本文建立一种简单的矩阵模型判断数据点k近邻空间关于该点的对称性，并使用对称率进行边界提取，提出一种基于矩阵模型的高维聚类边界检测技术（Clustering boundary detection based on matrix model，MMC）.该模型构造简单、直接、易于理解和使用.理论分析以及在人工合成和真实数据集的实验结果表明MMC算法能够有效地检测出低维和高维空间的聚类边界.

Clustering Boundary Pattern Discovery for High Dimensional Space Base on Matrix Model

Manifold learning aims to find a reasonable embed mode to map a high-dimensional space to a low dimensional space. However, the dimension of the latter may still be so high that any data mining task cannot be effectively finished. This paper proposes a simple matrix model to judge the symmetry of data object and its k nearest neighbors space, and use the symmetry rate to extract the clustering boundary. Finally, the MMC algorithm is developed. Theoretical analysis and experimental results show that the MMC can effectively detect the clustering boundary of low and high dimensional spaces.