Abstract: At present, effective visualization tools are needed urgently to understand the abundant multi-dimensional data in the science, engineering and commerce field. The traditional multi-dimensional data visualization based on dimension reduction is computation complexity and cannot offer the dimension distribution information of multi-dimensional object, so this paper proposes a new multi-dimensional visualization technique based on right regular polygon of even sides. The reference of the multi-dimensional data space—regular 2k polygon coordinates—in the Cartesian coordinates is defined; dimension reduction algorithm is used to the multi-dimensional object according to the optimization theory, using the minimum of the multi-dimensional object coordinates variation between in regular 2k polygon coordinates and in the multi-dimensional data space as criterion; they are rendered in the two-dimensional space using point cloud. The experiments show that the dimension reduction algorithm is highly efficient and easily implemented and adapts to the aggregation with a great amount of high dimensional data. The visualization method is easily understandable, and it can offer the dimension distribution information effectively and is helpful for common user to view the multi-dimensional data and discover the implicit information in knowledge discovery process, especially in the early stages of it, and has an important role in decision depending on the multi-dimensional data.

Key words: multi-dimensional data visualization, regular 2k polygon, dimension reduction, optimization

摘要： 当前，面对科学、工程和商业领域中海量的多维数据，用户迫切需要使用有效的可视化工具在知识发现、信息认知及信息决策过程中对其进行理解。针对传统基于降维映射的数据可视化方法计算复杂度高且无法提供维度分布信息的缺点，提出一种基于正2k边形的多维数据可视化方法RPES，通过建立多维数据空间的低维“参照物”——正2k边形坐标系，以减小多维对象在正2k边形坐标系及多维数据空间中的坐标差别为准则，使用最优化方法对其进行降维，以点云的形式标绘在低维可视空间中，完成多维数据的降维可视展现。实验证明，RPES的降维算法高效、容易实现，适用于数据量较大、维度较高的数据集，可视化结果不仅易于理解，而且能够有效提供维度分布信息，有利于用户发掘隐性知识，辅助其进行基于多维数据的决策。

关键词: 多维数据可视化, 正2k边形, 降维, 最优化