Heuristic representation and effective reduction for large scaled and high dimensional information and its computational environments

讨论了大规模高维数据在信息可视化、数据约简和变量选择问题中的启发式表示方法和有效的计算算法。我们开发了一个基于Web的图形应用程序，它具有使用触摸屏上的手指手势的交互界面，可以用颜色表示多个变量的一部分的彩色人脸图，以及一个在关联分析中发现有用规则的交互工具。我们还研究了非线性主成分分析中的加速技术，将加速算法应用于计算代价较高的定性变量选择问题，提出了一种两阶段加速算法以提高估计的速度。我们证实了所有工具都能很好地用于启发式和直观的观测，并且我们提出的加速算法在数值实验中提供了良好的性能。

We discussed heuristic representation methods and effective computational algorithms for large scaled and high dimensional data in information visu- alization, data reduction, and variable selection problems. We developed a web-based graphics application which has an interactive interface using finger gestures on the touch-screen, a colored face graph which can represent a part of multiple variables by color, and an interactive tool to find useful rules in association analysis. We also studied accel- eration techniques in non-linear principal component analysis by applying an acceleration algorithm to qualitative variable selection problem which needs high computation cost and proposed a two-stage acceleration algorithm to get estimations more speedy. We confirmed that all tools work well for heuristic and intuitive observations and that our proposed ac- celeration algorithms provide good performances in numerical experiments.