Information Repackaging via Multiresolution Transforms

这项研究将开发新的技术来描述大型天文数据集中的空间聚类。主要目标是一个新的边缘校正，带状双谱估计基于一个独特的思想组合：I)仔细分析并充分利用潜在的对称性，ii)纠正像素空间中窗口和噪声的对称性破坏，iii)使用启发式加权的边缘校正，近最优估计器，iv)使用快速分层计算算法v)使用正则化，分层（多分辨率）转换技术从像素空间估计器中恢复最优统计。数学、统计学、计算机科学和天文学的这种不同寻常的广泛协同作用，将在速度和映射空间集群的完整配置空间的能力上产生巨大飞跃。由此产生的技术是实用的，适用于其他统计和许多不同的大数据集。结果将反馈给新的高级统计课程，并将广泛传播。

AST-0434413SzapudiThis research will develop new techniques to characterize spatial clustering in large astronomical datasets. The principal goal is a new edge-corrected, banded bispectrum estimator based on a unique combination of ideas: i) carefully analyze and fully exploit the underlying symmetries, ii) correct for symmetry breaking by the window and noise in pixel space, iii) use edge corrected, nearly optimal estimators with heuristic weighting, iv) use fast, hierarchical computing algorithms v) use regularized, hierarchical (multi-resolution) transform techniques to recover the optimal statistics from pixel space estimators. This unusually broad synergy of mathematics, statistics, computer science, and astronomy will result in a quantum leap in speed and ability to map the full configuration space of spatial clustering. The resultant techniques are practical and applicable to other statistics and to many different large data sets. Results will feed back into a new advanced statistics class, and will be broadly disseminated.