Geometric Data Analysis: An Empirical Approach to Dimensionality Reduction and the Study of Patterns
Geometric Data Analysis: An Empirical Approach to Dimensionality Reduction and the Study of Patterns
复制标题
DOI：
--
复制
发表时间：
2000-12
期刊：
影响因子：
--
通讯作者：
M. Kirby
中科院分区：
文献类型：
--
作者：
M. Kirby
来自出版商：从经验和几何角度分析大数据集数据缩减是一个快速新兴的领域，在收集和分析大数据集的所有领域都有广泛的应用。 《几何数据分析》是第一本专注于用几何方法解决这一问题的教科书，即开发和区分低维数据表示的子空间和子流形技术。了解所研究数据的几何性质被认为是确定适当的简化技术的关键。重点关注构建降维映射以揭示数据中的重要几何结构，精心构建的章节顺序可引导读者从主题的开始到当前研究活动的领域。本书对数学先决条件进行了详细且基本独立的介绍，以帮助来自不同背景的读者。几何数据分析中讨论的其他主题包括： *标量场和矢量场的 Karhunen-Loeve 过程，扩展到缺失数据、噪声数据和对称数据 *非线性方法，包括径向基函数 (RBF) 和反向传播神经网络 *小波和傅立叶分析作为数据缩减的分析方法 *对近期研究的广泛讨论，包括惠特尼缩减网络和作者共同开发的自适应基 *还有更多 这些方法是在许多方法的背景下开发的现实世界的应用涉及大量数据集，包括由数字成像系统和物理现象的计算机模拟生成的数据集。基于经验的表示有助于他们的调查并产生传统分析工具无法获得的见解。
From the Publisher: An analysis of large data sets from an empirical and geometric viewpoint Data reduction is a rapidly emerging field with broad applications in essentially all fields where large data sets are collected and analyzed. Geometric Data Analysis is the first textbook to focus on the geometric approach to this problem of developing and distinguishing subspace and submanifold techniques for low-dimensional data representation. Understanding the geometrical nature of the data under investigation is presented as the key to identifying a proper reduction technique. Focusing on the construction of dimensionality-reducing mappings to reveal important geometrical structure in the data, the sequence of chapters is carefully constructed to guide the reader from the beginnings of the subject to areas of current research activity. A detailed, and essentially self-contained, presentation of the mathematical prerequisites is included to aid readers from a broad variety of backgrounds. Other topics discussed in Geometric Data Analysis include: *The Karhunen-Loeve procedure for scalar and vector fields with extensions to missing data, noisy data, and data with symmetry *Nonlinear methods including radial basis functions (RBFs) and backpropa-gation neural networks *Wavelets and Fourier analysis as analytical methods for data reduction *Expansive discussion of recent research including the Whitney reduction network and adaptive bases codeveloped by the author *And much more The methods are developed within the context of many real-world applications involving massive data sets, including those generated by digital imaging systems and computer simulations of physical phenomena.Empirically based representations are shown to facilitate their investigation and yield insights that would otherwise elude conventional analytical tools.