主流形的弹性映射和弹性网及其在微阵列数据可视化中的应用
Elastic Maps and Nets for Approximating Principal Manifolds and Their Application to Microarray Data Visualization
摘要：
主流形被定义为通过数据分布“中间”的线或面。线性主流形（主成分分析）通常用于降维，噪声过滤和数据可视化。最近，提出了构造非线性主流形的方法，包括我们的弹性映射方法，该方法基于与弹性膜的物理类比。我们已经开发了一个通用的几何框架，用于构建各种尺寸和拓扑结构的“主要对象”，具有最简单的二次型的平滑度惩罚，允许非常有效的并行实现。我们的方法用三种编程语言（C++、Java和Delphi）实现，具有两个图形用户界面（VidaExpert http://bioinfo.curie.fr/projects/vidaexpert和ViMiDa http://bioinfo-out.curie.fr/projects/vimida应用程序）。在本文中，我们概述了弹性地图的方法，并详细介绍了它的主要应用之一：在生物信息学中的微阵列数据的可视化。我们表明，弹性映射的方法优于线性PCA的数据近似，点间距离结构的表示，保持局部点邻域和表示点类在低维空间。
英文摘要：
Principal manifolds are defined as lines or surfaces passing through ``the middle'' of data distribution. Linear principal manifolds (Principal Components Analysis) are routinely used for dimension reduction, noise filtering and data visualization. Recently, methods for constructing non-linear principal manifolds were proposed, including our elastic maps approach which is based on a physical analogy with elastic membranes. We have developed a general geometric framework for constructing ``principal objects'' of various dimensions and topologies with the simplest quadratic form of the smoothness penalty which allows very effective parallel implementations. Our approach is implemented in three programming languages (C++, Java and Delphi) with two graphical user interfaces (VidaExpert http://bioinfo.curie.fr/projects/vidaexpert and ViMiDa http://bioinfo-out.curie.fr/projects/vimida applications). In this paper we overview the method of elastic maps and present in detail one of its major applications: the visualization of microarray data in bioinformatics. We show that the method of elastic maps outperforms linear PCA in terms of data approximation, representation of between-point distance structure, preservation of local point neighborhood and representing point classes in low-dimensional spaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
