支持向量机在函数型数据分类中的应用
Support vector machine for functional data classification
摘要：
在许多应用中，输入数据是在无限维空间中取值的采样函数，而不是标准向量。这一事实对数据分析算法产生了复杂的影响，从而促使它们进行修改。事实上，大多数用于回归、分类和聚类的传统数据分析工具已经适应了函数输入，其通用名称为函数数据分析（FDA）。在本文中，我们研究使用支持向量机（SVM）的功能数据分析，我们专注于曲线的歧视问题。支持向量机是一种基于核函数的高维空间隐式非线性映射的大间隔分类器。我们将展示如何定义简单的内核，考虑到数据的功能性质，并导致一致的分类。对真实世界数据进行的实验强调了考虑问题的某些功能方面的好处。
英文摘要：
In many applications, input data are sampled functions taking their values in infinite dimensional spaces rather than standard vectors. This fact has complex consequences on data analysis algorithms that motivate modifications of them. In fact most of the traditional data analysis tools for regression, classification and clustering have been adapted to functional inputs under the general name of functional Data Analysis (FDA). In this paper, we investigate the use of Support Vector Machines (SVMs) for functional data analysis and we focus on the problem of curves discrimination. SVMs are large margin classifier tools based on implicit non linear mappings of the considered data into high dimensional spaces thanks to kernels. We show how to define simple kernels that take into account the unctional nature of the data and lead to consistent classification. Experiments conducted on real world data emphasize the benefit of taking into account some functional aspects of the problems.
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