Functional data analysis has become a research hotspot in the field of data mining. Traditional data mining methods regard functional data as a discrete and limited observation sequence, ignoring the continuity. In this paper, the functional data classification is addressed, proposing a functional generalized eigenvalue proximal support vector machine (FGEPSVM). Specifically, we find two nonparallel hyperplanes in function space, a positive functional hyperplane, and a functional negative hyperplane. The former is closest to the positive functional data and furthest from the negative functional data, while the latter has the opposite properties. By introducing the orthonormal basis, the problem in function space is transformed into the ones in vector space. It should be pointed out that the higher-order derivative information is applied from two aspects. We apply the derivatives alone or the weighted linear combination of the original function and the derivatives. It can be expected that to improve the classification accuracy by using more data information. Experiments on artificial datasets and benchmark datasets show the effectiveness of our FGEPSVM for functional data classification.

中文翻译：

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广义特征值近邻支持向量机的功能数据分类

功能数据分析已成为数据挖掘领域的研究热点。传统的数据挖掘方法将功能数据视为离散且有限的观察序列，而忽略了连续性。在本文中，解决了功能数据分类问题，提出了一种功能广义特征值近端支持向量机（FGEPSVM）。具体来说，我们在功能空间中找到两个非平行超平面，一个正功能超平面和一个功能负超平面。前者最接近正功能数据，而最远离负功能数据，而后者则具有相反的特性。通过引入正交标准，将函数空间中的问题转化为向量空间中的问题。应当指出，从两个方面应用了高阶导数信息。我们单独应用导数，或者应用原始函数和导数的加权线性组合。可以期望通过使用更多的数据信息来提高分类精度。在人工数据集和基准数据集上进行的实验表明，我们的FGEPSVM对于功能数据分类的有效性。