Fractional signature: A generalisation of the signature inspired by fractional calculus

IF 0.7 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters Pub Date : 2025-08-18 DOI:10.1016/j.spl.2025.110533

José Manuel Corcuera, Rubén Jiménez

引用次数: 0

Abstract

In this paper, we propose a novel generalisation of the signature of a path, motivated by fractional calculus, which is able to describe the solutions of linear Caputo controlled FDEs. We also propose another generalisation of the signature, inspired by the previous one, but more convenient to use in machine learning. Finally, we test this last signature in a toy application to the problem of handwritten digit recognition, where significant improvements in accuracy rates are observed compared to those of the original signature.

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分数签名：由分数微积分启发的签名的推广

在本文中，我们提出了一种新的由分数阶微积分驱动的路径签名的推广，它能够描述线性Caputo控制的FDEs的解。我们还提出了签名的另一种推广，受前一种的启发，但更便于在机器学习中使用。最后，我们在一个玩具应用程序中测试了最后一个签名，以解决手写数字识别问题，与原始签名相比，准确率有了显着提高。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Statistics & Probability Letters 数学-统计学与概率论

CiteScore

1.60

自引率

0.00%

发文量

173

审稿时长

6 months

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