离散弹性内向量空间及其在时间序列挖掘中的应用
Discrete Elastic Inner Vector Spaces with Application in Time Series and Sequence Mining
摘要：
本文提出了一个框架，致力于建设我们所说的离散弹性内积，允许一个嵌入集的非均匀采样的多元时间序列或序列的长度变化到内积空间结构。该框架基于递归定义，该定义涵盖了多个嵌入式时间弹性维度的情况。我们证明，这样的内积存在于我们的一般框架，并显示如何一个简单的例子，这个内积类操作的一些潜在的应用程序，而推广的欧几里得内积。时间序列和符号序列数据集上的分类实验证明了将时间序列或序列嵌入到弹性内部空间而不是经典的欧几里得空间中所能带来的好处。这些实验显示出良好的准确性相比，欧几里德距离甚至动态规划算法，同时保持在开发阶段的线性算法的复杂性，虽然需要一个二次索引阶段预先。
英文摘要：
This paper proposes a framework dedicated to the construction of what we call discrete elastic inner product allowing one to embed sets of non-uniformly sampled multivariate time series or sequences of varying lengths into inner product space structures. This framework is based on a recursive definition that covers the case of multiple embedded time elastic dimensions. We prove that such inner products exist in our general framework and show how a simple instance of this inner product class operates on some prospective applications, while generalizing the Euclidean inner product. Classification experimentations on time series and symbolic sequences datasets demonstrate the benefits that we can expect by embedding time series or sequences into elastic inner spaces rather than into classical Euclidean spaces. These experiments show good accuracy when compared to the euclidean distance or even dynamic programming algorithms while maintaining a linear algorithmic complexity at exploitation stage, although a quadratic indexing phase beforehand is required.
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。
