Abstract Kernel methods are known to be effective to analyse complex objects by implicitly embedding them into some feature space. To interpret and analyse the obtained results, it is often required to restore in the input space the results obtained in the feature space, by using pre-image estimation methods. This work proposes a new closed-form pre-image estimation method for time series kernel analytics that consists of two steps. In the first step, a time warp function, driven by distance constraints in the feature space, is defined to embed time series in a metric space where analytics can be performed conveniently. In the second step, the time series pre-image estimation is cast as learning a linear (or a nonlinear) transformation that ensures a local isometry between the time series embedding space and the feature space. The proposed method is compared to the state of the art through three major tasks that require pre-image estimation: 1) time series averaging, 2) time series reconstruction and denoising and 3) time series representation learning. The extensive experiments conducted on 33 publicly-available datasets show the benefits of the pre-image estimation for time series kernel analytics.

中文翻译：

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通过图像前估计进行可解释的时间序列内核分析

摘要 众所周知，内核方法通过将复杂对象隐式嵌入某些特征空间来分析它们是有效的。为了解释和分析获得的结果，通常需要通过使用前像估计方法在输入空间中恢复特征空间中获得的结果。这项工作为时间序列内核分析提出了一种新的封闭形式的原像估计方法，该方法由两个步骤组成。在第一步中，由特征空间中的距离约束驱动的时间扭曲函数被定义为将时间序列嵌入到可以方便地执行分析的度量空间中。在第二步中，时间序列原像估计被转换为学习线性（或非线性）变换，以确保时间序列嵌入空间和特征空间之间的局部等距。通过需要预图像估计的三个主要任务将所提出的方法与现有技术进行比较：1) 时间序列平均，2) 时间序列重建和去噪以及 3) 时间序列表示学习。在 33 个公开可用的数据集上进行的大量实验显示了时间序列内核分析的前像估计的好处。