Frameworks for efficient and accurate data processing often rely on a suitable representation of measurements that capture phenomena of interest. Typically, such representations are high-dimensional vectors obtained by a transformation of raw sensor signals such as time-frequency transform, lag-map, etc. In this work, we focus on representation learning approaches that consider the measurements as the nodes of a weighted graph, with edge weights computed by a given kernel. If the kernel is chosen properly, the eigenvectors of the resulting graph affinity matrix provide suitable representation coordinates for the measurements. Consequently, tasks such as regression, classification, and filtering, can be done more efficiently than in the original domain of the data. In this paper, we address the problem of representation learning from measurements, which besides the phenomenon of interest contain undesired sources of variability. We propose data-driven kernels to learn representations that accurately parametrize the phenomenon of interest, while reducing variations due to other sources of variability. This is a non-linear filtering problem, which we approach under the assumption that certain geometric information about the undesired variables can be extracted from the measurements, e.g., using an auxiliary sensor. The applicability of the proposed kernels is demonstrated in toy problems and in a real signal processing task.

中文翻译：

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具有可变带宽指数核的非线性滤波

高效准确的数据处理框架通常依赖于捕获感兴趣现象的测量的合适表示。通常，此类表示是通过原始传感器信号（例如时频变换、滞后图等）的变换获得的高维向量。在这项工作中，我们专注于将测量值视为加权节点的表示学习方法。图，边权重由给定的内核计算。如果正确选择了内核，则生成的图亲和度矩阵的特征向量将为测量提供合适的表示坐标。因此，可以比在数据的原始域中更有效地完成回归、分类和过滤等任务。在本文中，我们解决了从测量中学习表征的问题，除了感兴趣的现象之外，它还包含不希望的可变性来源。我们提出数据驱动的内核来学习精确参数化感兴趣的现象的表示，同时减少由于其他可变性来源引起的变化。这是一个非线性过滤问题，我们在假设可以从测量中提取有关不需要的变量的某些几何信息（例如，使用辅助传感器）来处理该问题。在玩具问题和实际信号处理任务中证明了所提出的内核的适用性。这是一个非线性过滤问题，我们在假设可以从测量中提取有关不需要的变量的某些几何信息（例如，使用辅助传感器）来处理该问题。在玩具问题和实际信号处理任务中证明了所提出的内核的适用性。这是一个非线性过滤问题，我们在假设可以从测量中提取有关不需要的变量的某些几何信息（例如，使用辅助传感器）来处理该问题。在玩具问题和实际信号处理任务中证明了所提出的内核的适用性。