Kernel methods play a critical role in many machine learning algorithms. They are useful in manifold learning, classification, clustering and other data analysis tasks. Setting the kernel’s scale parameter, also referred to as the kernel’s bandwidth, highly affects the performance of the task in hand. We propose to set a scale parameter that is tailored to one of two types of tasks: classification and manifold learning. For manifold learning, we seek a scale which is best at capturing the manifold’s intrinsic dimension. For classification, we propose three methods for estimating the scale, which optimize the classification results in different senses. The proposed frameworks are simulated on artificial and on real datasets. The results show a high correlation between optimal classification rates and the estimated scales. Finally, we demonstrate the approach on a seismic event classification task.

内核方法在许多机器学习算法中起着至关重要的作用。它们在流形学习、分类、聚类和其他数据分析任务中很有用。设置内核的规模参数，也称为内核的带宽，会极大地影响手头任务的性能。我们建议设置一个适合以下两种任务之一的尺度参数：分类和流形学习。对于流形学习，我们寻求一个最能捕捉流形内在维度的尺度。对于分类，我们提出了三种估计尺度的方法，它们在不同意义上优化了分类结果。所提出的框架在人工和真实数据集上进行了模拟。结果表明，最佳分类率和估计尺度之间存在高度相关性。最后，