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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,
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