  Knowledge distillation has emerged as a highly effective method for bridging
the representation discrepancy between large-scale models and lightweight
models. Prevalent approaches involve leveraging appropriate metrics to minimize
the divergence or distance between the knowledge extracted from the teacher
model and the knowledge learned by the student model. Centered Kernel Alignment
(CKA) is widely used to measure representation similarity and has been applied
in several knowledge distillation methods. However, these methods are complex
and fail to uncover the essence of CKA, thus not answering the question of how
to use CKA to achieve simple and effective distillation properly. This paper
first provides a theoretical perspective to illustrate the effectiveness of
CKA, which decouples CKA to the upper bound of Maximum Mean Discrepancy~(MMD)
and a constant term. Drawing from this, we propose a novel Relation-Centered
Kernel Alignment~(RCKA) framework, which practically establishes a connection
between CKA and MMD. Furthermore, we dynamically customize the application of
CKA based on the characteristics of each task, with less computational source
yet comparable performance than the previous methods. The extensive experiments
on the CIFAR-100, ImageNet-1k, and MS-COCO demonstrate that our method achieves
state-of-the-art performance on almost all teacher-student pairs for image
classification and object detection, validating the effectiveness of our
approaches. Our code is available in https://github.com/Klayand/PCKA
