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User-defined keyword spotting is a task to detect new spoken terms defined by users. This can be viewed as a few-shot learning problem since it is unreasonable for users to define their desired keywords by providing many examples. To solve this problem, previous works try to incorporate self-supervised learning models or apply meta-learning algorithms. But it is unclear whether self-supervised learning and meta-learning are complementary and which combination of the two types of approaches is most effective for few-shot keyword discovery. In this work, we systematically study these questions by utilizing various self-supervised learning models and combining them with a wide variety of meta-learning algorithms. Our result shows that HuBERT combined with Matching network achieves the best result and is robust to the changes of few-shot examples.