Project idea about clustering and sentences similarity

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I have a current project of put sentences embeddings into clusters. I already have my embeddings and some clusters associated to a part of my sentences dataset.

My goal is to use sentence similarity to my embeddings in order to apply a cluster to each of my sentence.

I have in mind to use K nearest neighbours algorithm to label each of my sentence with a cluster. But I am not sure if it would work efficiently.

What do you think of this approach ? Should I consider another method ?

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