Do you have any idea about why the author define the target distribution in such a format?

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Hi, do you have any idea about why the author define the target distribution in such a format?

The author defined the target distribution because it can 1) improve cluster purity, 2) put more emphasis on data points assigned with high confidence, and 3) normalize the loss contribution of each centroid to prevent large clusters from distorting the hidden feature space.

But I feel confused about why such a definition can achieve the above goals? I would be extremely grateful if you could give me an answer.