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Jan 20, 2020 at 20:16 comment added Mathmath thank you for your answer and codes. While I've to still go through it in detail, I've upvoted it! But yes, I'd like to have a mathematical understanding of why the 'blobs' in the non-flat manifold in $\mathbb{R}^d$ would be mapped onto convex balls in $\mathbb{R}^k$ so that we're in a position to apply a distortion minimizing maps like k-means. You can either write out the detail or point me to a resource that discusses this in detail!
Jan 20, 2020 at 18:19 history answered Charles Pehlivanian CC BY-SA 4.0