What is the mathematical objective of UMAP (Uniform Manifold Approximation and Projection)?

Machine Learning Hard

Machine Learning — Hard

What is the mathematical objective of UMAP (Uniform Manifold Approximation and Projection)?

Key points

  • UMAP minimizes cross-entropy between high-dimensional and low-dimensional fuzzy set representations
  • UMAP constructs a high-dimensional fuzzy topological graph from the data
  • Optimization is done using stochastic gradient descent
  • The objective is to find low-dimensional embeddings that best represent the data
  • UMAP does not assume linear relationships like PCA

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