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High-dimensional Vector Spaces

  • The queries “cholera” and “john snow” are far from each other in vector space.

  • How can the document “John Snow and Cholera” be close to both of them?

  • Our intuitions for 2- and 3-dimensional space don't work in >10,000 dimensions.

  • 3 dimensions: If a document is close to many queries, then some of these queries must be close to each other.

  • Doesn't hold for a high-dimensional space.

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