Module 6: Dimensionality Reduction
  Lecture 32: Embedding
 

                                            

 

 

Embedding
  • Transformation from one space and distance function to another space (generally vector) and distance function (generally Euclidean)
  • Both nature of space and distance function are important
  • Example: Given a metric space with distance function with objects, embed into -dimensional vector space with distance function
 
 
  • Dimension of a point is dependent on
 
  • Distance-preserving
 
  • In general, not possible for other norms
 
  • Example
   
  • Original:
   
  • Embeddings:
   
  • Distance-preserving: