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  <title>MLG 032 Cartesian Similarity Metrics</title>
  <description> Try a walking desk to stay healthy while you study or work! Show notes at&amp;amp;nbsp;ocdevel.com/mlg/32. L1/L2 norm, Manhattan, Euclidean, cosine distances, dot product    Normed distances&amp;amp;nbsp;link  A norm is a function that assigns a strictly positive length to each vector in a vector space.&amp;amp;nbsp;link Minkowski is generalized.&amp;amp;nbsp;p_root(sum(xi-yi)^p). &amp;quot;p&amp;quot; = ? (1, 2, ..) for below. L1: Manhattan/city-block/taxicab.&amp;amp;nbsp;abs(x2-x1)+abs(y2-y1). Grid-like distance (triangle legs). Preferred for high-dim space. L2: Euclidean.&amp;amp;nbsp;sqrt((x2-x1)^2+(y2-y1)^2.&amp;amp;nbsp;sqrt(dot-product). Straight-line distance; min distance (Pythagorean triangle edge) Others: Mahalanobis, Chebyshev (p=inf), etc  Dot product  A type of inner product. Outer-product: lies outside the involved planes. Inner-product: dot product lies inside the planes/axes involved&amp;amp;nbsp;link. Dot product: inner product on a finite dimensional Euclidean space&amp;amp;nbsp;link  Cosine (normalized dot)   </description>
  <author_name>Machine Learning Guide</author_name>
  <author_url>https://ocdevel.com/mlg</author_url>
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