{"version":1,"type":"rich","provider_name":"Libsyn","provider_url":"https:\/\/www.libsyn.com","height":90,"width":600,"title":"MLG 032 Cartesian Similarity Metrics","description":" Try a walking desk to stay healthy while you study or work! Show notes at&amp;nbsp;ocdevel.com\/mlg\/32. L1\/L2 norm, Manhattan, Euclidean, cosine distances, dot product    Normed distances&amp;nbsp;link  A norm is a function that assigns a strictly positive length to each vector in a vector space.&amp;nbsp;link Minkowski is generalized.&amp;nbsp;p_root(sum(xi-yi)^p). &quot;p&quot; = ? (1, 2, ..) for below. L1: Manhattan\/city-block\/taxicab.&amp;nbsp;abs(x2-x1)+abs(y2-y1). Grid-like distance (triangle legs). Preferred for high-dim space. L2: Euclidean.&amp;nbsp;sqrt((x2-x1)^2+(y2-y1)^2.&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;nbsp;link. Dot product: inner product on a finite dimensional Euclidean space&amp;nbsp;link  Cosine (normalized dot)   ","author_name":"Machine Learning Guide","author_url":"https:\/\/ocdevel.com\/mlg","html":"<iframe title=\"Libsyn Player\" style=\"border: none\" src=\"\/\/html5-player.libsyn.com\/embed\/episode\/id\/16722518\/height\/90\/theme\/custom\/thumbnail\/yes\/direction\/forward\/render-playlist\/no\/custom-color\/88AA3C\/\" height=\"90\" width=\"600\" scrolling=\"no\"  allowfullscreen webkitallowfullscreen mozallowfullscreen oallowfullscreen msallowfullscreen><\/iframe>","thumbnail_url":"https:\/\/assets.libsyn.com\/secure\/item\/16722518"}