Show notes at <a href="https://ocdevel.com/mlg/32">ocdevel.com/mlg/32</a>. 
L1/L2 norm, Manhattan, Euclidean, cosine distances, dot product
Normed distances <a href="https://medium.com/@kunal_gohrani/different-types-of-distance-metrics-used-in-machine-learning-e9928c5e26c7" rel="noopener" target="_blank">link</a>
<ul>
<li>A norm is a function that assigns a strictly positive length to each vector in a vector space. <a href="https://towardsdatascience.com/how-to-measure-distances-in-machine-learning-13a396aa34ce" rel="noopener" target="_blank">link</a></li>
<li>Minkowski is generalized. p_root(sum(xi-yi)^p). &#8220;p&#8221; = ? (1, 2, ..) for below.</li>
<li>L1: Manhattan/city-block/taxicab. abs(x2-x1)+abs(y2-y1). Grid-like distance (triangle legs). Preferred for high-dim space.</li>
<li>L2: Euclidean. sqrt((x2-x1)^2+(y2-y1)^2. sqrt(dot-product). Straight-line distance; min distance (Pythagorean triangle edge)</li>
<li>Others: Mahalanobis, Chebyshev (p=inf), etc</li>
</ul>
Dot product
<ul>
<li>A type of inner product. Outer-product: lies outside the involved planes. Inner-product: dot product lies inside the planes/axes involved <a href="https://www.quora.com/Whats-the-difference-between-inner-product-dot-product-and-scalar-product/answer/Urgunoon-Saleem" rel="noopener" target="_blank">link</a>. Dot product: inner product on a finite dimensional Euclidean space <a href="https://www.quora.com/Whats-the-difference-between-inner-product-dot-product-and-scalar-product/answer/Richard-Morris-34" rel="noopener" target="_blank">link</a></li>
</ul>
Cosine (normalized dot)

Tyler Renelle

MLG 032 Cartesian Similarity Metrics

Show notes at ocdevel.com/mlg/32. L1/L2 norm, Manhattan, Euclidean, cosine distances, dot product Normed distances link A norm is a function that assigns a strictly positive length to each vector in a vector space. link Minkowski is generalized. p_root(sum(xi-yi)^p). &#8220;p&#8221; = ? (1, 2, ..) for below. L1: Manhattan/city-block/taxicab. abs(x2-x1)+abs(y2-y1). Grid-like distance (triangle legs). Preferred for high-dim space. L2: Euclidean. sqrt((x2-x1)^2+(y2-y1)^2. sqrt(dot-product). [&hellip;]

Machine Learning Guide Episode #43

MLG 032 Cartesian Similarity Metrics