MLG 032 Cartesian Similarity Metrics

Machine Learning Guide

OCDevel

Artificial, Introduction, Learning, Courses, Technology, Ml, Intelligence, Ai, Machine, Education

4.9 • 848 Ratings

🗓️ 8 November 2020

⏱️ 42 minutes

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Summary

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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). "p" = ? (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). 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 link. Dot product: inner product on a finite dimensional Euclidean space link

Cosine (normalized dot)

Transcript

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0:00.0	Welcome back to Machine Learning Guide. I'm your host, Tyler Rinelli.
0:05.0	MLG teaches the fundamentals of machine learning and artificial intelligence.
0:09.0	It covers intuition, models, math, languages, frameworks, and more.
0:13.0	Where your other machine learning resources provide the trees, I provide the forest.
0:18.0	Visual is the best primary learning modality, but audio is a great supplement during exercise commute and chores.
0:25.6	Consider MLG your syllabus with highly curated resources for each episode's details at OCdevel.com forward slash MLG.
0:35.6	I'm also starting a new podcast which could use your support. It's called
0:39.9	Lefnear's Life Hacks and teaches productivity focused tips and tricks, some which could prove
0:45.5	beneficial in your machine learning education journey. Find that at Ocdevel.com forward slash
0:51.9	LLH. Today we're going to be talking about Cartesian similarity metrics or Cartesian distance metrics.
1:00.4	The key words here you might have heard in working with machine learning are things like Euclidean distance, Manhattan distance, L1 and L2 norms, cosine distance, and things like this.
1:13.1	So we'll break these all down in this episode.
1:15.6	But before we get into the details,
1:17.6	I want to break down two words here.
1:20.1	One word being Cartesian,
1:22.1	and the other being the distinction between similarity and distance.
1:26.1	So when I say Cartesian, I'm talking about the Cartesian coordinate system.
1:31.7	Renee Descartes, Cartesian, the invention of points in space and how they relate to each
1:36.8	other.
1:37.8	So the Cartesian coordinate system is exactly what you'd expect.
1:41.0	It's an x, y, axis plane, or it's an x, y an xyz in three dimensions and so on into infinity dimensions.
1:47.9	It's space where vectors represent points in space like stars in a galaxy and then you can compare vectors
	...

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