Distance | Pythagorean theorem | Length | Metric geometry
In mathematics, the Euclidean distance between two points in Euclidean space is the length of a line segment between the two points.It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, therefore occasionally being called the Pythagorean distance. These names come from the ancient Greek mathematicians Euclid and Pythagoras, although Euclid did not represent distances as numbers, and the connection from the Pythagorean theorem to distance calculation was not made until the 18th century. The distance between two objects that are not points is usually defined to be the smallest distance among pairs of points from the two objects. Formulas are known for computing distances between different types of objects, such as the distance from a point to a line. In advanced mathematics, the concept of distance has been generalized to abstract metric spaces, and other distances than Euclidean have been studied. In some applications in statistics and optimization, the square of the Euclidean distance is used instead of the distance itself. (Wikipedia).
Weird notions of "distance" || Intro to Metric Spaces
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From playlist Cool Math Series
k-NN 4: which distance function?
[http://bit.ly/k-NN] The nearest-neighbour algorithm is sensitive to the choice of distance function. Euclidean distance (L2) is a common choice, but it may lead to sub-optimal performance. We discuss Minkowski (p-norm) distance functions, which generalise the Euclidean distance, and can a
From playlist Nearest Neighbour Methods
Determine the distance between two points on a coordinate axis
👉 Learn how to find the distance between two points. The distance between two points is the length of the line joining the two points in the coordinate plane. To find the distance between two points in the coordinate plane, we make use of the formula d = sqrt((x2 - x1)^2 + (y2 - y1)^2). 👏
From playlist Find the Distance of the Line Segment
Example: Determine the Distance Between Two Points
This video shows an example of determining the length of a segment on the coordinate plane by using the distance formula. Complete Video List: http://www.mathispower4u.yolasite.com or http://www.mathispower4u.wordpress.com
From playlist Using the Distance Formula / Midpoint Formula
Find the distance between the two coordinate points ex 1
👉 Learn how to find the distance between two points. The distance between two points is the length of the line joining the two points in the coordinate plane. To find the distance between two points in the coordinate plane, we make use of the formula d = sqrt((x2 - x1)^2 + (y2 - y1)^2). 👏
From playlist Find the Distance of the Line Segment
Find the distance between two coordinate points ex1
👉 Learn how to find the distance between two points. The distance between two points is the length of the line joining the two points in the coordinate plane. To find the distance between two points in the coordinate plane, we make use of the formula d = sqrt((x2 - x1)^2 + (y2 - y1)^2). 👏
From playlist Find the Distance of the Line Segment
Using the distance formula to determine the distance between two coordinate points
👉 Learn how to find the distance between two points. The distance between two points is the length of the line joining the two points in the coordinate plane. To find the distance between two points in the coordinate plane, we make use of the formula d = sqrt((x2 - x1)^2 + (y2 - y1)^2). 👏
From playlist Find the Distance of the Line Segment
Find the distance between two coordinate points ex 2
👉 Learn how to find the distance between two points. The distance between two points is the length of the line joining the two points in the coordinate plane. To find the distance between two points in the coordinate plane, we make use of the formula d = sqrt((x2 - x1)^2 + (y2 - y1)^2). 👏
From playlist Find the Distance of the Line Segment
Every Distance in Data Science (Almost 100K Subs!)
0:00 Intro 2:19 Euclidean Distance 5:47 Manhattan Distance 9:14 Minkowski Distance 12:49 Chebyshev Distance 15:40 Cosine Distance 19:35 Hamming Distance 20:17 Haversine Distance Lasso Regression : https://www.youtube.com/watch?v=jbwSCwoT51M Curse of Dimensionality : https://www.youtube.c
From playlist Data Science Basics
CS224W: Machine Learning with Graphs | 2021 | Lecture 19.2 - Hyperbolic Graph Embeddings
For more information about Stanford’s Artificial Intelligence professional and graduate programs, visit: https://stanford.io/3Brc7vN Jure Leskovec Computer Science, PhD In previous lectures, we focused on graph representation learning in Euclidean embedding spaces. In this lecture, we in
From playlist Stanford CS224W: Machine Learning with Graphs
Data Science for Uncertainty Quantification
Chapter 3 of the book, covers mostly dimension reduction
From playlist Uncertainty Quantification
Anna Wienhard (7/29/22): Graph Embeddings in Symmetric Spaces
Abstract: Learning faithful graph representations has become a fundamental intermediary step in a wide range of machine learning applications. We propose the systematic use of symmetric spaces as embedding targets. We use Finsler metrics integrated in a Riemannian optimization scheme, that
From playlist Applied Geometry for Data Sciences 2022
11. Non-Euclidean Spaces: Closed Universes
MIT 8.286 The Early Universe, Fall 2013 View the complete course: http://ocw.mit.edu/8-286F13 Instructor: Alan Guth In this lecture, the professor reviewed Euclid's Postulates and talked about non-Euclidean geometry and a sphere in 4 Euclidean dimensions. License: Creative Commons BY-NC-
From playlist The Early Universe by Prof. Alan Guth
IGA: Rigidity of Riemannian embeddings of discrete metric spaces - Matan Eilat
Abstract: Let M be a complete, connected Riemannian surface and suppose that S is a discrete subset of M. What can we learn about M from the knowledge of all distances in the surface between pairs of points of S? We prove that if the distances in S correspond to the distances in a 2-dimens
From playlist Informal Geometric Analysis Seminar