In mathematics and statistics, random projection is a technique used to reduce the dimensionality of a set of points which lie in Euclidean space. Random projection methods are known for their power, simplicity, and low error rates when compared to other methods. According to experimental results, random projection preserves distances well, but empirical results are sparse. They have been applied to many natural language tasks under the name random indexing. (Wikipedia).
Random Processes and Stationarity
http://AllSignalProcessing.com for more great signal-processing content: ad-free videos, concept/screenshot files, quizzes, MATLAB and data files. Introduction to describing random processes using first and second moments (mean and autocorrelation/autocovariance). Definition of a stationa
From playlist Random Signal Characterization
What is the projection of one vector on another one and how is it useful? Free ebook https://bookboon.com/en/introduction-to-vectors-ebook (updated link) Test your understanding via a short quiz http://goo.gl/forms/CpZUX1mFLS
From playlist Introduction to Vectors
Automatic Pattern Matching for 3D Geometry in Blender
To help refining the alignment of multiple 3D scans with each other, I have written a new tool for Blender which automatically finds the best fit for mesh objects.
From playlist Random Blender Tests
In this video, I define the concept of orthogonal projection of a vector on a line (and on more general subspaces), derive a very nice formula for it, and show why orthogonal projections are so useful. You might even see the hugging formula again. Enjoy! This is the second part of the ort
From playlist Orthogonality
08d Machine Learning: Random Projection
Lecture on random projection for dimensionality reduction with feature projection. Follow along with the demonstration workflow in Python's scikit-learn package: https://github.com/GeostatsGuy/PythonNumericalDemos/blob/master/SubsurfaceDataAnalytics_Multidimensional_Scaling.ipynb
From playlist Machine Learning
11H Orthogonal Projection of a Vector
The orthogonal projection of one vector along another.
From playlist Linear Algebra
This video explains how to determine the projection of one vector onto another vector. http://mathispower4u.yolasite.com/
From playlist Vectors
http://AllSignalProcessing.com for more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. Representing multivariate random signals using principal components. Principal component analysis identifies the basis vectors that describe the la
From playlist Random Signal Characterization
11J Orthogonal Projection of a Vector
The orthogonal projection of one vector along another.
From playlist Linear Algebra
Fellow Short Talks: Professor Richard Samworth, Cambridge University
Bio Richard Samworth is Professor of Statistics in the Statistical Laboratory at the University of Cambridge and a Fellow of St John’s College. He received his PhD, also from the University of Cambridge, in 2004, and currently holds an EPSRC Early Career Fellowship. Research His main r
From playlist Short Talks
Zakhar Kabluchko: Random Polytopes, Lecture III
In these three lectures we will provide an introduction to the subject of beta polytopes. These are random polytopes defined as convex hulls of i.i.d. samples from the beta density proportional to (1 − ∥x∥2)β on the d-dimensional unit ball. Similarly, beta’ polytopes are defined as convex
From playlist Workshop: High dimensional spatial random systems
Lecture 1 | Random polytopes | Zakhar Kabluchko | EIMI
Online school "Randomness online" November 4 – 8, 2020 https://indico.eimi.ru/event/40/
From playlist Talks of Mathematics Münster's reseachers
Nina Holden: Random triangulations and bijectivepaths to Liouville quantum gravity
CIRM HYBRID EVENT Recorded during the meeting "Lattice Paths, Combinatorics and Interactions" the June 25, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Luca Recanzone Find this video and other talks given by worldwide mathematicians on CIR
From playlist Probability and Statistics
Fast and Memory Efficient Differentially Private-SGD via JL Projections
A Google TechTalk, presented by Sivakanth Gopi, 2021/05/21 ABSTRACT: Differential Privacy for ML Series. Differentially Private-SGD (DP-SGD) of Abadi et al. (2016) and its variations are the only known algorithms for private training of large scale neural networks. This algorithm requires
From playlist Differential Privacy for ML
An average-case depth hierarchy theorem for Boolean - Li-Yang Tan
Computer Science/Discrete Mathematics Seminar I Topic: An average-case depth hierarchy theorem for Boolean circuits I Speaker: Li-Yang Tan Affiliation: Toyota Technological Institute, Chicago Date: Monday, April 4 We prove an average-case depth hierarchy theorem for Boolean circuits
From playlist Mathematics
Factors of sparse polynomials: structural results and some algorithms - Shubhangi Saraf
Computer Science/Discrete Mathematics Seminar II Topic: Factors of sparse polynomials: structural results and some algorithms Speaker: Shubhangi Saraf Affiliation: Member, School of Mathematics Date: March 26, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Joscha Prochno: The large deviations approach to high-dimensional convex bodies, lecture III
Given any isotropic convex body in high dimension, it is known that its typical random projections will be approximately standard Gaussian. The universality in this central limit perspective restricts the information that can be retrieved from the lower-dimensional projections. In contrast
From playlist Workshop: High dimensional spatial random systems
Recordings of the corresponding course on Coursera. If you are interested in exercises and/or a certificate, have a look here: https://www.coursera.org/learn/pca-machine-learning
From playlist Projections
Randomized Singular Value Decomposition (SVD)
This video describes how to use recent techniques in randomized linear algebra to efficiently compute the singular value decomposition (SVD) for extremely large matrices. Book Website: http://databookuw.com Book PDF: http://databookuw.com/databook.pdf These lectures follow Chapter 1 fro
From playlist Data-Driven Science and Engineering