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Questions tagged [geometry]

For on-topic questions involving geometry. For purely mathematical questiona about geometry it is better to ask on math SE https://math.stackexchange.com/

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62 views

Sampling from/near boundary of a region in R^n

Suppose $\Omega$ is a region in $\mathbb R^n$, and suppose we are given a function $\chi(x)$ with $\chi(x)=1$ if $x\in \Omega$ and $\chi(x)=0$ otherwise. If it helps we can assume $\Omega\subseteq B$ ...
28 views

Geometric interpretation of Cholesky Decomposition

I understand that a square matrix, say $A$, can be thought of as a linear transformation within the same space. I could be as simple as basis change or some other transformation. In this way of ...
36 views

Is there a geometric interpretation for the surprising result of $E[x(y-\mu_y)] = COV(x,y)$?

I was playing around with non-central second moments, and noticed that $E[x(y-\mu_y)] = E[(x-\mu_x + \mu_x)(y-\mu_y)] = COV[x,y] + E[\mu_x(y-\mu_y) = COV[x,y] + 0$. I find this very surprising. It ...
33 views

Bounding data by two parallel lines with minimum distance between them

I have a set of data samples that approximately follow a straight line in 2D. I need to find two parallel lines that are spaced as close as possible such that all of the samples lie between the lines. ...
13 views

Maximize volume of convex hull [closed]

Suppose I have N points (labeled 1, 2, ..., k, ..., N) in D dimensions. I'd like to choose ...
40 views

How to calculate the midpoint between 2 latitude and longitude coordinates in R? [closed]

I have two sets of lat and long coordinates. I would like to find the midpoint between them. Not sure how to calculate this in R.
11 views

Is there work for statistical properties analysis of road curvatures?

I looking for an analysis about the most suitable stochastic process to model distribution of road curvatures and its properties. I have been googling for several days and could not find it yet. For ...
58 views

What is the geometric meaning of correlation matrix

I recently read this article explaining the geometric meaning of covariance matrix. http://www.visiondummy.com/2014/04/geometric-interpretation-covariance-matrix/ My question is : is there an ...
36 views

Does skipgram(word2vec) decreases the euclidean distance or increases cosine similarity between similar words?

The skip-gram model tends to predict the surrounding words or in other words, it tries to maximize the co-occurrence in the output of the Network. According to my knowledge, this makes a similar word ...
18 views

Expected number of quadrilaterals

There are N points on the plane and the probability that the probability that two points are connected is p. What is the expected number of Quadrilaterals you can find? Assume that there is no three ...
41 views

Is the Franke-Wolfe algorithm the same as Manifold optimization?

The Frank-Wolfe optimization algorithm describes optimization over a constrained domain. In the Manifold Optimization literature (e.g. ) a Gradient-Step is done using an exponential map. This maps ...
58 views

Limitations to using the principle of least squares to fit an ellipse to experimental data?

I have used the method described below many times without issue to determine the major and minor axes of the "data ellipse". However, for this set of data (Fig. A) the method described below is ...
23 views

Probability that some coefficients will be zero with lasso regression

Maybe it is duplicate, but I don't know how to ask a right question. Suppose I fixed some lambda, for instance lambda = 1. I draw the usual "square" |x| + |y| = 1. Now I want to find probability, ...
27 views

How would one carry out principal component analysis in the Beltrami-Klein model of hyperbolic space?

This is a follow up to a comment by @whuber in response to this question: Is there an extension of PCA for data embedded in hyperbolic spaces? Sorry, I would have posted it there as a comment but it ...
383 views

Drawing 95% ellipse over scatter plot

The context is regression analysis using Eviews, but first I wanted to create a few scatter plots and overlay error ellipses on them. Eviews doesn't support that kind of graph ornamentation so I am ...
27 views

Sampling from the surface of a sphere in n dimensions with specific centre

I have a point $p$ on the surface of a unit sphere. I want to sample points from the surface of the sphere, such that the probability density of a point $q$ on the surface is given by \begin{equation} ...
24 views

When is the result of multidimensional-scaling unique up to isometry?

What conditions on the ambient space and/or the given matrix of dissimilarities guarantee that all point configurations that minimise the error function of multidimensional scaling (MDS) are congruent,...
127 views

Expected value as an orthogonal projection

I'm reading a paper in which the expected value of a random variable, $\mathbb{E}[X]$, is characterized as an orthogonal projection. This is on page 10. I've seen the geometric interpretation of ...
17 views

31 views

mean and least error on the line

Suppose I have a line on which i have points in non-decreasing order. My intuition tells me that if I want to minimize the squared mean error on some subset of 3 (or other number) points, I would like ...
359 views

How can I solve this joint probability problem?

Two points are dropped at random onto the unit interval, creating three sub intervals this way. Find the probability that the central sub interval will be two times shorter than the right ...
863 views

85 views

What is Geometrical Probability? [closed]

Is it a technique where Geometry is used to solve probabilistic problems? Is it a kind of probability which grows Geometrically when we conduct experiments? Is it a kind of distribution? I am ...
88 views

Finding the non-linear curve that minimize the (sum of squared) distance to a set of point

I'm looking for the best approach to find the non-linear curve that minimize the mean square of perpendicular distance from a set of points. In essence, I would like to do non-linear major axis ...