# Questions tagged [geometry]

For on-topic questions involving geometry. For purely mathematical question about geometry it is better to ask on the math SE site

140 questions
Filter by
Sorted by
Tagged with
24 views

4k views

### Impractical question: is it possible to find the regression line using a ruler and compass?

The ancient greeks famously sought to construct geometrical relationships using only a ruler and a compass. Given a set of points in a two dimensional plane, is it possible to find the OLS line using ...
• 808
1 vote
60 views

### How to find the average distance between randomly distributed points in a rectangle?

Assume there are n points randomly distributed in a rectangle (x being the height y being the width) shown below in the figure. I would like to calculate the average distance between 2 random red ...
1 vote
18 views

### Geometric properties of independence between random variables [closed]

Suppose $Y$ and $X$ are two independent random variables. Are there any geometrical properties (of PDF/CDF/PMF/etc.) that capture this independence? I know that the Support has to be rectangular and ...
• 2,277
61 views

### Does the distribution $f(x) \propto (1-x^2)^{n/2}$ have a name?

The distribution $f(x) \propto (1-x^2)^{n/2}$ for $-1 \leq x \leq 1$ It occurs in a problem like Law of the norm of the empirical mean of uniforms on the sphere? It relates to intersections of high ...
• 48.6k
1 vote
31 views

### Calculating the mean or median "whereabout" of a joystick

I have recently collected data using the NASA TLX tool, which includes a tracking task, where subjects have to keep the joystick deadcenter while having to react to multiple tasks. The raw data looks ...
• 11
1 vote
45 views

### Finding a Projection Plane in Dimensionality Reduction (e.g., Multidimensional Scaling)

I have a set of data points in high-dimensional space that I wish to map onto a lower dimension (3D or 2D). Question : How do I obtain the Projection (Hyper)Plane (e.g., its normal vector or its set ...
447 views

### How to find the weighted midpoint between n-points?

I was hoping if someone could guide me to the right algorithm to find the weighted midpoint of n-points. The photo attached below perfectly describes my problem. Let's just say we have three points ...
83 views

### Non-Euclidean analogue to MSE loss

The most basic machine learning model called OLS uses the RSS (squared loss) or its average, mean squared error (MSE), for its loss function, which is aligned with Euclidean geometry. What is the ...
• 3,089
130 views

### Why do we need to triangulate a convex polygon in order to sample uniformly from it?

Suppose I want to uniformly sample points inside a convex polygon. One of the most common approaches described here and on the internet in general consists in triangulation of the polygon and generate ...
• 41
1 vote
56 views

### What are the principal components of a set of points lying on a circle? [closed]

So if there are a set of points lying on a circle (2 dimensional), what will be the principal components given that the variance of points vary equally along any 2 perpendicular directions
35 views

### How to do statistics on different geometries?

The original motivation: Let's say, we have two particles, doing random one motion on an infinite 1-D lattice $\mathbb{Z}$, and we are interested in the autocorrelation of the trajectory of each ...
• 207
50 views

• 407
156 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. ...
• 143
95 views

### MLE for an ellipse

I'm not at all a statistician, but in the course of my work I've come across a non-trivial maximum likelihood estimation problem, and I'm looking for ideas and/or references on how to approach it. ...
• 121
1 vote
49 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 ...
• 619
1 vote
968 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.
133 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 ...
• 1,289
1 vote
30 views