Questions tagged [simplex]
11 questions
5
votes
1 answer
What algorithm do SVMs use to minimize their objective function?
Support Vector Machines turn machine learning linear classification tasks into a linear optimization problems.
$$ \text{minimize } J(\theta,\theta_0) = \frac1n \sum_1^n \text{HingeLoss}(\theta,\theta_0) + \frac{\lambda}{2} ||\theta||^2 $$
My…
HelloWorld
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3
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0 answers
Periodic 4D Triangulations
I am looking for references and/or algorithms for generating 4-dimensional periodic triangulations on unit 4 lattices. That is, generating a space filling triangulation of the 4D integer lattice (Z^4) that is invariant under lattice translations. I…
user143907
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3
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1 answer
How to uniformly sample a sorted simplex
I am looking for an algorithm to uniformly generate a descending array of N random numbers, such that the sum of the N numbers is 1, and all numbers lie within 0 and 1. For example, N=3, the random point (x, y, z) should satisfy:
x + y + z = 1
0 <=…
cloudygoose
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2
votes
1 answer
Sort array of 3D points to maximize number of tetrahedra in the array
Let $P$ be a indexable set(array) of points in $\mathbb{R}^3$ s.t. $P = \{p_0,p_1,p_2,...,p_n\}, p_i \in\mathbb{R}^3$.
I want to sort $P$ so that every 4 consecutive points forms a non-coplanar tetrahedra/3D-simplex/triangular pyramid (whatever you…
yosmo78
- 187
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2
votes
1 answer
Better way to decide if a set is a pure simplicial complex
Setup
I am trying to write a function that determines if a set of vertices, edges and faces is a pure simplicial complex.
A pure simplicial complex is a set where all facets have the same degree, a facet is a simplex that is not contained in a…
Makogan
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1
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1 answer
Why is infeasibility of linear programming considered to be an NP problem?
I recently came across this question, and the way I think people usually go about this is to find a certificate that answers 'yes' to the decision problem 'Is this LP infeasible?' Or, given a certificate, verify if that yields infeasibility or not.…
Namrata Banerji
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1
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0 answers
How does Bowyer-Watson algorithm for Delaunay triangulation run in $O(n^2)$ but runs over all the simplexes?
The Bowyer-Watson algorithm for Delaunay triangulation is known to run in $O(n^2)$ according to the authors, where $n$ is the number of data points in $\mathbb R^d$.
In addition, the algorithm (for example, as is written in Bowyer's paper, at stage…
Joe Doe
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0
votes
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What software can compute restricted matching numbers of graphs?
Let $\Delta$ be a simplicial complex and $F, G$ be two facets of $\Delta$. We say that $F$ and $G$ form a gap in $\Delta$ if $F \cap G = \emptyset$ and the induced subcollection on the vertex set $F \cup G$ is exactly $\langle F, G \rangle$.
A…
user181751
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0 answers
Solving a problem with linear programming
Suppose we wish to create a speech. Assume we have $n$ words to choose from numbered from $1$ to $n$. Every word holds a list of words that can come after it $S_i$. For example: if $2 \in S_1$ then the speech can contain the sequence of words $1,2$.…
MathStudent101
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0
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Solving linear programming problem with mixed type of constraints
I have a query in solving the problem below:
An automobile company has two factories. One factory has 400 cars (of a certain model)
in stock and the other factory has 300 cars (of the model) in stock. Two customers order
this car model. The first…
Jayajit
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0
votes
1 answer
In a LP problem Ax = b, how to solve for A instead of x?
I have a multi-objective linear programming problem of the form Ax = b, where A is a matrix and x and b are vectors. x is known, and I'm looking to minimise each row of b by solving for A.
Constraints are:
Each column of A must add up to 1.
A will…
Dom J
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