# Questions tagged [high-dimensional]

A high-dimensionality space is one that can only be spanned by a basis set with a large number of elements. High-dimensional problems often suffer from the *Curse of Dimensionality*, which is exponential growth in the problem size as a function of the number of dimensions.

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### PDEs in Many Dimensions

I know that most methods of finding approximate solutions to PDEs scale poorly with the number of dimensions, and that Monte Carlo is used for situations that call for ~100 dimensions. What are good ...
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### Fastest PCA algorithm for high-dimensional data

I would like to perform a PCA on a dataset composed of approximately 40 000 samples, each sample displaying about 10 000 features. Using Matlab princomp function consistently takes over half an hour ...
337 views

### What is the current state of the art in solving higher dimensional parabolic PDEs (multi-electron Schrödinger equation)

What is the current state of the art for solving higher dimensional (3-10) parabolic PDEs in the complex domain with simple poles (of the form $\frac{1}{|\vec{r}_1 - \vec{r}_2|}$) and absorbing ...
1k views

### N-dimensional Delaunay Tesselation Software Libraries

I have a set of known points/nodes irregularly spaced in N-Dimensional space (N>=2), and I would like a way to generate the Delaunay triangulation of these points, and return the corresponding ...
1k views

### Kolmogorov–Smirnov test for multivariate data

I have a set of files consisting of randomly selected points from a dataset, each file belonging to a particular class. Each row in these files contains the coordinates in n-space of the point. I'd ...
327 views

### Working with multi-dimensional functions

How would you represent functions of type $[-1, 1]^n \to \mathbb R \;$ for moderate $n$? How would you integrate them? For small $n$ (1-2) such functions can be represented as histograms, vectors in ...
231 views

### Enumerating hexahedral cell vertices and faces in arbitrary dimension

I have a Cartesian mesh in $d$ dimensions, and I would like to enumerate all the subcells of a given hexahedral cell. If I am just enumerating the vertices of a cell (or cells that contain a vertex) I ...
302 views

### Dimensionality reduction of the domain of f(x)

I'm wondering if there is something analogous to a PCA for data sets where there is a dependent variable. (Though I am interested in any method of dimensionality reduction, PCA is just an example.) ...
975 views

218 views

### $k$-Nearest Neighbor Search using examples

I want to perform $k$-Nearest Neighbor Search in multidimensional space, but not using for example $L_2$-distance. I want the user to specify some "similar"-pairs examples and then perform a search ...
97 views

### application of oscillatory high-dimensional functions

Has anybody stumbled upon any kind of application of high-frequency high-dimensional problems ($d\geq 4$)? My interest comes from the following: there is quite a decent amount of papers where people ...
106 views

### What kinds of maths to learn for understanding dynamical systems in cognitive science? [closed]

A current trend in cognitive science is to view the mind as a dynamical system (e.g., Continuity of Mind by Spivey, in which cognition is understood as a "continuous and often recurrent trajectory ...