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https://github.com/jefferis/manifoldreduction
Manifold Dimension Reduction after Chigirev and Bialek
https://github.com/jefferis/manifoldreduction
Last synced: 27 days ago
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Manifold Dimension Reduction after Chigirev and Bialek
- Host: GitHub
- URL: https://github.com/jefferis/manifoldreduction
- Owner: jefferis
- Created: 2015-06-30T21:22:23.000Z (over 9 years ago)
- Default Branch: master
- Last Pushed: 2019-10-23T08:16:30.000Z (about 5 years ago)
- Last Synced: 2023-04-16T09:10:56.684Z (over 1 year ago)
- Language: R
- Homepage: https://jefferis.github.io/manifoldreduction/
- Size: 598 KB
- Stars: 1
- Watchers: 1
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.Rmd
Awesome Lists containing this project
README
---
output: github_document
---
```{r, include = FALSE}
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>",
fig.path = "man/figures/README-",
out.width = "100%"
)
```
# manifoldreduction
[](https://travis-ci.org/jefferis/manifoldreduction)
[](https://jefferis.github.io/manifoldreduction/reference/)
An implementation of Chigirev and Bialek's algorithm described in "Optimal Manifold Representation of Data: An Information Theoretic Approach".
## Quick Start
For the impatient ...
```{r, eval=FALSE}
# install
if (!require("devtools")) install.packages("devtools")
devtools::install_github("jefferis/manifoldreduction")
# use
library(manifoldreduction)
# help for functions
?manifold_reduction
# run tests
library(testthat)
test_package("manifoldreduction")
```
## Installation
Currently there isn't a released version on [CRAN](http://cran.r-project.org/) but you can use the **remotes** package to install the development version:
```{r, eval=FALSE}
if (!require("remotes")) install.packages("remotes")
devtools::install_github("jefferis/manifoldreduction")
```
Note: Windows users may need [Rtools](http://www.murdoch-sutherland.com/Rtools/) and [remotes](http://CRAN.R-project.org/package=devtools) to install this way.
## Example
As an example, let's use a noisy 2D circle. First a helper function for
the parametric form of the equation of a circle:
```{r}
circle <- function(r = 1, x = 0, y = 0, n = 360) {
theta = seq(from = 0,
to = 2 * pi,
length.out = n)
cbind(X = x + r * cos(theta), Y = y + r * sin(theta))
}
```
Now we can add a bit of noise to the radius
```{r}
noisy_circle=circle(r=rnorm(360, mean=1, sd=.1))
plot(noisy_circle, asp = 1)
lines(circle(), col='black')
```
Now let's try recovering a low dimensional manifold. The default parameters
will essentially look for a line.
```{r}
library(manifoldreduction)
# NB expects d x N points (not N x d)
q=manifold_reduction(t(noisy_circle), no_iterations = 10, Verbose=FALSE)
```
This toy example converges fast, so I have reduced the number of iterations.
If you plot the results (red line), you can see that it does a good job of smoothly recovering the structure of the original input points.
```{r}
plot(noisy_circle, asp=1)
lines(circle(), col='black')
lines(t(q$gamma), col='red')
```
However there is a clear bias in the position of the recovered circle. This
is down to the structure in these data - distant points in the dataset still contribute to the reconstruction of the manifold which will therefore be biased towards a medial position. If one reduces the number of points
that are used:
```{r}
q2=manifold_reduction(t(noisy_circle), no_iterations = 10, Verbose=FALSE, knntouse = 40)
plot(noisy_circle, asp=1)
lines(circle(), col='black')
lines(t(q$gamma), col='red')
lines(t(q2$gamma), col='blue')
```
then one obtains a less biased but somewhat noisier estimate (blue) (compare with the previous estimate in red or the underlying circle in black).
Of course this toy example could be better solved if one used a knowledge
of the expected distribution (a circle) as part of the fitting process.
However the interesting point with this method is that it is a rather
general procedure that can be used for arbitrary point distributions
in higher dimensions.