s1k: Nine-dimensional "fuzzy" simplex

In jlmelville/sneer: Stochastic Neighbor Embedding Experiments in R

Nine-dimensional "fuzzy" simplex

Description

A synthetic data set, consisting of a "fuzzy" nine-dimensional simplex: ten points equidistant from each other (the length being 2). Each point in the simplex has a separate label, "0" to "9".

Usage

data(s1k)

Format

A data frame with 1000 rows and 10 variables

Details

Then for each vertex of the simplex, a further 99 points were generated, sampled from a nine-dimensional Gaussian distribution centered at the vertex, with a standard deviation of 0.5. Each of the points so generated was given the same label as their "parent" vertex. This generated a nine-dimensional dataset with 1000 instances and ten classes.

This data set is intended to fulfil the following criteria:

1. Not impossibly difficult: there's reasonable overlap of the ten clusters of points, but the variance is isotropic and identical for each cluster.

2. Have an obvious right answer by visual inspection of the output map: do we see ten reasonably well separated blobs?

3. Be sufficiently complex so that the "crowding problem" will manifest: in the original nine-dimensional input space, the ten classes are by definition equidistant from each other, so it's impossible for the input to be perfectly reproduced in the two-dimensional output map.

4. Traditional distance-preserving mapping methods (e.g. PCA, MDS, Sammon mapping) shouldn't do a very good job, otherwise there's no point using a probability-based method.

The variables are as follows:

• D0, D1, D2 ... D8 Real values, ranging from -2.51 to 3.27.

• Label The id of the simplex vertex that this point is associated with, in the range 0-9. Stored as a factor.

jlmelville/sneer documentation built on Sept. 8, 2024, 9:58 p.m.