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Results tagged with tsne
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user 28666
T-distributed stochastic neighbor embedding (t-SNE) is a nonlinear dimensionality reduction algorithm introduced by van der Maaten and Hinton in 2008.
6
votes
Accepted
The usage of "variance" (vs. "standard deviation") in the 2008 t-SNE paper
You are right. It is clear from Equation (1) that $\sigma_i$ denotes the standard deviation and not the variance. So the text should have said
(for reasonable values of the variance of the Gaussia …
- 107k
24
votes
Accepted
What is the meaning of the axes in t-SNE?
Individual axes in t-SNE have no meaning at all.
Algorithms such as MDS, SNE, t-SNE, etc. only care about pairwise distances between points. They try to position the points on a plane such that the p …
- 107k
11
votes
Accepted
Why can't t-SNE capture a simple parabola structure?
%matplotlib notebook
import numpy as np
import pylab as plt
import seaborn as sns; sns.set()
from sklearn.manifold import TSNE
x = np.arange(-5, 5.001, .5)[:,None]
y = x**2
X = np.concatenate((x,y),axis … =1)
Z = TSNE(n_components=1, method='exact', perplexity=2,
early_exaggeration=2, learning_rate=1,
random_state=42).fit_transform(X)
plt.figure(figsize=(8,2))
plt.scatter(Z, Z*0, s …
- 107k
34
votes
Accepted
Intuitive explanation of how UMAP works, compared to t-SNE
You said that your understanding of t-SNE is based on https://www.youtube.com/watch?v=NEaUSP4YerM and you are looking for an explanation of UMAP on a similar level.
I watched this video and it is pret …
- 107k
3
votes
Accepted
Why do I get weird results when using high perpexity in t-SNE?
A popular t-SNE tutorial https://distill.pub/2016/misread-tsne/ says
The image for perplexity 100, with merged clusters, illustrates a pitfall: for the algorithm to operate properly, the perplexity … As explained by Laurens van der Maaten, https://github.com/distillpub/post--misread-tsne/issues/2:
I just had one small remark: you show some results with perplexity 100 that are a complete mess. …
- 107k
5
votes
Accepted
Perplexity formula in the t-SNE paper vs. in the implementation
For a given $i$, the similarities $p_{j|i}$ are obtained from Euclidean distances $d_{ij}$ via a Gaussian similarity kernel and then normalized to sum to one: $$p_{j|i} = \frac{\exp(-\beta d_{ij})}{\s …
- 107k
12
votes
Accepted
Why does larger perplexity tend to produce clearer clusters in t-SNE?
The larger the perplexity, the more non-local information will be retained in the dimensionality reduction result.
Yes, I believe that this is a correct intuition. The way I think about perplexi …
- 107k
73
votes
Clustering on the output of t-SNE
I am well aware of the ways in which t-SNE output may be misleading (see https://distill.pub/2016/misread-tsne/) and I agree that it can produce weird results in some situations. …
- 107k
11
votes
What is meant by PCA preserving only large pairwise distances?
Consider the following dataset:
PC1 axis is maximizing the variance of the projection. So in this case it will obviously go diagonally from lower-left to upper-right corner:
The largest pairwise …
- 107k
28
votes
Accepted
How can t-SNE or UMAP embed new (test) data, given that they are nonparametric?
The figure above is from https://github.com/berenslab/rna-seq-tsne/ which is a companion repository to this paper: https://www.nature.com/articles/s41467-019-13056-x. …
- 107k
18
votes
Should dimensionality reduction for visualization be considered a "closed" problem, solved b...
Somebody linked to this very popular account of some shortcomings of t-SNE: https://distill.pub/2016/misread-tsne/ (+1), but it only discusses very simple toy datasets and I find that it does not correspond …
- 107k