# Questions tagged [manifold]

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### Examples of distance "hyperparameters" used in clustering

From what I've seen in clustering, distance is taken as a hyper parameter (which is to be selected) when inferring the relationships/clusters between points. What are some examples of highly-cited ...
• 123
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### How do I interpret low dimentional embeddings of high dimentional embeddings?

I am trying to understand what I am supposed to learn about a problem when using dimensionality reduction methods. In particular, I am referring to methods like t-SNE and UMAP. For the most part I am ...
1 vote
54 views

### When visualizing graph nodes, should I use apply PCA to node2vec embedding?

I am trying to visualize graph nodes using node2vec embedding. The node2vec embeddings has lengths of 50~100 dimensions. I have two plans: use umap to project node2vec embeddings to 2D space use PCA ...
1 vote
90 views

### Can an Isomap be embedded in a manifold of higher dimension than the corresponding MDS?

I am using the Isomap algorithm to operate a dimension reduction on a distance matrix $M_{dist}$. For a given choice of nearest neighbors k to compute the geodesic distance, I use the following method ...
• 11
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### Generative Adversarial Text to Image Synthesis

Can anyone explain the meaning of this line: "Deep networks have been shown to learn representations in which interpolations between embedding pairs tend to be near the data manifold". ...
255 views

### Hyperbolic coordinates (Poincaré embeddings) as the output of a neural network

I'm trying to build a Deep Learning predictor that takes as the input a set of word vectors (in Euclidian space) and outputs Poincaré embeddings. So far I am not having much luck, because model ...
• 181
31 views

### Dimension of the manifold on which my data sits

Suppose that I have data points, in the form of vectors with binary entries. We create a metric space, or Vietoris-Rips complex, using the Hamming distance between the data points. I would like to ...
• 31
1 vote
91 views

### Can I use manifold learning to transform the feature set as a substitute of graph kernel of SVC

I just wonder since the manifold learning under scikit-learn has component of graph-based transformation (e.g. Shortest-path graph search under Isomap) I can then transform the feature data set (i.e. ...
356 views

### Difference between MDS and other manifold learning algorithms

From sklearn docs: Note that the purpose of the MDS is to find a low-dimensional representation of the data (here 2D) in which the distances respect well the distances in the original high-...
• 323
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### Can I apply Clustering algorithms to the result of Manifold Visualization Methods?

Some methods related to manifold-learning are commonly stated as good-for-visualization, such as T-SNE and self-organizing-maps (SOM). I understand that when referring specifically to "visualization" ...
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