Questions tagged [manifold]

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After using manifold, I get 2 dimensional data, then I can do cluster and label the data. But the question is that how can I reflect this label in raw

I use manifold to analyze image and want to do image segmentation. So my idea is to first use manifold to downsize the dimensions to 2D. In 2D, I can do cluster and label, but how can I put this label ...
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Low dimensional manifold in a high dimensional space and Geodesic distance

It is a common assumption that high-dimensional objects are lying in low-dimensional manifolds. And this constitutes a foundation for manifold learning or dimensional reduction techniques or (a way to ...
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State-of-the-art methods for out-of-sample-extension

I'm using a kernel based dimensionality reduction algorithms, and interested in extending out-of-sample data points for further analysis. I've been using the Nystrom method for this task, and some ...
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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 ...
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34 views

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". ...
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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 ...
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30 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 ...
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88 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. ...
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323 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-...
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343 views

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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Can closer points be considered more similar in T-SNE visualization?

I understand from Hinton's paper that T-SNE does a good job in keeping local similarities and a decent job in preserving global structure (clusterization). However I'm not clear if points appearing ...