Manifold Learning

Nonlinear dimensionality reduction.

Signals

Inputs:

• Data

  A data set

Outputs:

• Transformed Data

  A data set with new, reduced coordinates.

Description

Manifold Learning is a technique which finds a non-linear manifold within the higher-dimensional space. The widget then outputs new coordinates which correspond to a two-dimensional space. Such data can be later visualized with Scatter Plot or other visualization widgets.

1. Method for manifold learning:
   • t-SNE
   • MDS, see also MDS widget
   • Isomap
   • Locally Linear Embedding
   • Spectral Embedding
2. Set parameters for the method:

   • t-SNE (distance measures):

     • Euclidean distance
     • Manhattan
     • Chebyshev
     • Jaccard
     • Mahalanobis
     • Cosine

   • MDS (iterations and initialization):

     • max interations: maximum number of optimization interations
     • initialization: method for initialization of the algorithm (PCA or random)

   • Isomap:

     • number of neighbors

   • Locally Linear Embedding:

     • method:

       • standard
       • modified
       • hessian eigenmap
       • local

     • number of neighbors
     • max iterations

   • Spectral Embedding:

     • affinity:

       • nearest neighbors
       • RFB kernel

3. Output: the number of reduced features (components).
4. If Apply automatically is ticked, changes will be propagated automatically. Alternatively, click Apply.
5. Produce a report.

Manifold Learning widget produces different embeddings for high-dimensional data.

... figure:: images/collage-manifold.png

From left to right, top to bottom: t-SNE, MDS, Isomap, Locally Linear Embedding and Spectral Embedding.

Example

Manifold Learning widget transforms high-dimensional data into a lower dimensional approximation. This makes it great for visualizing data sets with many features. We used voting.tab to map 16-dimensional data onto a 2D graph. Then we used Scatter Plot to plot the embeddings.