Manifold Learning

../../_images/manifold-learning.png

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.

../../_images/manifold-learning-stamped.png
  1. Method for manifold learning:
  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:
      • 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.

../../_images/manifold-learning-example.png