Manifold Learning

Nonlinear dimensionality reduction.

Inputs

  • Data: input dataset

Outputs

  • Transformed Data: dataset with reduced coordinates

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 iterations: maximum number of optimization interactions

      • 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.

../../_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 datasets 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