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/ManifoldLearning-stamped.png{width=50%}

  1. Method for manifold learning:

    • t-SNE, see also t-SNE widget

      • Metric: set a distance measure (Euclidean, Manhattan, Chebyshev, Jaccard)

      • Perplexity: roughly the number of nearest neighbors to which distances will be preserved

      • Early exaggeration: increase the attractive forces between points

      • Learning rate: how much parameters are adjusted during each optimization step

      • Max iterations: maximum number of times optimization is run

      • Initialization: method for initialization of the algorithm (PCA or random)

    • MDS, see also MDS widget

      • max iterations: maximum number of times optimization is run

      • initialization: method for initialization of the algorithm (PCA or random)

    • Isomap

      • number of neighbors: local geometry to consider in dimensionality reduction

    • Locally Linear Embedding

      • method: standard, modified, hessian eigenmap, or local

      • number of neighbors: local geometry to consider in dimensionality reduction

      • max iterations: maximum number of times optimization is run

    • Spectral Embedding

      • affinity: method for constructing affinity matrix (nearest neighbors or RFB kernel)

  2. Output: the number of reduced features (components).

  3. If Apply automatically is ticked, changes will be propagated automatically. Alternatively, click Apply.

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.

Preprocessing

All projections use default preprocessing if necessary. It is executed in the following order:

  • continuization of categorical variables (with one feature per value)

  • imputation of missing values with mean values

To override default preprocessing, preprocess the data beforehand with Preprocess widget.

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/ManifoldLearning-Example.png