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.

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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.

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.