Manifold Learning

Nonlinear dimensionality reduction.

Inputs

  • Data: input dataset

Outputs

  • Transformed Data: dataset with reduced coordinates

[Manifold Learning](https://en.wikipedia.org/wiki/Nonlinear_dimensionality_reduction) 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](../visualize/scatterplot.md) or other visualization widgets.

![](images/manifold-learning-stamped.png)

  1. Method for manifold learning: - [t-SNE](http://scikit-learn.org/stable/modules/manifold.html#t-distributed-stochastic-neighbor-embedding-t-sne) - [MDS](http://scikit-learn.org/stable/modules/manifold.html#multi-dimensional-scaling-mds), see also [MDS widget](../unsupervised/mds.md) - [Isomap](http://scikit-learn.org/stable/modules/manifold.html#isomap) - [Locally Linear Embedding](http://scikit-learn.org/stable/modules/manifold.html#locally-linear-embedding) - [Spectral Embedding](http://scikit-learn.org/stable/modules/manifold.html#spectral-embedding)

  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](../visualize/scatterplot.md) to plot the embeddings.

![](images/manifold-learning-example.png)