# 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.

- Method for manifold learning:
- 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*

- number of

- Locally Linear Embedding:
*method*:- standard
- modified
- hessian eigenmap
- local

- number of
*neighbors* *max iterations*

- Spectral Embedding:
*affinity*:- nearest neighbors
- RFB kernel

- Output: the number of reduced features (components).
- If
*Apply automatically*is ticked, changes will be propagated automatically. Alternatively, click*Apply*. - 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 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.