# Manifold Learning¶

Nonlinear dimensionality reduction.

## Signals¶

**Inputs**:

**Data**A data set

**Outputs**:

**Transformed Data**A data set with new, reduced coordinates.

## Description¶

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: - t-SNE - MDS, see also MDS widget - Isomap - Locally Linear Embedding - Spectral Embedding

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 data sets 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.