# local_tangent_space_alignment

**Repository Path**: weirdochen/local_tangent_space_alignment

## Basic Information

- **Project Name**: local_tangent_space_alignment
- **Description**: LTSA, in MATLAB. Zhang and Zha's paper.
- **Primary Language**: Unknown
- **License**: Not specified
- **Default Branch**: master
- **Homepage**: None
- **GVP Project**: No

## Statistics

- **Stars**: 0
- **Forks**: 0
- **Created**: 2020-01-10
- **Last Updated**: 2020-12-19

## Categories & Tags

**Categories**: Uncategorized

**Tags**: None

## README

# local_tangent_space_alignment
LTSA, in MATLAB. Like LLE, LTSA is for nonlinear dimension reduction. But, LTSA is a method that constructs a principal manifold.

A principle manifold, a nonlinear mapping from one euclidean space to another. It's very interesting.

For example, given a spiral with gaussian noise we may want to find a 1d curve that describes it.

![image](spiral.jpg)

These are the coordinates that were found using LTSA, compared with the [0,1] interval.

![image](res_spiral_t.jpg)


So, using the same image as for the LLE example, we find this embedding with LTSA:

![image](res_purple_stp_25.jpg)

And finally, using 13 categories from the COIL-100 dataset, I apply this algorithm with k=100 and receive the following alignment:

![image](res_coil_100.jpg)