This power point contains information about how to learn and understand Manifolds concept with the help of MATLAB

1. Manifold Learning MATLAB
demo

2. Manifolds
 “According to mathematics, manifold is a collection of points
forming a certain kind of set, such as those of topologically
closed surface.”
 Example: Surface, Curve & point.

3. Terms to be used in code
 X = data as D x N matrix (D = dimensionality, N = #points)
 K = number of neighbors
 dmax = max embedding dimensionality
 Y = embedding as dmax x N matrix

4. General Code
 X=rand(10,50);
 k=20;
 dmax=2;
 [Y] = lle(X,k,dmax);

5. Functioning of code in MATLAB

6. Animated Version using MATLAB
The input data can be read from a
matrix in the workspace, from a text
file, or selected from one of 8 built-in
examples.

7. Description to every option
 Load Matrix: Enter the name of a matrix in the MATLAB workspace
and press this button.
The matrix should be NxD, where
N is the number of data items;
D is the dimension of the manifold.
 Load File: Enter the name of a text file and press this button. The text
file should contain numbers separated by spaces with each data
element as a row.

8. Parameters used in simulation
 Target Dimension d: The desired dimension of the embedding. In
general, the target dimension d should be less than the input
manifold dimension D.
 Nearest Neighbors K: Specifies the number of nearest neighbors
(KNN) used to build the graph for the following methods: ISOMAP,
LLE, Hessian LLE, Laplacian, and LTSA.

9.  Sigma: This specifies the width of the Gaussian kernel in the Diffusion Map
method.
 Alpha: This parameter controls the normalization used by Diffusion Map.
Alpha = 0 is the Graph Laplacian
Alpha = 1/2 is the Fokker-Plank propagator
Alpha = 1 is the Laplace-Beltrami operator

10. Output
The output for:
d = 2;
k = 8;
Sigma = 10.0;
Alpha = 1.0;