Understand Manifolds using MATLAB
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Transcript of Understand Manifolds using MATLAB
Manifold Learning MATLAB demo
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.
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
General Code
X=rand(10,50);
k=20;
dmax=2;
[Y] = lle(X,k,dmax);
Functioning of code in MATLAB
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.
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, whereN 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.
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.
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 LaplacianAlpha = 1/2 is the Fokker-Plank propagatorAlpha = 1 is the Laplace-Beltrami operator
Output
The output for:
d = 2; k = 8;Sigma = 10.0;Alpha = 1.0;