Local Tangent Space Alignment¶
Local tangent space alignment (LTSA) is a method for manifold learning, which can efficiently learn a nonlinear embedding into lowdimensional coordinates from highdimensional data, and can also reconstruct highdimensional coordinates from embedding coordinates [1].
This package defines a LTSA
type to represent a LTSA results, and provides a set of methods to access its properties.
Properties¶
Let M
be an instance of LTSA
, n
be the number of observations, and d
be the output dimension.

outdim
(M)¶ Get the output dimension
d
, i.e the dimension of the subspace.

projection
(M)¶ Get the projection matrix (of size
(d, n)
). Each column of the projection matrix corresponds to an observation in projected subspace.

neighbors
(M)¶ The number of nearest neighbors used for approximating local coordinate structure.

eigvals
(M)¶ The eigenvalues of alignment matrix.
Data Transformation¶
One can use the transform
method to perform LTSA over a given dataset.

transform
(LSTA, X; ...)¶ Perform LTSA over the data given in a matrix
X
. Each column ofX
is an observation.This method returns an instance of
LTSA
.Keyword arguments:
name description default k The number of nearest neighbors for determining local coordinate structure. 12
d Output dimension. 2
Example:
using ManifoldLearning
# suppose X is a data matrix, with each observation in a column
# apply LTSA transformation to the dataset
Y = transform(LTSA, X; k = 12, d = 2)
References
[1]  Zhang, Zhenyue; Hongyuan Zha. “Principal Manifolds and Nonlinear Dimension Reduction via Local Tangent Space Alignment”. SIAM Journal on Scientific Computing 26 (1): 313–338, 2004. DOI:10.1137/s1064827502419154 