Locally Linear Embedding¶
Locally Linear Embedding (LLE) technique builds a single global coordinate system of lower dimensionality. By exploiting the local symmetries of linear reconstructions, LLE is able to learn the global structure of nonlinear manifolds [1].
This package defines a LLE
type to represent a LLE results, and provides a set of methods to access its properties.
Properties¶
Let M
be an instance of LLE
, 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 HLLE over a given dataset.
-
transform
(LLE, X; ...)¶ Perform LLE over the data given in a matrix
X
. Each column ofX
is an observation.This method returns an instance of
LLE
.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 LLE transformation to the dataset
Y = transform(LLE, X; k = 12, d = 2)
References
[1] | Roweis, S. & Saul, L. “Nonlinear dimensionality reduction by locally linear embedding”, Science 290:2323 (2000). DOI:10.1126/science.290.5500.2323 |