The representative methods are Locally Linear Embedding (LLE) , Isomaptic Map (Isomap) , Laplacian Eigenmap
(LE)  and so on.
The representation map generated by the algorithm may be viewed as a linear discrete approximation to a continuous map that naturally arises from the geometry of the manifold locality preserving projection (LPP) which is a linear approximation of the nonlinear Laplacian Eigenmap
. In the proposed work, the algorithm procedure that is used as show in 21-23].
Li, "Using laplacian eigenmap
as heuristic information to solve nonlinear constraints defined on a graph and its application in distributed range-free localization ofwireless sensor networks" Neural Processing Letters, vol.
LPP is a linear approximation of the nonlinear Laplacian Eigenmap
for learning a locality preserving subspace which preserves the intrinsic geometry of the data and local structure.
The representative algorithms include locally linear embedding (LLE), Isomap, and Laplacian eigenmap
Among them, isometric feature mapping (ISOMAP) , locally linear embedding (LLE) [8, 9], Laplacian eigenmap
(LE) [10, 11] and local tangent space alignment (LTSA)  are widely used.
The representative methods include Isomap , Laplacian eigenmap
 and locally linear embedding (LLE) , etc.
A spatiotemporal Laplacian eigenmap
method (Hou et al., 2013) is proposed to extract different crowd activities from videos.
In order to detect the underlying manifold structure, nonlinear dimensionality reduction algorithms such as ISOMAP , locally linear embedding (LLE) , and Laplacian eigenmap
(LE)  have been proposed.
In order to detect the underlying manifold structure, many manifold learning algorithms have been proposed, such as isometric feature mapping (ISOMAP) , local linear embedding (LLE) , and Laplacian eigenmap
Besides, some manifold learning methods have been proposed including Laplacian eigenmaps
[19, 20], locally linear embedding , and Isometric Mapping method [22, 23].
Belkin and P Niyogi, "Laplacian eigenmaps
and spectral techniques for embedding and clustering," in Proceedings of the 15th Annual Neural Information Processing Systems Conference (NIPS '01), pp.