3- Positioning :
The purpose of LOCAL TANGENT SPACE ALIGNMENT and other dimensionality reduction algorithms like Locally Linear Embedding (LLE) ), Principal Component Analysis (PCA) and Isomap, is to find correlations and connections between different samples of an observed object and plotting them into a drawn that can be visualized. Also it is able to maps the resource data into a single global coordinate system, optimizing it not using local minima and learning form nonlinear manifolds as it is shown in the source article .
Several different algorithms have been developed to dimensionality reduction so he Produce a compact low-dimensional encoding from high-dimensiona , While all of these methods have a similar goal, approaches
to the problem are different.
we have linear and nolinear dimensionality we have a several methods
use to dimentionality reduction for exemple :
a-Principal components analysis (PCA)
Is a very popular technique for dimensionality reduction. PCA aims to
find a linear subspace of dimension ādā lower than ānā such that the
data points lie mainly on this linear subspace.