Performing nonlinear dimension reduction with Local Linear Embedding

Local Linear Embedding (LLE) is an extension of PCA, which reduces data that lies on a manifold embedded in a high dimensional space into a low dimensional space. In contrast to ISOMAP, which is a global approach for nonlinear dimension reduction, LLE is a local approach that employs a linear combination of the k-nearest neighbor to preserve local properties of data. In this recipe, we will give a short introduction of how to use LLE for s-curve data.

Getting ready

In this recipe, we will use digit data from lle_scurve_data within the lle package as our input source.

How to do it...

Perform the following steps to perform nonlinear dimension reduction with LLE:

1. First, you need to install and load the package, lle:

        > install.packages("lle")
        > library(lle)  

2. You can then load ll_scurve_data from lle:

        > data( lle_scurve_data ) 

3. Next, perform lle on lle_scurve_data:

        > X = lle_scurve_data
  ...