Question: In this problem you will examine a method for nonlinear dimensionality reduction known as locally linear embedding (LLE). Let x1, . . . , xn

In this problem you will examine a method for nonlinear dimensionality reduction known as locally linear embedding (LLE). Let x1, . . . , xn Rq. The idea behind LLE is that even though the data points may lie on a nonlinear structure/manifold, at least locally the data appear linear. Therefore, it should be possible to represent each data point as

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