Choice of weights for the Laplacian Eigenmaps algorithm
Recall the definition he makes for the graph Laplacian earlier, $L = D -W $. Now consider the map in the RHS parentheses which I'll call $L^*$,
$$ L^*f(x_i) := f(x_i) - \alpha \sum_{x_j, ||x_i-x_j||&lt;\epsilon}e^{-\frac{||x_i-x_j||^2}{4t}}f(x_j).$$
The suggested weight matrix definition is natural because it lets us write
$$ L^* := I - D^{-1}W. $$ Here's a reference to a related paper with some easy to read exposition. Hope this helps!