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The local linear embedding algorithm (LLE) is a widely used nonlinear dimension-reducing algorithm. However, its large sample properties are still not well understood. In this paper we present new theoretical results for LLE based on the way that LLE computes its weight vectors. We show that LLE's weight vectors are computed from the high-dimensional neighborhoods and are thus highly sensitive to noise. We also demonstrate that in some cases LLE's output converges to a linear projection of thedoi:10.1080/10618600.2012.679221 fatcat:llywresyt5avjbfsyvqkqushfe