An Introduction to Locally Linear Embedding.
Locally-linear embedding. Locally-Linear Embedding (LLE) was presented at approximately the same time as Isomap. It has several advantages over Isomap, including faster optimization when implemented to take advantage of sparse matrix algorithms, and better results with many problems. LLE also begins by finding a set of the nearest neighbors of each point.
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Principal component analysis, as one of the most popular methods used, is optimal when the data points reside on a linear subspace. Nevertheless, it may fail to preserve the local structure if the data reside on some nonlinear manifold, which is indisputably important in many real applications, especially when nearest-neighbor search is involved.
Component Analysis), Locally Linear Embedding (LLE) is a method of non-linear dimensionality reduction introduced by Sam T. Roweis and Lawrence K. Saul(2). This method recovers global nonlinear.
As we can see from subfigures (b) of Fig. 2, Fig. 3, Fig. 4, LLE cannot preserve well the local geometry of the data manifolds in the embedding space when there are outliers in the data.In fact, in the presence of outliers, the K nearest neighbors of a (clean) data point on the manifold may no longer lie on a locally linear patch of the manifold, leading to a small bias to the reconstruction.
Francesco Camastra Alessandro Vinciarelli Machine Learning for Audio, Image and Video Analysis SPIN Springer’s internal project number October 5, 2007.
Rdimtools: Dimension Reduction and Estimation Methods. Rdimtools is an R package for dimension reduction, manifold learning, and intrnsic dimension estimation methods.