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 ...

Nonlinear dimensionality reduction is the problem of retrieving a low-dimensional representation of a manifold that is embedded in a high-dimensional observation space. Locally Linear Embedding (LLE), a prominent dimensionality reduction technique is an unsupervised algorithm; as such, it is not possible to guide it toward modes of variability that may be of particular interest. This paper prop...

The locally linear embedding (LLE) algorithm can be used to discover a low-dimensional subspace from face manifolds. However, it does not mean that a good accuracy can be obtained when classifiers work under the subspace. Based on the proposed ULLELDA (Unified LLE and linear discriminant analysis) algorithm, an ensemble version of the ULLELDA (En-ULLELDA) is proposed by perturbing the neighbor ...

Abstract Locally linear embedding (LLE) is a highly popular manifold learning and nonlinear dimensionality reduction technique. However, the neighborhood parameters of the algorithm are sensitive to the mapping results and difficult to choose. In this paper, we propose an adaptive neighborhood selection method based on Silhouette index for LLE algorithm. From the point of the cluster quality of...

This paper describes a novel exemplar-based spectral conversion (SC) system developed by the AST (Academia Sinica, Taipei) team for the 2016 voice conversion challenge (vcc2016). The key feature of our system is that it integrates the locally linear embedding (LLE) algorithm, a manifold learning algorithm that has been successfully applied for the super-resolution task in image processing, with...

Locally Linear Embedding (LLE) is a widely used non-linear dimensionality reduction (NLDR) method that projects multi-dimensional data into a low-dimensional embedding space while attempting to preserve object adjacencies from the original high-dimensional feature space. A limitation of LLE, however, is the presence of free parameters, changing the values of which may dramatically change the lo...

Many problems in information processing involve some form of dimensionality reduction. Here we describe locally linear embedding (LLE), an unsupervised learning algorithm that computes low dimensional, neighborhood preserving embeddings of high dimensional data. LLE attempts to discover nonlinear structure in high dimensional data by exploiting the local symmetries of linear reconstructions. No...

In this paper, we propose a novel linear subspace learning algorithm called Flexible Orthogonal Neighborhood Preserving Embedding (FONPE), which is a linear approximation of Locally Linear Embedding (LLE) algorithm. Our novel objective function integrates two terms related to manifold smoothness and a flexible penalty defined on the projection fitness. Different from Neighborhood Preserving Emb...

Recently manifold learning algorithm for dimensionality reduction attracts more and more interests, and various linear and nonlinear, global and local algorithms are proposed. The key step of manifold learning algorithm is the neighboring region selection. However, so far for the references we know, few of which propose a generally accepted algorithm to well select the neighboring region. So in...