Machine learning models are successfully being used for problems in language, vision, and biology that have millions or tens of millions of features. A common approach to alleviating the complexity of high dimensional feature spaces is to penalize the L1 or L2 norm of the parameter vector. We may be able to design more effective regularizers, though, if we possess external information about whi...

Methods and properties regarding the linear perturbations are discussed for some spatially closed (vacuum) solutions of Einstein’s equation. The main focus is on two kinds of spatially locally homogeneous solution; one is the Bianchi III (Thurston’s H × R) type, while the other is the Bianchi II (Thurston’s Nil) type. With a brief summary of previous results on the Bianchi III perturbations, as...

Locally linear embedding is an effective nonlinear dimensionality reduction method for exploring the intrinsic characteristics of high dimensional data. This paper proposes a new manifold learning method, which is based on locally linear embedding and growing neural gas and is termed growing locally linear embedding (GLLE). GLLE overcomes the major limitations of the original locally linear emb...

A novel method based on the local nonlinear mapping is presented in this research. The method is called Locally Linear Discriminate Embedding LLDE . LLDE preserves a local linear structure of a high-dimensional space and obtains a compact data representation as accurately as possible in embedding space low dimensional before recognition. For computational simplicity and fast processing, Radial ...

Many areas of science depend on exploratory data analysis and visualization. The need to analyze large amounts of multivariate data raises the fundamental problem of dimensionality reduction: how to discover compact representations of high-dimensional data. Here, we introduce locally linear embedding (LLE), an unsupervised learning algorithm that computes low-dimensional, neighborhood-preservin...

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...

Kernelized Support Vector Machines (SVM) have gained the status of off-the-shelf classifiers, able to deliver state of the art performance on almost any problem. Still, their practical use is constrained by their computational and memory complexity, which grows super-linearly with the number of training samples. In order to retain the low training and testing complexity of linear classifiers an...

We present a novel discriminant analysis learning method which is applicable to non-linear data structures. The method can deal with pattern classification problems which have a multi-modal distribution for each class and samples of other classes may be closer to a class than those of the class itself. Conventional linear discriminant analysis (LDA) and LDA mixture model can not solve this line...

We study the problem of image denoising where images are assumed to be samples from low dimensional (sub)manifolds. We propose the algorithm of locally linear denoising. The algorithm approximates manifolds with locally linear patches by constructing nearest neighbor graphs. Each image is then locally denoised within its neighborhoods. A global optimal denoising result is then identified by ali...

www.sciencemag.org (this information is current as of July 17, 2007 ): The following resources related to this article are available online at http://www.sciencemag.org/cgi/content/full/290/5500/2323 version of this article at: including high-resolution figures, can be found in the online Updated information and services, found at: can be related to this article A list of selected additional ar...