Sentence examples for manifold structures in from inspiring English sources

Recently, many studies have shown that naturally occurring data may reside on or near manifold structures in ambient space.

An effective image representation method, namely, Laplacian regularized uncorrelated tensor representation, is developed to explicitly consider the manifold structures in the high-order image space.

In this paper, we propose an unsupervised method with Laplacian regularized uncorrelated tensor representation to explicitly consider manifold structures in the high-order image space.

Moreover, as natural images usually generate an enormous size of high-dimensional data in annotation applications, an efficient descriptor based on Laplacian regularized uncorrelated tensor representation is proposed for explicitly exploiting the manifold structures in the high-order image space.

By studying the intrinsic manifold structures in the space of image patches, this paper proposes an approach for representing and recognizing objects with a massive number of local image patches (e.g. 17×17 pixels).

In this paper, we propose a novel multiple graph regularized generative model to exploit the manifold structure in multiple views.

The Kulis [58] method has comparable results to the baseline method (possibly due to some uniqueness in the data set) and the Wang [121] method slightly outperforms the baseline method (possibly due to a weak manifold structure in the data set).

Lie groups (in honor of Sophus Lie) are groups which also have a manifold structure, i.e. they are spaces looking locally like some Euclidean space of the appropriate dimension.

First, the manifold regularization mechanism, adapted from the Laplacian support vector machine (LapSVM), is adopted to mine the manifold structure embedded in all training data, especially in numerous label-unknown data.

Assume that M is the manifold structure embedded in R m Euclidean space.

I-ESLLE can not only acquire the low-dimensional intrinsic manifold structure embedded in the high-dimensional input space, but also can deal with new fault samples in an iterative and batch model.