Sentence examples for data manifolds from inspiring English sources

In particular, we design a low complexity solution that is able to exploit the properties of the data manifolds with a graph-based algorithm.

Manifold regularization (MR) is a promising regularization framework for semi-supervised learning, which introduces an additional penalty term to regularize the smoothness of functions on data manifolds and has been shown very effective in exploiting the underlying geometric structure of data for classification.

Specifically, we model the data manifold using a similarity graph with local and geometrical consistency properties.

The significance of our research is fourfold: 1) The MPCJRF is an underlying adjustment, with respect to the pairwise constraints, to the graph Laplacian enlisted for approximating the potential data manifold.

This type of adjustment plays the correction role, as an unbiased estimation of the data manifold is difficult to obtain, whereas the pairwise constraints, converted from the given labels, have an overall high confidence level.

In this paper, combining the ideas of MVU and Laplacian eigenmaps, we propose a new nonlinear dimensionality reduction method called distinguishing variance embedding (DVE), which unfolds the data manifold by maximizing the global variance subject to the proximity relation preservation constraint originated in Laplacian eigenmaps.

Once acquiring the vanishing component, the natural feature of a data manifold pattern can be captured.

Geometrically, this is equivalent to thinking of a data manifold or subspace.

D. Cai at al. [31] study the locality sensitive discriminant analysis (LSDA) method, which utilizes local geometry structure of the data manifold and discriminant information at the same time.

The pre-formed clusters - the model of the data manifold - in the SOM help prevent the learning of inconsistent labels and thus greatly support accurate learning of class labels in the supervised phase.

Livni et al. put forward a vanishing component analysis method with stable values, i.e., the VCA method, to solve the generator (i.e., vanishing component) for vanishing ideal of fitting data manifold pattern.