One of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data. We consider the problem of constructing a representation for data lying on a low-dimensional manifold embedded in a high-dimensional space. Drawing

Many areas of science

Dimensionality reduction studies methods that effectively reduce data dimensionality for efficient data process-ing tasks such as pattern recognition, machine learning, text retrieval, and data mining. We introduce the field of dimensionality reduction by dividing it into two parts: feature

reduction of such higher-dimensional instanton equations. In the particular case of an 8-dimensional Riemannian manifold M with Spin(7)-holonomy, the instanton equations require the vanishing of the curvature component contained in a 7-dimensional subbundle of Λ2T∗M. After a short review

A dimensionality reduction technique for enhancing information context.

We investigate the use of dimensionality reduction to improve performance for a new class of data analysis software called "recommender systems". Recommender systems apply knowledge discovery techniques to the problem of making product recommendations during a live customer interaction

Similarity search in large time series databases has attracted much research interest recently. It is a difficult problem because of the typically high dimensionality of the data.. The most promising solutions' involve performing dimensionality reduction on the data, then indexing the reduced

reduction for energies with linear growth involving the bending moment

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