Manifold integration

Manifold integration

Manifold integration is a combined concept of manifold learning and data integration, or an extension of manifold learning for multiple measurements.


Various manifold learning methods have been developed. However, they consider only one dissimilarity matrix corresponding to one kernel matrix, which represents one manifold of the data set. In practice, however, we use multiple sensors at a time, and each sensor generates data set on one manifold. In such a case, manifold integration is a desirable task, combining these dissimilarity matrices into a compromise matrix that faithfully reflects multiple sensory information on one integrated manifold.

For more information, see [1]

Notes

  1. ^ H. Choi, S. Choi and Y. Choe, "Manifold Integration with Markov Random Walks," in Proc. 23rd Association for the Advancement of Artificial Intelligence (AAAI-08), Chicago, Illinois, July 13–17, 2008.

Wikimedia Foundation. 2010.

Игры ⚽ Нужен реферат?

Look at other dictionaries:

  • Integration — In te*gra tion ([i^]n t[ e]*gr[=a] sh[u^]n), n. [L. integratio a renewing, restoring: cf. F. int[ e]gration.] [1913 Webster] 1. The act or process of making whole or entire. [1913 Webster] 2. (Math.) The operation of finding the primitive… …   The Collaborative International Dictionary of English

  • Differentiable manifold — A nondifferentiable atlas of charts for the globe. The results of calculus may not be compatible between charts if the atlas is not differentiable. In the middle chart the Tropic of Cancer is a smooth curve, whereas in the first it has a sharp… …   Wikipedia

  • Density on a manifold — In mathematics, and specifically differential geometry, a density is a spatially varying quantity on a differentiable manifold which can be integrated in an intrinsic manner. Abstractly, a density is a section of a certain trivial line bundle,… …   Wikipedia

  • Addition — is the mathematical process of putting things together. The plus sign + means that two numbers are added together. For example, in the picture on the right, there are 3 + 2 apples meaning three apples and two other apples which is the same as… …   Wikipedia

  • definite integral — Integration In te*gra tion ([i^]n t[ e]*gr[=a] sh[u^]n), n. [L. integratio a renewing, restoring: cf. F. int[ e]gration.] [1913 Webster] 1. The act or process of making whole or entire. [1913 Webster] 2. (Math.) The operation of finding the… …   The Collaborative International Dictionary of English

  • multiple integral — Integration In te*gra tion ([i^]n t[ e]*gr[=a] sh[u^]n), n. [L. integratio a renewing, restoring: cf. F. int[ e]gration.] [1913 Webster] 1. The act or process of making whole or entire. [1913 Webster] 2. (Math.) The operation of finding the… …   The Collaborative International Dictionary of English

  • Differential form — In the mathematical fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates. Differential forms provide a better[further explanation needed] definition… …   Wikipedia

  • Stokes' theorem — For the equation governing viscous drag in fluids, see Stokes law. Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Differential calculus  Derivative Change of variables Implicit differentiatio …   Wikipedia

  • Integral — This article is about the concept of integrals in calculus. For the set of numbers, see integer. For other uses, see Integral (disambiguation). A definite integral of a function can be represented as the signed area of the region bounded by its… …   Wikipedia

  • mathematics — /math euh mat iks/, n. 1. (used with a sing. v.) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. 2. (used with a sing. or pl. v.) mathematical procedures,… …   Universalium

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”