Manifold integration is a combined concept of manifold learning and data integration

Data integration

Data integration involves combining data residing in different sources and providing users with a unified view of these data.This process becomes significant in a variety of situations, which include both commercial and scientific domains...

, 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

Data set

A data set is a collection of data, usually presented in tabular form. Each column represents a particular variable. Each row corresponds to a given member of the data set in question. Its values for each of the variables, such as height and weight of an object or values of random numbers. Each...

. 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.

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