 When estimating intrinsic dimension, however, a slightly broader definition based on manifold dimension is often used, where a representation in the intrinsic dimension does only need to exist locally.Such intrinsic dimension estimation methods can thus handle data sets with different intrinsic dimensions in different parts of the data set.The intrinsic dimension can be used as a lower bound of what dimension it is possible to compress a data set into through dimension reduction, but it can also be used as a measure of the complexity of the data set or signal.