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In many data analysis tasks, one is often confronted with very high dimensional data. The manifold assumption, which states that the data is sampled from a submanifold embedded in much higher dimensional Euclidean space, has been widely adopted by many researchers. In the last 15 years, a large number of manifold learning algorithms have been proposed. Many of them rely on the evaluation of the geometrical and topological of the data manifold. In this paper, we present a review of these methodsdoi:10.1186/s40535-015-0006-6 fatcat:zzbifclg5nf7tkqxxjap3bkxsq