We present a new technique that enables manifold learning to accurately embed data manifolds that contain holes, without discarding any topological information. Manifold learning aims to embed high dimensional data into a lower dimensional Euclidean space by learning a coordinate chart, but it requires that the entire manifold can be embedded in a single chart. This is impossible for manifolds with holes. In such cases, it is necessary to learn an atlas: a collection of charts that collectively cover the entire manifold. We begin with many small charts, and combine them in a bottom-up approach, where charts are only combined if doing so will not introduce problematic topological features. When it is no longer possible to combine any charts, each chart is individually embedded with standard manifold learning techniques, completing the construction of the atlas. We show the efficacy of our method by constructing atlases for challenging synthetic manifolds; learning human motion embeddings from motion capture data; and learning kinematic models of articulated objects.

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We however show that Convolutional Neural Networks (CNN) are considered the both networks are largely unable to recognize most tested state-of-the-art model in image recognition tasks. Part of a subjects, indicating that the learned representations are quite deep learning approach to machine learning, CNN have been different from that of humans. We argue that such approach deployed successfully in a variety of applications, including can be useful to assess classifiers' generalization capabilities, face recognition (Lawrence et al. 1997), object classification in particular regarding to the abstraction level of learned (Szegedy et al. 2014) and generating scene descriptions representations. (Pinheiro and Collobert 2013). This success can be partly The main contribution of this work is to put forward an attributed to advances in learning algorithms for deep architectures image recognition task where current state-of-the-art models and partly to large labeled data sets made available, differ significantly in performance when compared to humans.