Lizard Brain: Tackling Locally Low-Dimensional Yet Globally Complex Organization of Multi-Dimensional Datasets - Bac, Jonathan; Zinovyev, Andrei (Frontiers in Neurorobotics, 2020)
Machine learning deals with datasets characterized by very high dimensionality. However, in many cases, the intrinsic dimensionality of the datasets is surprisingly low. Multidimensional data point clouds can be effectively located in the vicinity of subspaces possessing locally small dimensionality, but having a globally complicated organization which is sometimes difficult to represent with regular mathematical objects (such as manifolds). We review modern machine learning approaches for extracting low-dimensional geometries from multi-dimensional data and their applications in various scientific fields.