Machine learning deals with datasets characterized by high dimensionality. However, in many cases, the intrinsic dimensionality of the datasets is surprisingly low. For example, the dimensionality of a robot's perception space can be large and multi-modal but its variables can have more or less complex non-linear interdependencies. Thus multidimensional data point clouds can be effectively located in the vicinity of principal varieties 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.

中文翻译：

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蜥蜴脑：解决局部低维但全局复杂的多维数据集组织。


机器学习处理具有高维特征的数据集。然而，在许多情况下，数据集的内在维度低得惊人。例如，机器人感知空间的维度可能很大并且是多模态的，但其变量可能具有或多或少复杂的非线性相互依赖性。因此，多维数据点云可以有效地位于具有局部小维度但具有全局复杂组织的主要品种附近，该组织有时难以用常规数学对象（例如流形）表示。我们回顾了从多维数据中提取低维几何的现代机器学习方法及其在各个科学领域的应用。