Manifold learning

Popular learning (manifold learning) It is a kind of dimensionality reduction method that draws lessons from the popular concept of topology .“ manifold ” Is a space which is locally homeomorphic with a Euclidean space , In other words , It has the properties of European Space locally , Can use Euclidean distance to calculate distance , This brings great inspiration to the dimensionality reduction method ： If low dimensional fashion is embedded into high dimensional space , The distribution of data samples in high-dimensional space seems very complex , But it still has the properties of European Space locally , therefore , It is easy to establish the relationship of reduced dimension mapping locally , Then try to extend the local mapping relation to the global mapping relation , When the dimension is reduced to two or three dimensions , Be able to visually display the data , So popular learning can also be used for visualization .