Statistical Embedding: Beyond Principal Components

There has been an intense recent activity in embedding of very high-dimensional and nonlinear data structures, much it the science machine learning literature. We survey this four parts. In first part, we cover methods such as principal curves, multidimensional scaling, local linear methods, ISOMAP, graph-based diffusion mapping, kernel based random projections. The second part is concerned with topological particular mapping properties into persistence diagrams Mapper algorithm. Another type sets a tremendous growth network data. task considered three how to embed vector space moderate dimension make amenable traditional techniques cluster classification techniques. Arguably, where contrast between algorithmic statistical modeling, represented by so-called stochastic block model, at its greatest. paper, discuss pros cons for two approaches. final deals R2, that is, visualization. Three are presented: t-SNE, UMAP LargeVis on parts one, three, respectively. illustrated compared simulated sets; one consisting triplet noisy Ranunculoid networks increasing complexity generated models types nodes.