Stochastic Neighbor Embedding separates well-separated clusters
Stochastic Neighbor Embedding and its variants are widely used dimensionality reduction techniques -- despite their popularity, no theoretical results are known. We prove that the optimal SNE embedding of well-separated clusters from high dimensions to any Euclidean space R^d manages to successfully separate the clusters in a quantitative way. The result also applies to a larger family of methods including a variant of t-SNE.
Code (0)
등록된 구현이 없습니다.
Tasks
Dimensionality ReductionSimilar Papers 제목 키워드 기반
Stochastic Neighbor Embedding
We describe a probabilistic approach to the task of placing objects, de- scribed by high-dimensional vectors or by pairwise dissimilarities, in a low-dimensional space in a way that preserves neighbor identities. A Gauss…
Dimensionality ReductionObjectClustering with t-SNE, provably
t-distributed Stochastic Neighborhood Embedding (t-SNE), a clustering and visualization method proposed by van der Maaten & Hinton in 2008, has rapidly become a standard tool in a number of natural sciences. Despite its …
ClusteringSPI-Optimizer: an integral-Separated PI Controller for Stochastic Optimization
To overcome the oscillation problem in the classical momentum-based optimizer, recent work associates it with the proportional-integral (PI) controller, and artificially adds D term producing a PID controller. It suppres…
Stochastic OptimizationEquilibrium Distribution for t-Distributed Stochastic Neighbor Embedding with Generalized Kernels
T-distributed stochastic neighbor embedding (t-SNE) is a well-known algorithm for visualizing high-dimensional data by finding low-dimensional representations. In this paper, we study the convergence of t-SNE with genera…
DR-SNE: Density-Regularized Stochastic Neighbor Embedding
Dimensionality-reduction methods such as t-SNE preserve local neighborhood structure but can substantially distort the local distribution of data. We introduce Density-Regularized Stochastic Neighbor Embedding (DR-SNE), …
Dimensionality ReductionAnomaly Detection