Neighbor embedding XOM for dimension reduction and visualization

Stochastic neighbor embedding (SNE) for dimension reduction and visualization using arbitrary divergences

We present a systematic approach to the mathematical treatment of the t-distributed stochastic neighbor embedding (t-SNE) and the stochastic neighbor embedding (SNE) method. This allows an easy adaptation of the methods or exchange of their respective modules. In particular, the divergence which measures the difference between probability distributions in the original and the embedding space ca...

Mathematical Foundations of the Self Organized Neighbor Embedding (SONE) for Dimension Reduction and Visualization

Abstract. In this paper we propose the generalization of the recently introduced Neighbor Embedding Exploratory Observation Machine (NEXOM) for dimension reduction and visualization. We provide a general mathematical framework called Self Organized Neighbor Embedding (SONE). It treats the components, like data similarity measures and neighborhood functions, independently and easily changeable. ...

Mathematical Foundations of Self Organized Neighbor Embedding (SONE) for Dimension Reduction and Visualization

In this paper we propose the generalization of the recently introduced Neighbor Embedding Exploratory Observation Machine (NE-XOM) for dimension reduction and visualization. We provide a general mathematical framework called Self Organized Neighbor Embedding (SONE). It treats the components, like data similarity measures and neighborhood functions, independently and easily changeable. And it en...

University of Groningen Mathematical Foundations of the Self Organized Neighbor Embedding ({SONE}) for Dimension Reduction and Visualization

Scalable Optimization of Neighbor Embedding for Visualization

Neighbor embedding (NE) methods have found their use in data visualization but are limited in big data analysis tasks due to their O(n) complexity for n data samples. We demonstrate that the obvious approach of subsampling produces inferior results and propose a generic approximated optimization technique that reduces the NE optimization cost to O(n log n). The technique is based on realizing t...