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

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

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...

Doubly supervised embedding based on class labels and intrinsic clusters for high-dimensional data visualization

Visualization of data can assist decision-making processes by presenting the underlying information in a perceptible manner. Many dimension reduction techniques have been proposed to generate faithful visualization snapshots given high-dimensional data. When class labels associated with the data are already provided, supervised dimension reduction methods, which utilize such pre-given label inf...

Model Based Method for Determining the Minimum Embedding Dimension from Solar Activity Chaotic Time Series

Predicting future behavior of chaotic time series system is a challenging area in the literature of nonlinear systems. The prediction's accuracy of chaotic time series is extremely dependent on the model and the learning algorithm. On the other hand the cyclic solar activity as one of the natural chaotic systems has significant effects on earth, climate, satellites and space missions. Several m...