Non-parametric dimensionality reduction techniques, such as t-SNE and UMAP, are proficient in providing visualizations for fixed or static datasets , but they cannot incrementally map and insert new data points into existing data visualizations . We present Self-Organizing Nebulous Growths (SONG), a parametric nonlinear dimensionality reduction technique that supports incremental data visualization, i.e., incremental addition of new data while preserving the structure of the existing visualization. In addition, SONG is capable of handling new data increments  no matter whether they are similar or heterogeneous to the existing observations in distribution. We test SONG on a variety of real and simulated datasets. The results show that SONG is superior to Parametric t-SNE, t-SNE and UMAP in incremental data visualization. Specifically, for heterogeneous increments, SONG improves over Parametric t-SNE by 14.98 \% on the Fashion MNIST dataset and 49.73\% on the MNIST dataset regarding the cluster quality measured by the Adjusted Mutual Information scores. On similar or homogeneous increments, the improvements are 8.36\% and 42.26\% respectively. Furthermore, even in static cases , SONG performs better or comparable to UMAP, and superior to t-SNE. We also demonstrate that the algorithmic foundations of SONG render it more tolerant to noise compared to UMAP and t-SNE, thus providing greater utility for data with high variance or high mixing of clusters  or noise.
Non-parametric dimensionality reduction techniques, such as t-SNE and UMAP, are proficient in providing visualizations for datasets of fixed sizes. However, they cannot incrementally map and insert new data points into an already provided data visualization . We present Self-Organizing Nebulous Growths (SONG), a parametric nonlinear dimensionality reduction technique that supports incremental data visualization, i.e., incremental addition of new data while preserving the structure of the existing visualization. In addition, SONG is capable of handling new data increments , no matter whether they are similar or heterogeneous to the already observed data distribution. We test SONG on a variety of real and simulated datasets. The results show that SONG is superior to Parametric t-SNE, t-SNE and UMAP in incremental data visualization. Specifically, for heterogeneous increments, SONG improves over Parametric t-SNE by 14.98 \% on the Fashion MNIST dataset and 49.73\% on the MNIST dataset regarding the cluster quality measured by the Adjusted Mutual Information scores. On similar or homogeneous increments, the improvements are 8.36\% and 42.26\% respectively. Furthermore, even when the above datasets are presented all at once , SONG performs better or comparable to UMAP, and superior to t-SNE. We also demonstrate that the algorithmic foundations of SONG render it more tolerant to noise compared to UMAP and t-SNE, thus providing greater utility for data with high variance , high mixing of clusters , or noise.
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in static cases
when the above datasets are presented all at once
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