Ofer Neiman
Dimensionality reduction: theoretical perspective on practical measures
Yair Bartal, Nova Fandina, Ofer Neiman
Dimensionality reduction plays a central role in real world applications for Machine Learning, among many fields. In particular, metric dimensionality reduction, where data from a general metric is mapped into low dimensional space, is often used as a first step before applying machine learning algorithms. In almost all these applications the quality of the embedding is measured by various average case criteria. Metric dimensionality reduction has also been studied in Math and TCS, within the extremely fruitful and influential field of metric embedding. Yet, the vast majority of theoretical research has been devoted to analyzing the worst case behavior of embeddings, and therefore has little relevance to practical settings.