Dimensionality reduction as a non-cooperative game

A novel non-cooperative game theory-based approach for dimensionality reduction is proposed. We regard the sample elements in a higher-dimensional space as players in a game each of which has its strategy. A set of these strategies was implemented as an embedding of dimensionality reduction, which maps the sample elements into lower-dimensional spaces. Based on the theory of non-cooperative $N$-player games, we show the existence of Nash equilibria. We also provide an algorithm that yields Nash equilibrium based on the theory of nonlinear functional analysis.