FINDING EXPLICIT SOLUTIONS FOR LINEAR REGRESSION WITHOUT CORRESPONDENCES BASED ON REARRANGEMENT INEQUALITY

A least squares problem without correspondences is expressed as the following optimization: min ∥Ax − Πy∥, Π∈P_m, x∈ℝn where A ∈ ℝ^m×n and y ∈ ℝ^m are given. In general, solving such an optimization problem is highly challenging. In this paper we use the rearrangement inequalities to find the closed form of solutions for certain cases. Moreover, despite the stringent constraints, we successfully tackle the nonlinear least squares problem without correspondences by leveraging rearrangement inequalities.