Decentralized Estimation Using Learning Vector Quantization

A decentralized estimation system consists of n distributed data sources S₁... S_n and a fusion center. The data sources produce multivariate random vectors X₁... X_n that are transmitted to the fusion center in the form of messages Z₁... Z_n, Z_i = alpha₁(X₁). Due to communication constraints, Z_i is a discrete variable with cardinality M_i represented as an integer from a set {1...M_i}. At the fusion center, the goal is to estimate the conditional expectation of unobserved variable Y, E(Y|x₁... x_n), by fusion function h(z₁... z_n). The challenge is to find quantization functions alpha₁... alpha_n and fusion function h such that the estimation error is minimized under given communication constraints.