Consistency Analysis for the Doubly Stochastic Dirichlet Process

This technical report proves components consistency for the Doubly Stochastic Dirichlet Process with exponential convergence of posterior probability. We also present the fundamental properties for DSDP as well as inference algorithms. Simulation toy experiment and real-world experiment results for single and multi-cluster also support the consistency proof. This report is also a support document for the paper "Computationally Efficient Hyperspectral Data Learning Based on the Doubly Stochastic Dirichlet Process".