Random projections and random sketches have emerged as an important tool for high dimensional and big data analysis due to their scalability. In some dimension reduction problems (supervised and unsupervised), each random sketch results in a point on a matrix manifold, and multiple sketches lead to multiple points on manifold. To sum up these multiple points for a final answer to the original big data problem, we need to study robust estimation of sample mean on matrix manifold. In this talk I will introduce a minimum matrix divergence criterion for sample mean estimation and a geometric algorithm based on gradient geodesic flow for solving the estimation. Some theoretical properties as well as numerical examples will be presented.