Inference of topological and geometric attributes of a hidden manifold from
its point data is a fundamental problem arising in many scientific studies and
engineering applications. In this paper we present an algorithm to compute a
set of loops from a point data which approximates a {\em shortest} basis of the
one dimensional homology group $\homo(M)$ of the sampled manifold $M$. Previous
results addressed the issue of computing the rank of the homology groups from
point data, but there is no result on approximating the shortest basis of a
manifold from its point sample. In arriving our result, we also present a
polynomial time algorithm for computing a shortest basis of $\homo(\KK)$ for
any finite simplicial complex $\KK$ embedded in Euclidean space.