  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 that presumably sample a smooth manifold
$M\subset \mathbb{R}^d$. These loops approximate a {\em shortest} basis of the
one dimensional homology group $H_1(M)$ over coefficients in finite field
$\mathbb{Z}_2$. 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
$H_1(K)$ for any finite {\em simplicial complex} $K$ whose edges have
non-negative weights.
