A technique for clustering data by common attribute values involves grouping rows and columns of a binary matrix to make the minimum number of submatrices all 1.s. As binary matrices can be viewed as adjacency matrices of bipartite graphs, the problem is equivalent to partitioning a bipartite graph into the smallest number of complete bipartite sub-graphs (commonly called .bicliques.). We show that the Biclique Partition Problem (BPP) does not have a polynomial time a-approximation algorithm, for any a = 1, unless P=NP. We also show that the Biclique Partition Problem, restricted to whether at most k bicliques are sufficient (i.e. BPP(k)) for each positive integer k, has a polynomial time 2-approximation algorithm. In addition, we give an O(VE) time algorithm and BPP(2), and an O(V) algorithm to find an optimum biclique partition of trees.