Figure 1

Process of divide-and-conquer mode. First, a dissimilarity matrix is randomly decomposed into p submatrices along the diagonal, D₁, ..., D _p . Second, s objects are sampled from each of the submatrices. Then, the sampled objects are merged to construct a new dissimilarity submatrix M _align . The one-shot MDS method is applied to D₁, ..., D _p as well as M _align . The resulting coordinates are dMDS₁, ..., dMDS _p as well as mMDS, respectively. After that, the objects sampled from each of D₁, ..., D _p are extracted from the resulting coordinates matrices, comprising subdMDS₁, ..., subdMDS _p as well as mMDS₁, ..., mMDS _p . For each pair, subdMDS _i and mMDS _i (i = 1, 2, ..., p), a linear transformation matrix A _i is obtained by minimizing ||A _i subdMDS _i - mMDS _i ||, where || · || denotes L² norm. The linearly transformed objects new dMDS _i on a reduced dimension are obtained by A _i dMDS _i . Finally, new dMDS₁, ..., new dMDS _p are combined to produce the MDS result for the entire objects.