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Figure 1 | BMC Bioinformatics

Figure 1

From: CFMDS: CUDA-based fast multidimensional scaling for genome-scale data

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 || ยท || 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.

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