Figure 1
**Process of divide-and-conquer mode**. First, a dissimilarity matrix is randomly decomposed into *p* submatrices along the diagonal, **D**
_{1}, ..., **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 **D**
_{1}, ..., **D**
_{
p
} as well as **M**
_{
align
}. The resulting coordinates are **dMDS**
_{1}, ..., **dMDS**
_{
p
} as well as **mMDS**, respectively. After that, the objects sampled from each of **D**
_{1}, ..., **D**
_{
p
} are extracted from the resulting coordinates matrices, comprising sub**dMDS**
_{1}, ..., sub**dMDS**
_{
p
} as well as **mMDS**
_{1}, ..., **mMDS**
_{
p
}. For each pair, sub**dMDS**
_{
i
} and **mMDS**
_{
i
} (*i* = 1, 2, ..., *p*), a linear transformation matrix **A**
_{
i
} is obtained by minimizing ||**A**
_{
i
}sub**dMDS**
_{
i
} - **mMDS**
_{
i
}||, where || · || denotes *L*
^{2} norm. The linearly transformed objects *new*
**dMDS**
_{
i
} on a reduced dimension are obtained by **A**
_{
i
}
**dMDS**
_{
i
}. Finally, *new*
**dMDS**
_{1}, ..., *new*
**dMDS**
_{
p
} are combined to produce the MDS result for the entire objects.