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  "body": "\n## Summary\n\nMultidimensional scaling places objects as points in a low-dimensional space so that their distances match given dissimilarities as well as possible.\nIts input is only a table of pairwise dissimilarities, not coordinates.\nClassical multidimensional scaling does this exactly when the dissimilarities are [[Euclidean distances|0NPPGHQNXQ]], using the [[eigenvectors|0N6960W0BV]] of a centred matrix.\nIt is used to visualise similarity data in two or three dimensions.\n\n## Explanations\n\n### L1 human\n\nGiven only the road distances between cities, one can try to redraw the map.\nMultidimensional scaling does exactly this: it finds points in the plane whose distances are close to the given ones.\nThe map comes out correct up to shifting, turning and mirroring, since these do not change distances.\nFor three points with distances $1$, $1$ and $2$, it puts them on a line at $-1$, $0$ and $1$.\n",
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