Multi-Dimensional Scaling (also as known as Principal Coordinate Analysis) by Python

cmdscale.py

import matplotlib.pyplot as plt
import numpy as np
from sklearn import manifold

cities = "Athens Barcelona Brussels Calais Cherbourg Cologne Copenhagen Geneva Gibraltar Hamburg HookOfHolland Lisbon Lyons Madrid Marseilles Milan Munich Paris Rome Stockholm Vienna".split(" ")
d = np.array([
    # from eurodist dataset: https://rstudio-pubs-static.s3.amazonaws.com/221886_5c57ad0f5ff546e8af6386162f29fabc.html
    [   0, 3313, 2963, 3175, 3339, 2762, 3276, 2610, 4485, 2977, 3030, 4532, 2753, 3949, 2865, 2282, 2179, 3000,  817, 3927, 1991],
    [3313,    0, 1318, 1326, 1294, 1498, 2218,  803, 1172, 2018, 1490, 1305,  645,  636,  521, 1014, 1365, 1033, 1460, 2868, 1802],
    [2963, 1318,    0,  204,  583,  206,  966,  677, 2256,  597,  172, 2084,  690, 1558, 1011,  925,  747,  285, 1511, 1616, 1175],
    [3175, 1326,  204,    0,  460,  409, 1136,  747, 2224,  714,  330, 2052,  739, 1550, 1059, 1077,  977,  280, 1662, 1786, 1381],
    [3339, 1294,  583,  460,    0,  785, 1545,  853, 2047, 1115,  731, 1827,  789, 1347, 1101, 1209, 1160,  340, 1794, 2196, 1588],
    [2762, 1498,  206,  409,  785,    0,  760, 1662, 2436,  460,  269, 2290,  714, 1764, 1035,  911,  583,  465, 1497, 1403,  937],
    [3276, 2218,  966, 1136, 1545,  760,    0, 1418, 3196,  460,  269, 2971, 1458, 2498, 1778, 1537, 1104, 1176, 2050,  650, 1455],
    [2610,  803,  677,  747,  853, 1662, 1418,    0, 1975, 1118,  895, 1936,  158, 1439,  425,  328,  591,  513,  995, 2068, 1019],
    [4485, 1172, 2256, 2224, 2047, 2436, 3196, 1975,    0, 2897, 2428,  676, 1817,  698, 1693, 2185, 2565, 1971, 2631, 3886, 2974],
    [2977, 2018,  597,  714, 1115,  460,  460, 1118, 2897,    0,  550, 2671, 1159, 2198, 1479, 1238,  805,  877, 1751,  949, 1155],
    [3030, 1490,  172,  330,  731,  269,  269,  895, 2428,  550,    0, 2280,  863, 1730, 1183, 1098,  851,  457, 1683, 1500, 1205],
    [4532, 1305, 2084, 2052, 1827, 2290, 2971, 1936,  676, 2671, 2280,    0, 1178,  668, 1762, 2250, 2507, 1799, 2700, 3231, 2937],
    [2753,  645,  690,  739,  789,  714, 1458,  158, 1817, 1159,  863, 1178,    0, 1281,  320,  328,  724,  471, 1048, 2108, 1157],
    [3949,  636, 1558, 1550, 1347, 1764, 2498, 1439,  698, 2198, 1730,  668, 1281,    0, 1157, 1724, 2010, 1273, 2097, 3188, 2409],
    [2865,  521, 1011, 1059, 1101, 1035, 1778,  425, 1693, 1479, 1183, 1762,  320, 1157,    0,  618, 1109,  792, 1011, 2428, 1363],
    [2282, 1014,  925, 1077, 1209,  911, 1537,  328, 2185, 1238, 1098, 2250,  328, 1724,  618,    0,  331,  856,  586, 2187,  898],
    [2179, 1365,  747,  977, 1160,  583, 1104,  591, 2565,  805,  851, 2507,  724, 2010, 1109,  331,    0,  821,  946, 1754,  428],
    [3000, 1033,  285,  280,  340,  465, 1176,  513, 1971,  877,  457, 1799,  471, 1273,  792,  856,  821,    0, 1476, 1827, 1249],
    [ 817, 1460, 1511, 1662, 1794, 1497, 2050,  995, 2631, 1751, 1683, 2700, 1048, 2097, 1011,  586,  946, 1476,    0, 2707, 1209],
    [3927, 2868, 1616, 1786, 2196, 1403,  650, 2068, 3886,  949, 1500, 3231, 2108, 3188, 2428, 2187, 1754, 1827, 2707,    0, 2105],
    [1991, 1802, 1175, 1381, 1588,  937, 1455, 1019, 2974, 1155, 1205, 2937, 1157, 2409, 1363,  898,  428, 1249, 1209, 2105,    0]
], dtype=np.float32)

mds = manifold.MDS(2, dissimilarity='precomputed')
coords = mds.fit_transform(d)
x, y = coords[:, 0], coords[:, 1]

fig, ax = plt.subplots()
ax.scatter(x, y)
for (city, _x, _y) in zip(cities, x, y):
    ax.annotate(city, (_x, _y))
plt.show()

This result is consistent with http://hoxo-m.hatenablog.com/entry/20120313/p1