A fast dimensionality reduction method scaleable to large numbers of samples. Landmark Multi-Dimensional Scaling (LMDS) is an extension of classical 'Torgerson MDS', but rather than calculating a complete distance matrix between all pairs of samples, only the distances between a set of landmarks and the samples are calculated.
Arguments
- x
A matrix, optionally sparse.
- ndim
The number of dimensions
- distance_method
The distance metric to use. Options are "euclidean" (default), "pearson", "spearman", "cosine", "manhattan".
- landmark_method
The landmark selection method to use. Options are "sample" (default).
- num_landmarks
The number of landmarks to use,
Examples
library(Matrix)
x <- Matrix::rsparsematrix(1000, 1000, .01)
lmds(x, ndim = 3)
#> comp_1 comp_2 comp_3
#> [1,] -0.32744001 -5.469474e-03 0.2011463844
#> [2,] -0.30961065 7.276987e-03 0.1758819494
#> [3,] -0.27842870 -1.524229e-02 0.1439829652
#> [4,] -0.27421847 1.769585e-02 0.1472096580
#> [5,] -0.29360131 3.106276e-02 0.1520043726
#> [6,] -0.29997098 8.199960e-03 0.1707871533
#> [7,] -0.26624939 1.232338e-01 0.0711097350
#> [8,] -0.30737189 1.041641e-02 0.1771724597
#> [9,] -0.22493806 2.232000e-02 0.1693231072
#> [10,] -0.31778718 5.255387e-03 0.2107662314
#> [11,] -0.31039231 2.373425e-03 0.1803610160
#> [12,] -0.29917712 4.012345e-02 0.1544087496
#> [13,] -0.31523567 1.220795e-03 0.1852644624
#> [14,] -0.31168122 1.228987e-03 0.1837770268
#> [15,] -0.30141395 -2.732933e-03 0.1693055511
#> [16,] -0.29364581 7.102768e-03 0.1707395530
#> [17,] -0.30041224 8.501822e-03 0.1653830211
#> [18,] -0.25003904 1.117788e-01 -0.0065637258
#> [19,] 0.10449888 2.395394e-02 0.1579795778
#> [20,] -0.29388494 -2.836360e-03 0.1733198862
#> [21,] -0.30625486 -3.111152e-03 0.1801069618
#> [22,] -0.31735536 -1.002496e-02 0.1873508987
#> [23,] -0.28942500 2.159636e-02 0.1785463856
#> [24,] -0.33088645 6.075026e-03 0.2117371341
#> [25,] -0.31166236 2.426848e-03 0.1901467240
#> [26,] -0.28799897 -1.730064e-03 0.1507587341
#> [27,] -0.28426010 2.280831e-02 0.1691339591
#> [28,] -0.29619910 8.898059e-03 0.1706198641
#> [29,] -0.31005313 5.675196e-03 0.1703021425
#> [30,] -0.27494324 9.098009e-02 0.1388913098
#> [31,] -0.30690810 -2.208061e-03 0.1843508494
#> [32,] -0.30497289 3.694296e-04 0.1185371769
#> [33,] -0.29816431 5.044170e-03 0.1761221320
#> [34,] -0.28480684 1.445586e-02 0.1698831275
#> [35,] -0.32617775 -5.236507e-03 0.1935746672
#> [36,] -0.28808314 1.393241e-02 0.1502638178
#> [37,] -0.33484667 -1.665885e-02 0.2072908658
#> [38,] -0.31578009 8.201405e-04 0.1902414923
#> [39,] -0.31006991 -3.326576e-02 0.2003384272
#> [40,] -0.32603517 -8.824005e-03 0.1973407610
#> [41,] -0.29496099 1.014383e-02 0.1637747472
#> [42,] -0.31787139 4.704688e-03 0.1831738388
#> [43,] -0.29797343 9.741216e-03 0.1740012049
#> [44,] -0.27316793 2.217718e-02 0.1824985788
#> [45,] -0.31866922 -6.535551e-03 0.1913566708
#> [46,] -0.29314545 1.391345e-02 0.1240611882
#> [47,] -0.28459325 1.333933e-02 0.1573623806
#> [48,] -0.29351449 6.957326e-02 0.1626723798
#> [49,] -0.30246758 1.300491e-02 0.1763916235
#> [50,] -0.28682948 4.831052e-03 0.1831493773
#> [51,] -0.32129265 -4.170638e-03 0.1955561151
#> [52,] -0.28665541 7.672864e-03 0.1547183711
#> [53,] -0.28670509 1.724769e-02 0.1500867609
#> [54,] -0.26141791 -1.608047e-02 0.1478693734
#> [55,] -0.29998693 9.073688e-03 0.1668136604
#> [56,] -0.31803207 1.935029e-03 0.1846124629
#> [57,] -0.29941630 7.388136e-04 0.1720216627
#> [58,] -0.32317259 -5.651440e-03 0.1957196781
#> [59,] -0.29570033 5.489351e-03 0.1708802206
#> [60,] -0.26577293 2.624833e-02 0.1383043569
#> [61,] -0.32401615 -5.080582e-03 0.1971816833
#> [62,] -0.31093213 -1.747865e-03 0.1829176016
#> [63,] -0.28319298 1.121859e-02 0.1575471156
#> [64,] -0.29553005 1.147207e-02 0.1512745574
#> [65,] -0.28799753 1.261739e-02 0.1651537422
#> [66,] -0.30489975 7.743198e-03 0.1366783367
#> [67,] -0.33168503 -8.177589e-03 0.1998974273
#> [68,] -0.29429940 -1.735309e-03 0.1567105500
#> [69,] -0.29412352 2.165458e-02 0.1907880642
#> [70,] -0.28561217 1.890959e-02 0.1621928106
#> [71,] -0.29631448 5.617999e-02 0.2120682274
#> [72,] -0.29323762 3.537046e-03 0.1879630680
#> [73,] -0.23454667 4.764425e-02 0.1633647526
#> [74,] -0.30632212 6.479673e-04 0.1769540010
#> [75,] -0.30391586 2.249382e-03 0.1783979391
#> [76,] -0.28784982 1.813838e-02 0.1644924679
#> [77,] -0.29011278 3.120805e-02 0.1574900320
#> [78,] -0.30968787 6.351369e-04 0.1773067265
#> [79,] -0.29937378 1.519606e-02 0.1677859682
#> [80,] -0.31021390 -3.100171e-03 0.1831465761
#> [81,] -0.26219118 -2.282603e-02 0.1680917323
#> [82,] -0.29759112 1.851609e-02 0.1640759281
#> [83,] -0.30316382 2.242029e-02 0.1693853870
#> [84,] -0.33805950 -1.416640e-02 0.2047671599
#> [85,] -0.28368005 2.019595e-02 0.1666320527
#> [86,] -0.29011395 2.044520e-02 0.1743345872
#> [87,] -0.30860659 1.408926e-02 0.1958547143
#> [88,] -0.28334746 1.401979e-02 0.1657097366
#> [89,] -0.32103577 -3.357036e-03 0.1957087567
#> [90,] -0.28815040 3.096339e-02 0.1709456556
#> [91,] -0.32576670 -5.098756e-03 0.1892261278
#> [92,] -0.29132964 -2.565836e-03 0.1743604495
#> [93,] -0.32982221 -6.556476e-03 0.1975352725
#> [94,] -0.30554883 3.894985e-03 0.1397934613
#> [95,] -0.24838017 -2.349584e-03 0.1474757843
#> [96,] -0.31401268 -1.900981e-03 0.1811242292
#> [97,] -0.31732298 -1.517773e-03 0.1963866422
#> [98,] -0.23948416 1.466289e-02 0.1449117041
#> [99,] -0.23137056 4.605785e-02 0.1326246330
#> [100,] -0.27468866 2.097006e-02 0.1473358065
#> [101,] -0.29653305 1.179780e-02 0.1578013992
#> [102,] -0.29944805 1.114192e-02 0.1788411569
#> [103,] -0.27444158 1.732467e-02 0.1474853167
#> [104,] -0.29364359 9.803805e-03 0.1604971976
#> [105,] -0.29714605 -5.738810e-03 0.1663124750
#> [106,] -0.27468825 2.527417e-02 0.1414082233
#> [107,] -0.33024543 -8.220095e-03 0.1984179751
#> [108,] -0.28740739 6.174416e-02 0.1662962400
#> [109,] -0.29763315 1.718350e-02 0.1592366025
#> [110,] -0.28485012 1.561450e-03 0.1538915614
#> [111,] -0.32445450 -3.114352e-03 0.1946203979
#> [112,] -0.26985451 1.350888e-02 0.1698692703
#> [113,] -0.29249380 4.383301e-02 0.1811034683
#> [114,] -0.30143629 4.050977e-03 0.1881416653
#> [115,] -0.31997311 -2.817364e-03 0.1855985792
#> [116,] -0.27568134 1.709223e-02 0.1518263139
#> [117,] -0.27519845 2.104546e-02 0.1554841996
#> [118,] -0.31156055 1.129601e-03 0.1669764328
#> [119,] -0.25501150 3.177933e-02 0.1370453212
#> [120,] -0.31892504 -8.017074e-03 0.1858541165
#> [121,] -0.30920677 -2.679906e-03 0.1875281927
#> [122,] -0.27362318 2.740109e-02 0.0524599794
#> [123,] -0.30065606 1.260535e-02 0.1365687346
#> [124,] -0.28834278 3.350159e-02 0.1757930606
#> [125,] -0.31658740 -6.724731e-03 0.1959261571
#> [126,] -0.32747195 -3.238430e-03 0.1953441171
#> [127,] -0.28274793 1.213484e-01 0.1511303104
#> [128,] -0.29003628 1.162572e-02 0.1626393062
#> [129,] -0.29802648 7.477207e-03 0.1659454850
#> [130,] -0.30441091 -4.828176e-03 0.1782577391
#> [131,] -0.27543077 3.264833e-02 0.1536288547
#> [132,] -0.26616291 2.078352e-01 0.0346279267
#> [133,] -0.30559921 5.419938e-03 0.1779280031
#> [134,] -0.27690605 1.051629e-02 0.1514965659
#> [135,] -0.28806672 6.305463e-03 0.1413567667
#> [136,] -0.27916414 3.999972e-03 0.1693850095
#> [137,] -0.27819372 -1.248077e-02 0.1739272977
#> [138,] -0.30428414 3.879677e-03 0.1825783726
#> [139,] -0.27339389 6.097941e-02 0.1769781333
#> [140,] -0.25155163 -8.385647e-02 0.1998650020
#> [141,] -0.30245389 2.748000e-02 0.1431084795
#> [142,] -0.27777524 2.456723e-02 0.1531159784
#> [143,] -0.30237822 4.921276e-03 0.1775355452
#> [144,] -0.28824231 2.284836e-02 0.1577635967
#> [145,] -0.26436426 1.064019e-02 0.1493912370
#> [146,] -0.28090334 8.306763e-03 0.1655796311
#> [147,] -0.29664232 -2.454239e-02 0.1821911639
#> [148,] -0.29966545 -7.183526e-03 0.2003795197
#> [149,] -0.30451550 1.538938e-03 0.1777190556
#> [150,] -0.29250273 1.642942e-02 0.1892581843
#> [151,] -0.29965067 -7.148490e-03 0.1516159336
#> [152,] -0.32528873 6.353066e-03 0.1813249977
#> [153,] -0.28621352 1.315616e-02 0.1672255867
#> [154,] -0.30517491 1.046037e-02 0.1797472339
#> [155,] -0.28969209 -1.171107e-01 0.0739529558
#> [156,] -0.30308482 2.737372e-02 0.1565489370
#> [157,] -0.31553939 1.384118e-03 0.1875330929
#> [158,] -0.29237562 3.335897e-02 0.1730810095
#> [159,] -0.31097908 4.207234e-04 0.1784809458
#> [160,] -0.30971121 9.971684e-03 0.1715864066
#> [161,] -0.29414397 9.544357e-03 0.1595919285
#> [162,] -0.29990804 4.428986e-03 0.1750939319
#> [163,] -0.28546920 1.335748e-01 0.1281949355
#> [164,] -0.30230354 5.234302e-03 0.1818888399
#> [165,] -0.29035625 -6.768608e-02 0.2081548838
#> [166,] -0.30756975 9.973663e-03 0.1852107646
#> [167,] -0.31317064 -2.366169e-02 0.1900129277
#> [168,] -0.30307377 1.297496e-02 0.1649133526
#> [169,] -0.27052230 1.854736e-02 0.1532106219
#> [170,] -0.26003623 9.651962e-03 0.1613192738
#> [171,] -0.28575803 -1.955368e-03 0.1660930875
#> [172,] -0.28249529 2.254136e-02 0.1496724096
#> [173,] -0.28848994 3.486774e-03 0.1610368633
#> [174,] -0.29541090 5.577731e-03 0.1670100824
#> [175,] -0.29811128 1.025738e-02 0.1676710149
#> [176,] -0.31264335 2.354888e-04 0.1819081543
#> [177,] -0.26822751 4.121542e-02 0.1538165400
#> [178,] -0.29477546 1.169059e-02 0.1670564000
#> [179,] -0.28211429 5.459932e-03 0.1102751073
#> [180,] -0.28752445 3.789080e-03 0.1861001325
#> [181,] -0.32231275 -2.093544e-03 0.1835395627
#> [182,] -0.30158554 -2.974679e-02 0.1939722608
#> [183,] -0.30150166 8.482574e-03 0.1669660749
#> [184,] -0.28754167 2.149252e-02 0.2024403848
#> [185,] -0.29282379 1.646412e-02 0.1775679864
#> [186,] -0.29006085 2.448593e-01 0.3444840081
#> [187,] -0.29800938 1.669085e-02 0.1787930038
#> [188,] -0.31252173 -5.085301e-03 0.1876522606
#> [189,] -0.27758347 1.694962e-02 0.1504770495
#> [190,] -0.26380453 1.151360e-02 0.1315697120
#> [191,] -0.27659718 1.837037e-02 0.1518003622
#> [192,] -0.30808109 6.387319e-03 0.1597883682
#> [193,] -0.28806277 2.590880e-03 0.2860100913
#> [194,] -0.32093290 5.209357e-04 0.1879602733
#> [195,] -0.31267602 -2.857873e-02 0.1986797968
#> [196,] -0.25889762 4.304835e-01 -0.0928237157
#> [197,] -0.32086548 -3.763268e-04 0.1813799439
#> [198,] -0.28390357 -5.051504e-03 0.1649796854
#> [199,] -0.28381089 8.576784e-03 0.1688408043
#> [200,] -0.28989477 1.592683e-03 0.1618350693
#> [201,] -0.30950314 5.883482e-02 0.1567799294
#> [202,] -0.32120649 -4.451050e-03 0.1925518320
#> [203,] -0.34109027 -8.452883e-03 0.1490167051
#> [204,] -0.30886904 8.349366e-03 0.1780963850
#> [205,] -0.27791299 9.690702e-03 0.1691147332
#> [206,] -0.28417755 5.966258e-02 0.1397398709
#> [207,] -0.28128123 1.856025e-02 0.1456587050
#> [208,] -0.29484268 7.113150e-03 0.2113990275
#> [209,] -0.31266887 5.679037e-03 0.1814758523
#> [210,] -0.32148017 -4.320823e-03 0.1866897109
#> [211,] -0.24381705 -6.787615e-03 0.1973465155
#> [212,] -0.27768425 8.560123e-02 0.1689907553
#> [213,] -0.31716302 -5.980208e-03 0.1835889590
#> [214,] -0.30168312 8.556202e-03 0.1882130688
#> [215,] -0.27786342 1.910357e-02 0.1499916250
#> [216,] -0.31107573 -4.183660e-03 0.1794746023
#> [217,] -0.28900583 -7.945350e-03 0.1661368441
#> [218,] 0.50000000 5.775870e-02 0.1599968797
#> [219,] -0.31004562 7.445835e-04 0.1684915815
#> [220,] -0.30749850 1.009546e-02 0.2129597403
#> [221,] -0.29755924 -1.035287e-03 0.1620819609
#> [222,] -0.27697191 1.001658e-03 0.1528529322
#> [223,] -0.31910878 -1.781282e-02 0.1528647316
#> [224,] -0.30617235 1.023483e-02 0.1731168725
#> [225,] -0.31624469 -4.995137e-03 0.2025524718
#> [226,] -0.21459260 2.594372e-02 0.1896958069
#> [227,] -0.29524820 5.812117e-03 0.1621202942
#> [228,] -0.30064770 1.437385e-02 0.1543881555
#> [229,] -0.30852331 3.851383e-03 0.1790116020
#> [230,] -0.29956932 1.852129e-03 0.1620295006
#> [231,] -0.30853524 5.340494e-03 0.1696646208
#> [232,] -0.28146678 -2.892787e-02 0.1600866343
#> [233,] -0.27698154 5.819981e-02 0.1288188012
#> [234,] -0.30764433 5.616240e-03 0.1681267031
#> [235,] -0.26831099 2.915904e-02 0.1369023691
#> [236,] -0.29342894 1.001331e-02 0.1818769773
#> [237,] -0.28402003 1.420625e-02 0.1688949704
#> [238,] -0.30152195 2.979941e-03 0.1696098580
#> [239,] -0.29368674 2.350922e-02 0.1736118578
#> [240,] -0.28050188 1.623926e-02 0.1602156842
#> [241,] -0.30132334 2.422813e-03 0.1638693240
#> [242,] -0.32230402 -2.343686e-03 0.1966602881
#> [243,] -0.32814613 -9.799805e-03 0.1980092273
#> [244,] -0.28890989 9.740870e-03 0.1565252292
#> [245,] -0.28066536 2.950059e-03 0.1510563271
#> [246,] -0.32240043 -4.329130e-04 0.1912730662
#> [247,] -0.29470287 -4.458896e-03 0.1870475625
#> [248,] -0.28207023 6.726066e-03 0.1242229329
#> [249,] -0.28758764 7.673789e-03 0.1609687760
#> [250,] -0.30643755 4.881310e-03 0.1852321761
#> [251,] -0.33495034 -1.357272e-02 0.2012170526
#> [252,] -0.28520046 2.148536e-02 0.1686046344
#> [253,] -0.27485996 -4.387539e-02 0.0897395380
#> [254,] -0.28250601 7.467786e-03 0.1572992000
#> [255,] -0.28926418 -6.974284e-04 0.1672700041
#> [256,] -0.29351781 1.153690e-02 0.1644533775
#> [257,] -0.25555324 9.506886e-03 0.1533699537
#> [258,] -0.28769550 2.752194e-02 0.1373042180
#> [259,] -0.30052901 3.928777e-02 0.1820125573
#> [260,] -0.28880988 1.608892e-02 0.1603051209
#> [261,] -0.28437877 4.008870e-02 0.1531044939
#> [262,] -0.29949303 4.477339e-03 0.1624665591
#> [263,] -0.29970317 8.862897e-04 0.1923032883
#> [264,] -0.29047805 1.834707e-02 0.1471050018
#> [265,] -0.30193397 2.252633e-02 0.1475140181
#> [266,] -0.31067733 -1.499670e-03 0.1782233044
#> [267,] -0.30746447 -5.137301e-03 0.1693992074
#> [268,] -0.28535397 5.275250e-03 0.1369164409
#> [269,] -0.29710548 1.024253e-02 0.1814520903
#> [270,] -0.30864906 2.717552e-02 0.1673819746
#> [271,] -0.29565138 1.342781e-02 0.1694769873
#> [272,] -0.30402556 8.947438e-03 0.1695379871
#> [273,] -0.26786850 2.749875e-02 0.1768274021
#> [274,] -0.31805858 1.204985e-03 0.1979138425
#> [275,] -0.28190241 1.873516e-02 0.1510418936
#> [276,] -0.30726665 -2.666483e-03 0.1815707082
#> [277,] -0.29825729 2.738474e-03 0.1531075601
#> [278,] -0.32208518 1.218682e-03 0.1570896726
#> [279,] -0.28985140 1.794732e-02 0.1581751366
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#> attr(,"addend")
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#> attr(,"multiplier")
#> [1] 1.350224