# lmds: Landmark MDS In lmds: Landmark Multi-Dimensional Scaling

## Description

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.

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.

## Usage

 ```1 2 3``` ```lmds(x, ndim = 3, distance_method = c("euclidean", "pearson", "spearman", "cosine", "manhattan"), landmark_method = c("sample"), num_landmarks = 500) ```

## 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,

## Value

The dimensionality reduction in the form of a `nrow(x)` by `ndim` matrix.

## Examples

 ```1 2 3``` ```library(Matrix) x <- Matrix::rsparsematrix(1000, 1000, .01) lmds(x, ndim = 3) ```

### Example output

```              comp_1        comp_2       comp_3
[1,] -0.146491076  4.219631e-02  0.166807798
[2,] -0.182706004  7.446980e-02  0.074999373
[3,] -0.100892711  1.495415e-02  0.122063923
[4,] -0.161003265  4.128150e-02  0.173400141
[5,] -0.142148774  2.850009e-02  0.171421137
[6,] -0.165281596  5.290190e-02  0.179187576
[7,] -0.146223357  3.209290e-02  0.168891461
[8,] -0.169528251  6.140979e-02  0.187336448
[9,] -0.141784336  3.313490e-02  0.160210572
[10,] -0.116498657  2.794373e-02  0.174860783
[11,] -0.147243842  3.247395e-02  0.163240731
[12,] -0.044354400 -1.620196e-01  0.309631942
[13,] -0.166025755  5.268247e-02  0.181426054
[14,] -0.144497395  1.137605e-01  0.141143812
[15,] -0.162291371  4.500289e-02  0.157546814
[16,] -0.161907433  5.027023e-02  0.194041378
[17,] -0.151977987  6.361986e-02  0.150051439
[18,] -0.120981265 -6.155727e-03  0.129143141
[19,] -0.146721458 -2.564249e-02  0.104197816
[20,] -0.137924776  3.408264e-02  0.143757445
[21,] -0.148274440  5.739240e-02  0.134909723
[22,] -0.147120347  6.057807e-02  0.189884295
[23,] -0.135145373  2.742848e-02  0.160557793
[24,] -0.141019360  3.326589e-02  0.169932534
[25,] -0.169259835  5.184096e-02  0.185571797
[26,] -0.144723202  3.629392e-02  0.174667582
[27,] -0.168156011  5.180980e-02  0.188242465
[28,] -0.144021233  1.993126e-02  0.154687033
[29,] -0.137548865  3.291563e-02  0.178338271
[30,] -0.158484441  4.612448e-02  0.167965786
[31,] -0.171118490 -9.619855e-03  0.145843428
[32,] -0.160473133  4.486213e-02  0.172026794
[33,] -0.183826394  6.238580e-02  0.197373417
[34,] -0.142131756  6.323890e-02  0.172308906
[35,] -0.152951809  5.736377e-02  0.166158726
[36,] -0.145619907  2.174754e-02  0.176922320
[37,] -0.152929955  3.691416e-02  0.159339155
[38,] -0.167515662  5.432955e-02  0.187598204
[39,] -0.176327102  8.355221e-03  0.136164581
[40,] -0.159694258  6.643748e-02  0.165264442
[41,] -0.074178975  3.584687e-02  0.215085757
[42,] -0.152846986  4.888412e-02  0.208115425
[43,] -0.141891873  3.985578e-02  0.166009573
[44,] -0.159462287  5.444816e-02  0.178853778
[45,] -0.158715561  4.292146e-02  0.177310218
[46,] -0.156082754  4.319227e-02  0.165715935
[47,] -0.122871402  2.245238e-02  0.144746766
[48,] -0.167491046  9.046903e-02  0.169384673
[49,] -0.172876436  4.360728e-02  0.183690496
[50,] -0.165022218  1.515998e-02  0.152781871
[51,] -0.124740477 -3.247868e-02  0.165806568
[52,] -0.167592094  1.105755e-02  0.199242267
[53,] -0.151462730  4.170003e-02  0.171040749
[54,] -0.144295252  2.612502e-02  0.156917423
[55,] -0.116615063  2.298325e-02  0.127934129
[56,] -0.157732930  4.836978e-02  0.178065651
[57,] -0.162009068  4.585564e-02  0.192702659
[58,] -0.167194267  4.605688e-02  0.175292497
[59,] -0.229176259 -1.807532e-02  0.189102813
[60,] -0.181488183  5.144078e-02  0.180207050
[61,] -0.111253255 -1.805006e-01 -0.110958702
[62,] -0.140653595  2.812871e-02  0.148856532
[63,] -0.162781543 -3.223590e-02  0.207584366
[64,] -0.161570156  7.224109e-02  0.169858480
[65,] -0.136593180  4.432723e-02  0.157210306
[66,] -0.162260090  4.491010e-02  0.161529749
[67,] -0.153691052  3.830571e-02  0.177082410
[68,] -0.154142614  4.088749e-02  0.180005514
[69,] -0.128382896  5.261555e-02  0.161255292
[70,] -0.174392980  3.271504e-02  0.202708854
[71,] -0.166383548  2.561491e-02  0.178513409
[72,] -0.175097520  6.001380e-02  0.203252992
[73,] -0.135221195 -7.016180e-02  0.025123202
[74,] -0.145199593  3.242216e-02  0.165297231
[75,] -0.257577218  1.115395e-01  0.130713831
[76,] -0.143134987  3.954627e-02  0.159770284
[77,] -0.158994999  3.806054e-02  0.172777739
[78,] -0.155894065  4.084216e-02  0.177038119
[79,] -0.136160409  1.554597e-02  0.155744883
[80,] -0.182671082  2.058888e-02  0.181786564
[81,]  0.048017902  1.486510e-01  0.108398858
[82,] -0.160946047  4.726803e-02  0.183222408
[83,] -0.156908898  5.007176e-02  0.152335593
[84,] -0.174771898  5.007399e-02  0.186112984
[85,] -0.152837185  4.206293e-03  0.176927576
[86,] -0.157838642 -1.653564e-03  0.167701892
[87,] -0.165879120 -2.694060e-02  0.239800436
[88,] -0.164537244  5.433231e-02  0.184074631
[89,] -0.171924973  6.230610e-02  0.215370570
[90,] -0.160163048  4.459817e-02  0.179350706
[91,] -0.171190513  7.087657e-02  0.218761631
[92,] -0.169280670  3.852616e-02  0.154684096
[93,] -0.168165348  5.827686e-02  0.155953855
[94,] -0.174938369  5.714916e-02  0.187200227
[95,] -0.152272731  4.427233e-02  0.174392388
[96,] -0.138232138  1.001604e-01  0.121202339
[97,] -0.168550231  3.753008e-02  0.160464809
[98,] -0.120629946  2.419728e-02  0.161153324
[99,] -0.147440861  3.214688e-02  0.161037182
[100,] -0.129510099  2.000678e-02  0.182330061
[101,] -0.135679631  2.959471e-02  0.174820865
[102,] -0.174670104 -7.632670e-03  0.213951719
[103,] -0.145973908  3.514066e-02  0.183569242
[104,] -0.131031056 -1.467965e-01  0.269121980
[105,] -0.152536556  3.996409e-02  0.157585164
[106,] -0.171884194  3.238828e-02  0.175367842
[107,] -0.159150875  4.755613e-02  0.179234989
[108,] -0.182602830  6.913114e-02  0.200897143
[109,] -0.165551749  3.990540e-02  0.167584362
[110,] -0.144706519  4.314174e-02  0.167704282
[111,] -0.150581196  3.694528e-02  0.160624105
[112,] -0.158629488  4.127708e-02  0.175966163
[113,] -0.138392735  4.643119e-02  0.164863717
[114,] -0.168823227  2.441535e-03  0.199498014
[115,] -0.121565535  1.808948e-02  0.169117258
[116,] -0.152393115  3.918009e-02  0.178660558
[117,] -0.150439477  2.662832e-02  0.164317171
[118,] -0.158490980  7.601531e-02  0.212731360
[119,] -0.147727430  4.354792e-02  0.167414694
[120,] -0.213905974  1.607444e-01  0.312151950
[121,] -0.143964449 -8.264399e-03  0.117014388
[122,] -0.168408715  3.414518e-02  0.307424957
[123,] -0.158166766  5.986416e-02  0.165441867
[124,] -0.167109630  4.476924e-02  0.168001584
[125,] -0.145031621  3.513256e-02  0.155035291
[126,] -0.211016027  6.060014e-02  0.154001697
[127,] -0.147346936  3.427756e-02  0.159599040
[128,] -0.188240311  4.741420e-02  0.159158020
[129,] -0.143925345  2.551550e-02  0.161121737
[130,] -0.155075413  5.266236e-02  0.168862306
[131,] -0.127020866  3.969389e-02  0.136890691
[132,] -0.171102981  5.142901e-02  0.184509063
[133,] -0.157697494  4.612010e-02  0.184771696
[134,] -0.148997155 -1.013087e-02  0.130059911
[135,] -0.144254131  5.883930e-02  0.213814123
[136,] -0.148012153  9.956160e-02  0.183274847
[137,] -0.145949130  5.370636e-02  0.153969863
[138,] -0.143079495  3.941801e-02  0.178857817
[139,] -0.166959785  6.484646e-02  0.168172594
[140,] -0.127068354  3.101841e-03  0.160881108
[141,] -0.178417093  5.050191e-02  0.186328600
[142,] -0.151433906  3.110283e-02  0.181685160
[143,] -0.159248561  5.363325e-02  0.182255723
[144,] -0.152516243  4.684020e-02  0.172212564
[145,] -0.106281366  6.283001e-02  0.143896297
[146,] -0.161824232  3.392577e-02  0.159072526
[147,] -0.123539647  3.858826e-02  0.178063900
[148,] -0.135591529  2.919151e-02  0.157745217
[149,] -0.158050341  3.863846e-02  0.161619291
[150,] -0.138075775  3.332166e-02  0.154500408
[151,] -0.129209523  3.017463e-02  0.154332210
[152,] -0.151641348  4.077486e-02  0.175994689
[153,] -0.129516390  2.108079e-02  0.164882571
[154,] -0.104146466  3.503229e-02  0.172319039
[155,] -0.167735163  5.712239e-02  0.186106001
[156,] -0.172550779  5.001271e-02  0.181146946
[157,] -0.196633813  6.245122e-02  0.169417916
[158,] -0.149906585  3.881779e-02  0.176359488
[159,] -0.147588001  4.832196e-02  0.144797969
[160,] -0.181997358  5.576501e-02  0.186160060
[161,] -0.150589676  5.140404e-02  0.134057208
[162,] -0.164843824  5.012518e-02  0.183563301
[163,] -0.331912456  9.047939e-02  0.041158960
[164,] -0.144264455  3.036096e-03  0.102921690
[165,] -0.125554554  3.251832e-02  0.145577461
[166,] -0.187448501  6.646321e-02  0.158734452
[167,] -0.174660474  6.375285e-02  0.199334532
[168,] -0.143506468  4.024924e-02  0.156775102
[169,] -0.134781517  6.308310e-02  0.138627746
[170,] -0.182723286  6.232170e-02  0.150444110
[171,] -0.145446754  2.191039e-02  0.154993152
[172,]  0.154364640  1.342932e-02  0.130234479
[173,] -0.174122026  4.555385e-02  0.179402571
[174,] -0.133383740  1.784596e-02  0.151886990
[175,] -0.174330497  5.512036e-02  0.199272164
[176,] -0.156771382  3.705750e-02  0.183593797
[177,] -0.100209361  3.060724e-02  0.146876843
[178,] -0.176283718  5.594027e-02  0.186304574
[179,] -0.146131056  4.410532e-02  0.177423110
[180,] -0.144401028  3.945207e-02  0.176501660
[181,] -0.032892450 -3.125305e-01 -0.418850235
[182,] -0.157381971  7.325620e-02  0.167969807
[183,] -0.148189745  2.169886e-02  0.186469723
[184,] -0.125650076  6.415526e-04  0.153829480
[185,] -0.208360063  5.560265e-02  0.165008944
[186,] -0.161212090 -6.364242e-03  0.199471731
[187,] -0.136724424  2.458988e-02  0.157607085
[188,] -0.159021359  4.888885e-02  0.187487517
[189,] -0.156037395  2.355556e-02  0.168833458
[190,] -0.140944662  3.764433e-02  0.173864748
[191,] -0.171031364  4.409998e-02  0.183881276
[192,] -0.182644456  3.785164e-02  0.197755002
[193,] -0.174679118  3.434302e-02  0.188287220
[194,] -0.168055570  9.482341e-02  0.138533866
[195,] -0.159517743  5.703043e-02  0.173625836
[196,] -0.243306624  7.453427e-02  0.160685668
[197,] -0.130135745 -1.051370e-02  0.163139691
[198,] -0.027606486  4.243607e-02  0.172416891
[199,] -0.158034858  5.200346e-02  0.164054811
[200,] -0.151114563  3.313238e-02  0.175979841
[201,]  0.500000000 -3.572069e-02  0.307695927
[202,] -0.173499937  5.214684e-02  0.195429951
[203,] -0.156959565  3.252067e-02  0.173654048
[204,] -0.160343486  2.869572e-02  0.177059115
[205,] -0.142334075  3.505638e-02  0.147724278
[206,] -0.111707010  5.932032e-02  0.158902969
[207,] -0.179009354  5.129983e-02  0.196678234
[208,] -0.162477308  4.614789e-02  0.179455656
[209,] -0.155359127  3.964757e-02  0.181990075
[210,] -0.142632886  2.386089e-02  0.183402868
[211,] -0.197224419 -2.012158e-02  0.110630034
[212,] -0.118203959 -1.825675e-02  0.178296252
[213,] -0.150413141  4.878952e-02  0.177726979
[214,] -0.198149973  4.336494e-02  0.179430583
[215,] -0.147663188  3.380124e-02  0.162382975
[216,] -0.151130925  4.606187e-02  0.174479210
[217,] -0.178660720  5.811688e-02  0.193604627
[218,] -0.159384133  3.237182e-02  0.178443934
[219,] -0.149520634  4.659995e-02  0.171776286
[220,] -0.159341612  3.633388e-02  0.182879027
[221,] -0.158464841  4.749387e-02  0.179974358
[222,] -0.188283052  4.475016e-02  0.194421195
[223,] -0.316370065  1.287006e-01  0.116647462
[224,] -0.116929414  3.917508e-02  0.140546003
[225,] -0.115751418  2.870128e-02  0.174908242
[226,] -0.181686216  3.289818e-02  0.183039712
[227,] -0.158193298  4.173254e-02  0.162931907
[228,] -0.166528460  3.987825e-02  0.202767733
[229,] -0.147926497  4.518798e-03  0.205898435
[230,] -0.131248508  2.480962e-02  0.182102358
[231,] -0.168128151  6.263817e-02  0.161500171
[232,] -0.158158126  5.320075e-02  0.189423287
[233,] -0.111676676  1.358962e-01  0.093860247
[234,] -0.142463784  3.460451e-02  0.166743861
[235,] -0.132826028  4.000991e-02  0.142546334
[236,] -0.174559103  5.088471e-02  0.193936448
[237,] -0.089804355 -1.449320e-01 -0.193307484
[238,] -0.155342126  3.115731e-02  0.164583616
[239,] -0.143304026  6.073636e-02  0.155151348
[240,] -0.133297499  2.284075e-02  0.160225053
[241,] -0.157209517  3.141798e-02  0.185141086
[242,] -0.147630623  3.705421e-02  0.168063364
[243,] -0.179255721  4.370841e-02  0.167194752
[244,] -0.164582654  4.143695e-02  0.165903005
[245,] -0.167276381  5.159731e-02  0.180265821
[246,] -0.173179752  7.705958e-02  0.175095066
[247,] -0.141335635  3.526658e-02  0.154797770
[248,] -0.111490103  1.581681e-02  0.192274580
[249,] -0.147414736  4.911245e-02  0.165315775
[250,] -0.194335304  5.614812e-02  0.166257890
[251,] -0.152623689 -8.923584e-03  0.112854367
[252,] -0.133670773  3.953795e-02  0.164118779
[253,] -0.132225687  1.133355e-01  0.125084696
[254,] -0.159349644  3.576319e-02  0.156264803
[255,] -0.143518404  3.181909e-02  0.161487787
[256,] -0.159571531  4.404605e-02  0.170556339
[257,] -0.145501530  4.416277e-02  0.172270259
[258,] -0.152636653  2.929900e-02  0.157431826
[259,] -0.161574602  4.441181e-02  0.172028558
[260,] -0.161372035  6.411202e-02  0.174525761
[261,] -0.161440398  4.287986e-02  0.175769848
[262,] -0.146193672  9.657104e-02  0.106025844
[263,] -0.118493908  4.025151e-04  0.188471396
[264,] -0.120622569  3.519309e-02  0.181014105
[265,] -0.114030547  5.783164e-02  0.213437585
[266,] -0.140544556 -3.434039e-02  0.087840010
[267,] -0.061396918  2.517389e-02  0.169306046
[268,] -0.091352782  4.588471e-02  0.177801757
[269,] -0.152811657  4.689125e-02  0.170837211
[270,] -0.147066216  4.628609e-02  0.170266935
[271,] -0.132658004  2.556501e-03  0.185010845
[272,] -0.182242618  6.219572e-02  0.199996587
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