MDS Game of Thrones map
Benazir Kazhat
08 03 2020
Unfortunately, our intellectual abilities as humans, even though quite superior to other creatures, are still extremely limited. If we were asked to imagine the craziest version of the universe, our ideas would be nothing more than a random collection of things that we’ve already seen/known, nothing new. We do not even need to go that far, we cannot even imagine things in more than three dimensions.
But just like our ancestors managed to survive the harsh realities of the past, we(the humankind) found a workaround for this matter as well.One of those workarounds is “Multidimensional Scaling”(MDS).
It is a statistical technique used to plot multivariate data points into two dimensions, giving us an idea about the structure of the dataset & the relations(dissimilarities/distance) between the datapoints. Hence, if the observations are similar, they’ll be close to each other and vice-versa.
It is widely used in geography, in creating maps, that is why to explain how MDS works I decided to try and recreate a map.
For that I will need only the “wordcloud” package, as the MDS(cmdscale) function that i will need is already included in the base package “stats”
## Loading required package: RColorBrewerTo make it a bit more interesting, I decided to recreate a map of the Westeros(Game Of Thrones) and check, weather the distances mentioned in the books and the show add up to the map shown in the intro.:)
Fortunately for me, Game of Thrones has a huge fanbase that have alredy created a distance matrix with the main locations on asoiaf.westeros.org spreadsheet:
got <- read.csv2('gotmap.csv', header = TRUE, row.names = 1)
got## CastleBlack Winterfell WhiteHarbor MoatCailin TheTwins TheEyrie
## CastleBlack 0 680 1105 1080 1610 2650
## Winterfell 680 0 490 590 1120 1970
## WhiteHarbor 1105 490 0 180 710 1460
## MoatCailin 1080 590 180 0 530 1280
## TheTwins 1610 1120 710 530 0 930
## TheEyrie 2650 1970 1460 1280 930 0
## Gulltown 2970 2290 1880 1700 1350 450
## KneelingMan 2175 1495 1185 905 375 680
## TheTrident 2040 1360 950 770 420 545
## Riverrun 2295 1615 1205 1025 495 740
## HarrowaysTown 2240 1560 1150 970 555 440
## Harrenhal 2335 1655 1245 1065 615 535
## StoneySept 2515 1835 1525 1245 715 805
## Lannisport 2885 2205 1795 1615 1085 1330
## KingsLanding 2690 2010 1600 1420 1070 990
## Bitterbridge 2965 2285 1875 1695 1125 1165
## StormsEnd 3170 2490 2080 1900 1350 1370
## Summerhall 3150 2470 2060 1880 1555 1350
## Ashford 3185 2505 2095 1915 1345 1385
## Highgarden 3630 2950 2540 2360 1740 1830
## TowerofJoy 3365 2685 2275 2095 1525 1565
## Oldtown 3750 3070 2660 2480 1910 1950
## Nightsong 3395 2715 2305 2125 1555 1595
## Sunspear 4565 3885 3475 3295 2725 2765
## Gulltown KneelingMan TheTrident Riverrun HarrowaysTown Harrenhal
## CastleBlack 2970 2175 2040 2295 2240 2335
## Winterfell 2290 1495 1360 1615 1560 1655
## WhiteHarbor 1880 1185 950 1205 1150 1245
## MoatCailin 1700 905 770 1025 970 1065
## TheTwins 1350 375 420 495 555 615
## TheEyrie 450 680 545 740 440 535
## Gulltown 0 930 830 1050 750 845
## KneelingMan 930 0 135 120 180 240
## TheTrident 830 135 0 255 100 195
## Riverrun 1050 120 255 0 300 285
## HarrowaysTown 750 180 100 300 0 95
## Harrenhal 845 240 195 285 95 0
## StoneySept 1115 340 475 260 365 270
## Lannisport 1640 710 845 590 890 795
## KingsLanding 1200 630 550 750 450 380
## Bitterbridge 1475 750 825 670 725 630
## StormsEnd 1680 1110 1030 1230 930 860
## Summerhall 1660 1180 1010 1100 910 840
## Ashford 1695 970 1045 890 945 850
## Highgarden 2140 1365 1490 1285 1390 1295
## TowerofJoy 1875 1150 1225 1070 1125 1030
## Oldtown 2260 1535 1610 1455 1510 1415
## Nightsong 1905 1180 1255 1100 1155 1060
## Sunspear 3075 2350 2425 2270 2325 2230
## StoneySept Lannisport KingsLanding Bitterbridge StormsEnd
## CastleBlack 2515 2885 2690 2965 3170
## Winterfell 1835 2205 2010 2285 2490
## WhiteHarbor 1525 1795 1600 1875 2080
## MoatCailin 1245 1615 1420 1695 1900
## TheTwins 715 1085 1070 1125 1350
## TheEyrie 805 1330 990 1165 1370
## Gulltown 1115 1640 1200 1475 1680
## KneelingMan 340 710 630 750 1110
## TheTrident 475 845 550 825 1030
## Riverrun 260 590 750 670 1230
## HarrowaysTown 365 890 450 725 930
## Harrenhal 270 795 380 630 860
## StoneySept 0 650 470 410 950
## Lannisport 650 0 990 730 1470
## KingsLanding 470 990 0 520 480
## Bitterbridge 410 730 520 0 730
## StormsEnd 950 1470 480 730 0
## Summerhall 840 1210 460 410 350
## Ashford 630 950 650 220 650
## Highgarden 1025 730 915 395 990
## TowerofJoy 810 1100 755 400 645
## Oldtown 1195 1120 1305 785 1380
## Nightsong 840 1015 885 430 775
## Sunspear 2010 2185 2055 1600 1945
## Summerhall Ashford Highgarden TowerofJoy Oldtown Nightsong
## CastleBlack 3150 3185 3630 3365 3750 3395
## Winterfell 2470 2505 2950 2685 3070 2715
## WhiteHarbor 2060 2095 2540 2275 2660 2305
## MoatCailin 1880 1915 2360 2095 2480 2125
## TheTwins 1555 1345 1740 1525 1910 1555
## TheEyrie 1350 1385 1830 1565 1950 1595
## Gulltown 1660 1695 2140 1875 2260 1905
## KneelingMan 1180 970 1365 1150 1535 1180
## TheTrident 1010 1045 1490 1225 1610 1255
## Riverrun 1100 890 1285 1070 1455 1100
## HarrowaysTown 910 945 1390 1125 1510 1155
## Harrenhal 840 850 1295 1030 1415 1060
## StoneySept 840 630 1025 810 1195 840
## Lannisport 1210 950 730 1100 1120 1015
## KingsLanding 460 650 915 755 1305 885
## Bitterbridge 410 220 395 400 785 430
## StormsEnd 350 650 990 645 1380 775
## Summerhall 0 300 640 295 1030 425
## Ashford 300 0 340 180 730 210
## Highgarden 640 340 0 370 390 285
## TowerofJoy 295 180 370 0 760 130
## Oldtown 1030 730 390 760 0 675
## Nightsong 425 210 285 130 675 0
## Sunspear 1595 1380 1455 1300 1845 1170
## Sunspear
## CastleBlack 4565
## Winterfell 3885
## WhiteHarbor 3475
## MoatCailin 3295
## TheTwins 2725
## TheEyrie 2765
## Gulltown 3075
## KneelingMan 2350
## TheTrident 2425
## Riverrun 2270
## HarrowaysTown 2325
## Harrenhal 2230
## StoneySept 2010
## Lannisport 2185
## KingsLanding 2055
## Bitterbridge 1600
## StormsEnd 1945
## Summerhall 1595
## Ashford 1380
## Highgarden 1455
## TowerofJoy 1300
## Oldtown 1845
## Nightsong 1170
## Sunspear 0Now that we have the distance matrix,we will execute the simplest version of the MDS funtions available - cmdscale() also known as the principal coordinates analysis, which will perform the eigen-decomposition of the matrix above and will give us the eigenvectors that we can later plot into a map:
mds <- as.data.frame(cmdscale(got))
mds## V1 V2
## CastleBlack -2483.13521 630.90508
## Winterfell -1779.72337 360.22798
## WhiteHarbor -1367.38325 176.18218
## MoatCailin -1215.25999 153.84275
## TheTwins -668.53358 148.36160
## TheEyrie -279.03859 -849.49698
## Gulltown -274.60262 -1380.37007
## KneelingMan -260.34798 -87.34328
## TheTrident -360.34946 -113.16542
## Riverrun -170.06636 -44.08446
## HarrowaysTown -217.87059 -204.34004
## Harrenhal -121.39511 -169.18892
## StoneySept 81.99725 -27.27818
## Lannisport 260.69970 68.90649
## KingsLanding 191.64518 -104.35596
## Bitterbridge 521.53225 70.64874
## StormsEnd 562.40317 -94.82452
## Summerhall 670.22199 48.04302
## Ashford 737.23067 136.25348
## Highgarden 1140.15980 214.72837
## TowerofJoy 902.72741 171.32107
## Oldtown 1160.07722 132.96142
## Nightsong 944.92148 208.95578
## Sunspear 2024.08997 553.10986textplot(mds$V1,mds$V2, rownames(mds))
Now that we have our map, we can compare it to the one available in the internet. I chose the one that is most readable, though some titles are missing there we can compare a couple of the main ones. 
We can rotate our plot to make it easier to compare:
textplot(-mds$V2, -mds$V1,rownames(mds), xlim = c(-1000, 1500), ylim = c(-2500, 2500))
As we can see, the map turned out to be quite okay when it comes to the relative locations of the houses.
Which is quite impressive, as the data was collected by the fans from the distance references in the books such as the time that characters/ravens spent travelling from one place to another. Shows how the books are well-thought out to the very minor detail and how we could use the MDS in our day to day life, in case we ever have trouble imagining our favorite fiction universe.:)