- The aim of this problem is to familarize you with the
smacof package in R.
georgia.r -- R Program
georgia.txt -- Distances Data
- Run the program and turn in the plot.
- Note that R has chopped off
one of the names on the left side. We can fix this by telling R
to change the scale of the axes. To do this change the following line:
xlim=c(-axismax-0.1,axismax),ylim=c(-axismax,axismax),font=2)
Turn in the above plot.
- Run the program and turn in the plot.
- Continuing with the plotting exercise:
-
Produce a nice plot of the cities by adjusting the positions of the names
in the namepos[] vector and the offset control. Turn in this
plot.
- The Cities are clearly in the wrong orientation. Note that, because we are dealing with distances, the
configuration recovered by smacof is only going to be identified up to a choice of
origin and a rotation. In general, a rotation matrix in two dimensions is:
Where Q is the angle in radians. You can rotate the coordinates clockwise p/4 radians (45 degrees) with this code fragment:pi <- 3.141592653589793 pi4 <- pi/4 dimension1 <- cos(pi4)*xx + sin(pi4)*(-1.0)*yy dimension2 <- sin(pi4)*(-1.0)*xx + cos(pi4)*(-1.0)*yy
Note that I have flipped the sign on the second dimension in the formula above.
Use the above formula to rotate your configuration until it makes sense, properly label the X and Y axes by changing the labels in "mtext", and neatly arrange the city names. Turn in the Plot.
-
Produce a nice plot of the cities by adjusting the positions of the names
in the namepos[] vector and the offset control. Turn in this
plot.
- Download the data file:
U. S. Map Driving Distance Data
The data file is reproduced below. It contains the lower half of a driving distance matrix computed between 10 U.S. cities -- Atlanta, Boise, Boston, Chicago, Cincinnati, Dallas, Denver, Los Angeles, Miami, and Washington, D.C..Atlanta 0000 2340 1084 715 481 826 1519 2252 662 641 Boise 2340 0000 2797 1789 2018 1661 891 908 2974 2480 Boston 1084 2797 0000 976 853 1868 2008 3130 1547 443 Chicago 715 1789 976 0000 301 936 1017 2189 1386 696 Cincinnati 481 2018 853 301 0000 988 1245 2292 1143 498 Dallas 826 1661 1868 936 988 0000 797 1431 1394 1414 Denver 1519 891 2008 1017 1245 797 0000 1189 2126 1707 LosAngeles 2252 908 3130 2189 2292 1431 1189 0000 2885 2754 Miami 662 2974 1547 1386 1143 1394 2126 2885 0000 1096 WashingtonDC 641 2480 443 696 498 1414 1707 2754 1096 0000
Run this data set through smacof and get the coordinates.
- Modify the georgia.r program to make a plot of the 10 U.S. Cities. Turn in a
listing of the program and the two dimensional plot.
- Change metric=TRUE to
metric=FALSE and run it through smacof
(this tells smacof to do a Nonmetric MDS on
dissimilarity data). Compare the
Stress values for 1 to 3 dimensions with those obtained
above and compare the two dimensional plot obtained with this option to that in part (a).
- Modify the georgia.r program to make a plot of the 10 U.S. Cities. Turn in a
listing of the program and the two dimensional plot.
- In this problem we are going to do a classic non-metric MDS on the Morse Code data.
Download data files:
Morse Code Data Lower Half
Morse Code Data Upper Half
Here is what morse_code_U1.txt looks like:A 100 4 6 13 3 14 10 13 46 5 22 3 25 34 6 6 9 35 23 6 37 13 17 12 7 3 2 7 5 5 8 6 5 6 2 3 B 4 100 37 31 5 28 17 21 5 19 34 40 6 10 12 22 25 16 18 2 18 34 8 84 30 42 12 17 14 40 32 74 43 17 4 4 C 6 37 100 17 4 29 13 7 11 19 24 35 14 3 9 51 34 24 14 6 6 11 14 32 82 38 13 15 31 14 10 30 28 24 18 12 D 13 31 17 100 7 23 40 36 9 13 81 56 8 7 9 27 9 45 29 6 17 20 27 40 15 33 3 9 6 11 9 19 8 10 5 6 E 3 5 4 7 100 2 4 4 17 1 5 6 4 4 5 1 5 10 7 67 3 3 2 5 6 5 4 3 5 3 5 2 4 2 3 3 F 14 28 29 23 2 100 10 29 5 33 16 50 7 6 10 42 12 35 14 2 21 27 25 19 27 13 8 16 47 25 26 24 21 5 5 5 G 10 17 13 40 4 10 100 6 5 22 33 16 14 13 62 52 23 21 5 3 15 14 32 21 23 39 15 14 5 10 4 10 17 23 20 11 H 13 21 7 36 4 29 6 100 10 10 9 29 5 8 8 14 8 17 37 4 36 59 9 33 14 11 3 9 15 43 70 35 17 4 3 3 I 46 5 11 9 17 5 5 10 100 3 5 16 13 30 7 3 5 19 35 16 10 5 8 2 5 7 2 5 8 9 6 8 5 2 4 5 J 5 19 19 13 1 33 22 10 3 100 22 31 8 3 21 63 47 11 2 7 9 9 9 22 32 28 67 66 33 15 7 11 28 29 26 23 K 22 34 24 81 5 16 33 9 5 22 100 33 10 12 31 14 31 22 2 2 23 17 33 63 16 18 5 9 17 8 8 18 14 13 5 6 L 3 40 35 56 6 50 16 29 16 31 33 100 6 2 9 37 36 28 12 5 16 19 20 31 25 59 12 13 17 15 26 29 36 16 7 3 M 25 6 14 8 4 7 14 5 13 8 10 6 100 62 11 10 15 20 7 9 13 4 21 9 18 8 5 7 6 6 5 7 11 7 10 4 N 34 10 3 7 4 6 13 8 30 3 12 2 62 100 5 9 5 28 12 10 16 4 12 4 16 11 5 2 3 4 4 6 2 2 10 2 O 6 12 9 9 5 10 62 8 7 21 31 9 11 5 100 37 35 10 3 4 11 14 25 35 27 27 19 17 7 7 6 18 14 11 20 12 P 6 22 51 27 1 42 52 14 3 63 14 37 10 9 37 100 43 23 9 4 12 19 19 19 41 30 34 44 24 11 15 17 24 23 25 13 Q 9 25 34 9 5 12 23 8 5 47 31 36 15 5 35 43 100 11 2 3 6 14 12 37 50 63 34 32 17 12 9 27 40 58 37 24 R 35 16 24 45 10 35 21 17 19 11 22 28 20 28 10 23 11 100 16 2 23 23 62 14 12 13 7 10 13 4 7 12 7 9 1 2 S 23 18 14 29 7 14 5 37 35 2 2 12 7 12 3 9 2 16 100 9 56 24 12 10 6 7 8 2 2 15 28 9 5 5 5 2 T 6 2 6 6 67 2 3 4 16 7 2 5 9 10 4 4 3 2 9 100 8 5 4 2 2 6 5 5 3 3 3 8 7 6 14 6 U 37 18 6 17 3 21 15 36 10 9 23 16 13 16 11 12 6 23 56 8 100 57 34 17 9 11 6 6 16 34 10 9 9 7 4 3 V 13 34 11 20 3 27 14 59 5 9 17 19 4 4 14 19 14 23 24 5 57 100 17 57 35 10 10 14 28 79 44 36 25 10 1 5 W 17 8 14 27 2 25 32 9 8 9 33 20 21 12 25 19 12 62 12 4 34 17 100 22 25 22 10 22 19 16 5 9 11 6 3 7 X 12 84 32 40 5 19 21 33 2 22 63 31 9 4 35 19 37 14 10 2 17 57 22 100 48 26 12 20 24 27 16 57 29 16 17 6 Y 7 30 82 15 6 27 23 14 5 32 16 25 18 16 27 41 50 12 6 2 9 35 25 48 100 23 26 44 40 15 11 26 22 33 23 16 Z 3 42 38 33 5 13 39 11 7 28 18 59 8 11 27 30 63 13 7 6 11 10 22 26 23 100 16 21 27 9 10 25 66 47 15 15 1 2 12 13 3 4 8 15 3 2 67 5 12 5 5 19 34 34 7 8 5 6 10 10 12 26 16 100 63 13 8 10 8 19 32 57 55 2 7 17 15 9 3 16 14 9 5 66 9 13 7 2 17 44 32 10 2 5 6 14 22 20 44 21 63 100 54 20 5 14 20 21 16 11 3 5 14 31 6 5 47 5 15 8 33 17 17 6 3 7 24 17 13 2 3 16 28 19 24 40 27 13 54 100 31 23 41 16 17 8 10 4 5 40 14 11 3 25 10 43 9 15 8 15 6 4 7 11 12 4 15 3 34 79 16 27 15 9 8 20 31 100 42 44 32 10 3 3 5 8 32 10 9 5 26 4 70 6 7 8 26 5 4 6 15 9 7 28 3 10 44 5 16 11 10 10 5 23 42 100 42 24 10 6 5 6 6 74 30 19 2 24 10 35 8 11 18 29 7 6 18 17 27 12 9 8 9 36 9 57 26 25 8 14 41 44 42 100 69 14 5 14 7 5 43 28 8 4 21 17 17 5 28 14 36 11 2 14 24 40 7 5 7 9 25 11 29 22 66 19 20 16 32 24 69 100 70 20 13 8 6 17 24 10 2 5 23 4 2 29 13 16 7 2 11 23 58 9 5 6 7 10 6 16 33 47 32 21 17 10 10 14 70 100 61 26 9 2 4 18 5 3 5 20 3 4 26 5 7 10 10 20 25 37 1 5 14 4 1 3 17 23 15 57 16 8 3 6 5 20 61 100 78 0 3 4 12 6 3 5 11 3 5 23 6 3 4 2 12 13 24 2 2 6 3 5 7 6 16 15 55 11 10 3 5 14 13 26 78 100
This is the famous morse code data. If you compare this file to morsekystsu.txt they are exactly the same except the matrix is transposed.
- Run morsekystsl.txt and morsekystsu.txt through smacof (be sure to use
unique output file names) in 1 to 3 dimensions. To do this change:
ndim=2 to
ndim=1 and
ndim=3.
Report the Stress values for 1 to 3 dimensions for the two halves of the data.
- Make two-dimensional Plots for the two halves of the data
(put the 26 letters and 10 integers before the corresponding
coordinates). You can modify the
georgia.r program to do this. Turn in the plots and the
R code. Do the plots look the same?
- Run morsekystsl.txt and morsekystsu.txt through smacof (be sure to use
unique output file names) in 1 to 3 dimensions. To do this change: