Proximity Matrix

Here is the output of an SPSS distance matrix. The matrix is symmetric, meaning that the numbers on the lower half will be the same as the numbers in the top half. Quite often only the lower half of a symmetric matrix is displayed, with other information being displayed in the upper half (such as a combination between distances and correlation coefficients).

I've highlighted two numbers in this matrix. In green is the distance between the 2 closest cells (2 & 19) in 7 dimensional space (each dimension representing a different variable). In yellow are the 2 cells that are farthest apart (19 & 23).

This is useful in explaining something else as well. Cells 2 & 19 are close together, but 19 & 23 are far apart. You can imagine then that because 2 & 19 are clustered together in space 2 must also be far from 23. Looking at the matrix this shows that indeed 2 & 23 are relatively far apart.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1 0 1.273091 1.12288 1.008626 1.131625 1.230302 0.668893 1.06268 1.299697 1.18704 1.23804 1.299576 1.196235 0.618855 0.665795 0.54746 1.158025 1.278158 1.27371 1.075207 0.531415 0.701549 1.223166 1.182887 0.956577 1.063487 1.110752 1.290979 1.187189 1.19892
2 1.273091 0 0.980597 0.840149 0.928302 0.891628 1.142516 0.866625 1.259231 0.504748 1.125121 0.371013 0.760708 1.141332 0.955521 1.209867 0.862577 0.444649 0.188373 0.643415 0.995657 1.125258 1.74038 1.479599 1.465247 1.493416 1.522715 1.422669 1.487738 1.189664
3 1.12288 0.980597 0 0.500501 0.376001 0.362472 1.082317 0.265972 0.902611 0.892251 0.599579 1.002578 0.560964 1.050841 1.017548 1.165269 0.287241 0.931873 1.030943 0.631289 0.927306 0.978781 1.272868 1.113743 1.116642 1.023618 1.06467 0.846439 0.851927 0.689503
4 1.008626 0.840149 0.500501 0 0.512498 0.558006 1.001508 0.315122 0.701318 0.783516 0.549547 0.88278 0.540252 0.859854 0.918177 0.910809 0.36856 0.797291 0.879939 0.41629 0.739009 0.781714 1.400413 1.215507 1.097629 1.10128 1.161674 1.075774 0.989285 0.808469
5 1.131625 0.928302 0.376001 0.512498 0 0.436753 1.257965 0.382349 0.739377 0.861793 0.449417 0.827537 0.500326 1.077903 1.143161 1.185613 0.493578 0.779071 0.964978 0.449985 0.95813 0.925659 1.307955 1.069247 1.017394 1.095686 1.20998 0.996923 1.034318 0.785933
6 1.230302 0.891628 0.362472 0.558006 0.436753 0 1.156666 0.340489 0.998305 0.950152 0.71624 0.934672 0.342815 1.172887 1.042318 1.275073 0.373822 0.938009 0.899313 0.509279 1.020897 1.124946 1.303755 0.98758 1.050975 1.01624 1.053013 0.854709 1.007623 0.541313
7 0.668893 1.142516 1.082317 1.001508 1.257965 1.156666 0 1.028814 1.508507 1.13499 1.385958 1.335947 1.156748 0.732037 0.262941 0.697594 1.026523 1.311118 1.157045 1.140503 0.598434 0.949951 1.353931 1.319626 1.252699 1.112118 1.021524 1.192132 1.127319 1.120513
8 1.06268 0.866625 0.265972 0.315122 0.382349 0.340489 1.028814 0 0.760827 0.775155 0.513933 0.920736 0.505828 0.960048 0.957057 1.084179 0.235999 0.845577 0.906334 0.473764 0.857603 0.924401 1.276137 1.085939 1.04134 0.9678 1.015197 0.893504 0.857081 0.617177
9 1.299697 1.259231 0.902611 0.701318 0.739377 0.998305 1.508507 0.760827 0 1.002217 0.339485 1.182081 1.069632 1.055532 1.453775 1.23868 0.860223 1.011237 1.328424 0.843694 1.123626 0.943992 1.405014 1.359142 1.152356 1.190968 1.35203 1.260603 1.044504 1.071701
10 1.18704 0.504748 0.892251 0.783516 0.861793 0.950152 1.13499 0.775155 1.002217 0 0.914041 0.610368 0.954605 0.981486 1.031455 1.159442 0.808123 0.434747 0.638751 0.751498 0.959398 0.99611 1.61402 1.509281 1.437025 1.37683 1.42397 1.347339 1.256759 1.175614
11 1.23804 1.125121 0.599579 0.549547 0.449417 0.71624 1.385958 0.513933 0.339485 0.914041 0 1.049704 0.829555 1.026651 1.315511 1.208061 0.598341 0.899271 1.197162 0.680137 1.0304 0.897864 1.279529 1.191058 1.063456 1.068774 1.214896 1.029793 0.897967 0.862298
12 1.299576 0.371013 1.002578 0.88278 0.827537 0.934672 1.335947 0.920736 1.182081 0.610368 1.049704 0 0.75917 1.196501 1.133237 1.252352 0.943026 0.28334 0.425452 0.598741 1.046518 1.074504 1.753761 1.472285 1.430065 1.56314 1.647388 1.488928 1.568603 1.279363
13 1.196235 0.760708 0.560964 0.540252 0.500326 0.342815 1.156748 0.505828 1.069632 0.954605 0.829555 0.75917 0 1.171333 0.991084 1.185791 0.522434 0.829978 0.736452 0.340791 0.955333 1.066353 1.473265 1.093417 1.111248 1.208948 1.260726 1.085965 1.244388 0.77904
14 0.618855 1.141332 1.050841 0.859854 1.077903 1.172887 0.732037 0.960048 1.055532 0.981486 1.026651 1.196501 1.171333 0 0.70495 0.406511 0.969142 1.075495 1.216231 1.019441 0.331276 0.382049 1.093773 1.196759 1.001423 0.960882 1.036451 1.091829 0.913741 1.096156
15 0.665795 0.955521 1.017548 0.918177 1.143161 1.042318 0.262941 0.957057 1.453775 1.031455 1.315511 1.133237 0.991084 0.70495 0 0.657037 0.948424 1.140946 0.961707 0.97906 0.495037 0.867444 1.337258 1.217928 1.168593 1.109707 1.056164 1.155213 1.174098 1.056249
16 0.54746 1.209867 1.165269 0.910809 1.185613 1.275073 0.697594 1.084179 1.23868 1.159442 1.208061 1.252352 1.185791 0.406511 0.657037 0 1.092387 1.185866 1.250054 1.060132 0.301763 0.44519 1.358727 1.358062 1.141172 1.212851 1.265792 1.334497 1.202692 1.282908
17 1.158025 0.862577 0.287241 0.36856 0.493578 0.373822 1.026523 0.235999 0.860223 0.808123 0.598341 0.943026 0.522434 0.969142 0.948424 1.092387 0 0.85179 0.928948 0.567834 0.857454 0.931173 1.30512 1.149676 1.146966 1.026035 1.054834 0.846739 0.840021 0.657462
18 1.278158 0.444649 0.931873 0.797291 0.779071 0.938009 1.311118 0.845577 1.011237 0.434747 0.899271 0.28334 0.829978 1.075495 1.140946 1.185866 0.85179 0 0.576478 0.629673 0.985171 0.955268 1.684389 1.496597 1.429538 1.501044 1.593105 1.417819 1.42315 1.252607
19 1.27371 0.188373 1.030943 0.879939 0.964978 0.899313 1.157045 0.906334 1.328424 0.638751 1.197162 0.425452 0.736452 1.216231 0.961707 1.250054 0.928948 0.576478 0 0.632796 1.044793 1.203043 1.78631 1.46886 1.455258 1.520597 1.543672 1.480947 1.570341 1.200231
20 1.075207 0.643415 0.631289 0.41629 0.449985 0.509279 1.140503 0.473764 0.843694 0.751498 0.680137 0.598741 0.340791 1.019441 0.97906 1.060132 0.567834 0.629673 0.632796 0 0.85269 0.909121 1.461698 1.131394 1.050337 1.189165 1.276042 1.17081 1.227809 0.845935
21 0.531415 0.995657 0.927306 0.739009 0.95813 1.020897 0.598434 0.857603 1.123626 0.959398 1.0304 1.046518 0.955333 0.331276 0.495037 0.301763 0.857454 0.985171 1.044793 0.85269 0 0.380339 1.188123 1.146613 0.988463 1.02683 1.081507 1.092002 1.024229 1.04195
22 0.701549 1.125258 0.978781 0.781714 0.925659 1.124946 0.949951 0.924401 0.943992 0.99611 0.897864 1.074504 1.066353 0.382049 0.867444 0.44519 0.931173 0.955268 1.203043 0.909121 0.380339 0 1.211884 1.241849 1.029062 1.124693 1.247636 1.175577 1.043333 1.173268
23 1.223166 1.74038 1.272868 1.400413 1.307955 1.303755 1.353931 1.276137 1.405014 1.61402 1.279529 1.753761 1.473265 1.093773 1.337258 1.358727 1.30512 1.684389 1.78631 1.461698 1.188123 1.211884 0 0.638956 0.69 0.453356 0.624937 0.633601 0.761861 0.903073
24 1.182887 1.479599 1.113743 1.215507 1.069247 0.98758 1.319626 1.085939 1.359142 1.509281 1.191058 1.472285 1.093417 1.196759 1.217928 1.358062 1.149676 1.496597 1.46886 1.131394 1.146613 1.241849 0.638956 0 0.404254 0.567051 0.717915 0.708742 1.038811 0.646713
25 0.956577 1.465247 1.116642 1.097629 1.017394 1.050975 1.252699 1.04134 1.152356 1.437025 1.063456 1.430065 1.111248 1.001423 1.168593 1.141172 1.146966 1.429538 1.455258 1.050337 0.988463 1.029062 0.69 0.404254 0 0.576801 0.784341 0.890079 1.022617 0.762774
26 1.063487 1.493416 1.023618 1.10128 1.095686 1.01624 1.112118 0.9678 1.190968 1.37683 1.068774 1.56314 1.208948 0.960882 1.109707 1.212851 1.026035 1.501044 1.520597 1.189165 1.02683 1.124693 0.453356 0.567051 0.576801 0 0.268779 0.530916 0.590373 0.554163
27 1.110752 1.522715 1.06467 1.161674 1.20998 1.053013 1.021524 1.015197 1.35203 1.42397 1.214896 1.647388 1.260726 1.036451 1.056164 1.265792 1.054834 1.593105 1.543672 1.276042 1.081507 1.247636 0.624937 0.717915 0.784341 0.268779 0 0.567637 0.625095 0.582305
28 1.290979 1.422669 0.846439 1.075774 0.996923 0.854709 1.192132 0.893504 1.260603 1.347339 1.029793 1.488928 1.085965 1.091829 1.155213 1.334497 0.846739 1.417819 1.480947 1.17081 1.092002 1.175577 0.633601 0.708742 0.890079 0.530916 0.567637 0 0.531686 0.517798
29 1.187189 1.487738 0.851927 0.989285 1.034318 1.007623 1.127319 0.857081 1.044504 1.256759 0.897967 1.568603 1.244388 0.913741 1.174098 1.202692 0.840021 1.42315 1.570341 1.227809 1.024229 1.043333 0.761861 1.038811 1.022617 0.590373 0.625095 0.531686 0 0.732423
30 1.19892 1.189664 0.689503 0.808469 0.785933 0.541313 1.120513 0.617177 1.071701 1.175614 0.862298 1.279363 0.77904 1.096156 1.056249 1.282908 0.657462 1.252607 1.200231 0.845935 1.04195 1.173268 0.903073 0.646713 0.762774 0.554163 0.582305 0.517798 0.732423 0

What to do next with this kind of information depends on what clustering algorithm you choose. To see a description of these go to the next section: Forming Clusters.

 

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