Multi Voxel Pattern Analysis
Playing around with some methods for MVPA
Reading
See MvpaPapers (need Cambridge permissions)
Software
We're trying pymvpa
Which seems an excellent use for parallel computing with Ipython - see ParallelNotes
Covariance matrix shrinkage
Here is a set of multivariate data relating to paper production that I am using as a test bed for various things. It came from http://lib.stat.cmu.edu/datasets/papir
############################################################################## # # April 14. 1999 # # This file contains two multivariate regression data sets from # paper industry. They have been described and analysed in # # Aldrin, M. (1996), "Moderate projection pursuit regression for # multivariate response data", Computational Statistics and Data Analysis, # 21, p. 501-531. # # A short description is given above each data set. A more detailed # description is found in Aldrin (1996). # # These data sets are delivered by # Magne Aldrin, # Norwegian Computing Center, P.O. Box 114 Blindern,N-0314 Oslo # email: magne.aldrin@nr.no # WWW: http://www.nr.no/~aldrin/ # # Permission is hereby given to Statlib to redistribute these data sets. # They can be freely distributed and used for non-commercial purposes. # ############################################################################## ############################################################################### # Data set from an experiment at the paper plant Norske Skog, Skogn, Norway. # It were described and analysed in Aldrin (1996), and published there. # # It consists of 30 observations (rows) and 22 variables (colums), but all # response variables are missing for the 28th observation. # # Columns 1 to 13 are response variables that describes various qualities # of the paper. # # Columns 14 to 22 are 9 predictor variables. The first three predictor # variables (x1 in column 14, x2 in column 15 and x3 in column 16) were # varied systematically through the experiment, taking the values # 1, 0 and -1. The next three predictor variables (columns 17 to 19) # are constructed as x1**2, x2**2 and x3**2. # The last three predictor variables (columns 20 to 22) are constructed # as x1*x2, x1*x3 and x2*x3. ############################################################################## 33.8792 30.0246 8.6891 9.6493 15.2094 11.0984 11.5204 18.5718 22.7880 17.7415 21.9271 88.4072 24.8111 1 0 -1 1 0 1 0 -1 0 33.8792 30.2804 8.3624 9.5133 15.2094 12.2083 10.6563 20.2506 25.1815 17.2866 21.9271 87.1239 23.3873 1 0 -1 1 0 1 0 -1 0 32.5419 31.7637 7.0558 7.8825 15.2094 12.9482 9.8643 16.8930 24.0346 15.0121 21.5845 90.5461 23.2093 0 1 -1 0 1 1 0 0 -1 32.5419 31.3545 7.4478 8.3582 15.5262 11.4684 11.3764 18.7816 24.4335 16.8317 21.4866 91.2590 24.2060 0 1 -1 0 1 1 0 0 -1 32.5419 31.5080 7.5785 8.4941 15.2094 11.8383 10.8723 19.2013 23.0872 17.7415 21.4376 91.5442 23.9924 0 0 0 0 0 0 0 0 0 30.7588 32.8378 5.5532 6.1157 13.9419 11.4684 10.1523 19.3062 22.2395 18.6514 21.4376 91.1164 23.7788 0 0 0 0 0 0 0 0 0 31.2046 33.7585 4.7039 6.3875 12.9913 14.0580 7.7042 19.2013 20.4943 20.0161 21.9271 91.6868 23.7432 -1 0 1 1 0 1 0 -1 0 31.6503 32.3775 7.0558 7.3389 13.3082 12.2083 9.2163 17.9422 21.4915 17.7415 23.1507 90.9739 22.6397 -1 0 1 1 0 1 0 -1 0 32.0961 32.0706 7.2518 7.6107 13.9419 12.9482 9.1443 18.7816 22.2894 17.2866 22.7591 90.1183 22.0346 -1 -1 0 1 1 0 1 0 0 32.5419 31.7126 7.9705 8.2223 13.6251 12.9482 8.8563 18.6767 21.2422 19.1063 22.4655 89.6905 22.4261 -1 -1 0 1 1 0 1 0 0 32.0961 32.0706 7.8398 7.4068 12.9913 12.2083 8.8563 17.1028 22.0400 16.8317 22.7102 90.8313 25.9858 0 -1 1 0 1 1 0 0 -1 32.5419 31.4568 7.4478 7.8145 12.9913 11.4684 9.7203 18.6767 22.9376 17.7415 22.7591 90.4035 25.9858 0 -1 1 0 1 1 0 0 -1 32.9877 31.1499 7.5131 8.4261 15.2094 11.8383 10.8003 18.9915 22.5387 18.1964 22.6613 88.9776 23.9212 0 0 0 0 0 0 0 0 0 32.9877 31.5080 7.6438 8.1543 15.2094 12.5782 10.2963 17.2077 22.3392 16.8317 22.6613 88.9776 22.9601 0 0 0 0 0 0 0 0 0 32.9877 31.4057 6.9905 7.9504 14.5757 11.0984 10.9443 17.1028 21.3918 17.2866 23.0039 88.6924 23.1737 1 -1 0 1 1 0 -1 0 0 32.5419 31.3545 7.1211 7.8825 14.2588 11.0984 10.8723 15.7388 20.9929 16.3768 23.0039 89.2627 23.9212 1 -1 0 1 1 0 -1 0 0 34.7708 29.1551 8.2318 9.0377 16.4768 12.2083 11.2324 17.3127 22.6883 16.3768 21.0461 90.1183 23.4940 1 0 1 1 0 1 0 1 0 34.3250 29.6666 8.2971 9.1736 16.4768 13.3181 10.3683 17.2077 23.6856 15.9219 20.9971 89.8331 24.2416 1 0 1 1 0 1 0 1 0 34.3250 29.9223 8.5584 9.4454 15.2094 13.6881 9.3603 18.2570 23.6357 16.8317 20.9971 90.5461 24.0636 0 -1 -1 0 1 1 0 0 1 33.8792 30.0246 8.4931 9.4454 17.1106 12.5782 11.3044 18.8865 22.5387 18.1964 20.4098 90.9739 24.2772 0 -1 -1 0 1 1 0 0 1 32.5419 31.6103 7.1211 7.8825 14.2588 13.6881 8.6403 17.4176 21.7409 17.2866 20.1161 89.8331 22.9245 0 0 0 0 0 0 0 0 0 32.5419 31.4568 6.7945 7.8825 14.5757 13.3181 9.2163 18.8865 22.5387 18.1964 20.1161 90.5461 23.7076 0 0 0 0 0 0 0 0 0 31.6503 32.5821 6.3372 7.1350 14.2588 13.6881 8.6403 18.4668 22.4390 17.7415 20.0672 90.2609 24.2772 -1 1 0 1 1 0 -1 0 0 31.2046 32.6844 6.4678 7.0671 14.2588 13.3181 9.1443 20.0407 22.6883 19.1063 20.3609 89.9757 23.1737 -1 1 0 1 1 0 -1 0 0 32.0961 31.7637 7.9051 8.4261 14.5757 14.0580 8.9283 18.0471 23.1869 16.8317 20.2630 90.1183 21.9634 -1 0 -1 1 0 1 0 1 0 32.5419 31.5591 7.6438 7.8145 15.5262 13.6881 9.5763 19.8309 23.4363 18.1964 20.0183 89.1202 22.9245 -1 0 -1 1 0 1 0 1 0 31.2046 32.3775 5.5532 5.9798 14.2588 10.7285 10.9443 18.1521 23.2867 16.8317 20.9971 90.9739 24.6331 0 1 1 0 1 1 0 0 1 NA NA NA NA NA NA NA NA NA NA NA NA NA 0 1 1 0 1 1 0 0 1 32.5419 31.5591 5.8798 7.2709 14.5757 11.8383 10.5123 18.0471 22.0899 17.7415 20.9971 90.5461 25.4519 1 1 0 1 1 0 1 0 0 32.0961 31.5591 6.3372 7.4748 13.9419 12.5782 9.1443 17.7324 23.0373 16.8317 20.8993 89.5479 22.7821 1 1 0 1 1 0 1 0 0 ############################################################################### # Data set from an experiment at the paper plant Saugbruksforeningen, Norway. # It were described and analysed in Aldrin (1996), but not published then. # # It consists of 30 observations (rows) and 41 variables (colums). # # Columns 1 to 32 are response variables that describes various qualities # of the paper. # # Columns 33 to 41 are 9 predictor variables. The first three predictor # variables (x1 in column 33, x2 in column 34 and x3 in column 35) were # varied systematically through the experiment. The next three predictor # variables (columns 36 to 38) are constructed as x1**2, x2**2 and x3**2. # The last three predictor variables (columns 39 to 41) are constructed # as x1*x2, x1*x3 and x2*x3. ############################################################################## 13.571 12.402 14.136 12.332 12.073 17.608 12.256 14.323 13.851 13.637 15.153 13.122 12.361 16.906 12.126 12.019 17.256 20.557 13.957 18.191 15.190 17.712 12.099 17.371 16.923 13.227 16.760 12.498 14.536 15.621 13.139 10.298 0.190 0.984 1.382 0.036 0.969 1.911 0.187 0.262 1.361 16.890 13.494 15.583 11.565 11.801 16.775 12.821 13.104 14.193 13.153 15.297 13.319 13.396 15.280 12.969 12.701 16.012 21.743 14.662 16.675 15.624 16.480 15.002 18.045 15.646 12.235 16.510 13.149 14.536 13.571 13.467 13.269 0.861 1.528 1.588 0.742 2.334 2.520 1.316 1.367 2.425 14.742 13.990 16.139 14.365 12.527 17.132 13.010 14.323 15.216 14.053 17.390 14.303 16.159 17.881 14.331 12.391 17.878 24.707 15.790 19.538 16.637 18.944 14.035 19.900 18.519 14.549 17.260 14.646 15.844 15.409 15.175 14.787 -0.102 0.432 0.151 0.010 0.187 0.023 -0.044 -0.015 0.065 14.449 13.990 16.028 13.191 13.435 15.823 12.821 14.730 15.148 14.191 16.235 13.975 14.363 16.987 14.396 13.568 18.655 22.533 17.905 19.538 17.071 18.944 13.914 20.912 17.162 15.475 17.010 13.995 16.207 15.338 14.847 14.589 0.015 0.114 -0.055 0.000 0.013 0.003 0.002 -0.001 -0.006 15.816 14.387 15.917 13.100 13.707 17.965 13.858 15.949 13.306 12.184 13.998 11.023 13.673 16.093 13.812 11.338 17.411 22.533 16.213 18.864 15.913 18.482 13.672 18.888 15.087 14.086 17.010 13.605 13.446 15.762 12.416 13.071 0.277 -1.215 1.588 0.077 1.476 2.520 -0.337 0.440 -1.929 14.352 13.692 17.141 13.281 13.435 17.727 14.047 15.339 14.397 12.184 14.576 12.860 14.018 17.231 12.515 12.453 18.188 24.114 15.931 19.370 17.071 18.020 14.760 19.732 16.603 12.301 16.843 11.977 15.117 13.642 12.219 14.589 0.686 -1.266 1.245 0.471 1.603 1.551 -0.868 0.854 -1.577 15.230 14.684 16.362 14.365 15.159 18.560 14.613 16.355 13.920 13.430 15.297 13.450 14.778 18.775 14.331 12.887 18.033 23.521 16.636 19.875 17.215 17.866 13.914 19.900 15.406 12.896 16.760 12.824 14.899 13.712 13.205 13.929 0.598 0.063 0.219 0.358 0.004 0.048 0.038 0.131 0.014 14.742 16.073 16.362 12.739 13.707 18.441 15.744 15.441 13.442 13.499 14.720 12.925 13.535 17.231 13.877 12.267 19.743 23.917 16.354 19.538 17.071 18.944 14.156 19.394 15.965 14.946 15.676 13.800 14.681 16.822 13.270 13.269 0.248 0.347 0.219 0.062 0.121 0.048 0.086 0.054 0.076 14.742 14.387 16.362 12.829 12.799 17.965 14.330 14.425 14.943 13.845 14.648 12.729 14.639 18.044 13.488 13.320 17.411 20.952 15.508 18.696 15.479 16.942 14.277 20.406 17.482 14.020 15.426 13.800 14.245 14.490 13.073 12.477 -1.766 1.549 0.287 3.119 2.399 0.083 -2.736 -0.508 0.445 14.840 14.784 17.364 12.107 13.707 18.322 12.916 14.526 12.896 13.914 14.070 14.762 14.156 17.312 12.321 12.515 18.188 22.336 17.059 19.875 16.926 18.636 14.639 18.551 15.566 14.086 16.676 13.475 14.972 14.560 12.876 14.325 -0.920 1.388 0.151 0.845 1.926 0.023 -1.276 -0.138 0.209 15.523 16.073 16.251 14.004 13.162 18.084 13.387 15.644 15.080 14.122 14.359 14.828 15.537 17.475 12.840 12.577 17.411 22.929 15.508 19.538 17.071 18.020 14.156 20.237 16.524 14.880 18.010 13.149 14.972 14.631 14.913 13.731 0.920 1.124 0.424 0.845 1.264 0.180 1.034 0.390 0.477 15.914 15.081 18.699 12.468 13.435 16.775 12.538 16.457 14.261 14.191 16.163 14.106 15.261 17.800 14.137 13.196 19.588 23.126 17.200 20.549 18.228 18.482 14.639 19.900 17.242 13.888 16.927 14.711 16.425 14.772 14.387 14.457 1.007 1.600 -0.465 1.014 2.560 0.217 1.611 -0.469 -0.744 14.840 15.478 17.141 14.185 13.616 18.798 15.178 16.050 16.035 15.160 17.101 13.778 15.813 18.450 14.591 14.435 19.899 23.521 17.764 20.886 18.083 20.022 15.244 21.081 18.998 15.277 19.595 15.297 15.989 15.197 15.241 14.853 1.182 0.063 -1.013 1.398 0.004 1.026 0.074 -1.197 -0.064 15.914 14.982 17.809 13.823 14.705 17.727 13.576 16.660 17.058 15.576 15.225 13.844 14.916 18.857 14.655 14.188 18.344 24.510 16.777 20.044 18.517 19.098 15.123 20.575 17.641 16.203 18.094 16.794 17.152 15.338 14.847 15.382 1.445 0.538 -1.013 2.088 0.290 1.026 0.778 -1.463 -0.545 14.059 13.891 17.141 13.281 12.981 18.084 13.858 15.034 16.581 16.753 17.462 14.500 16.504 19.426 15.304 14.621 17.722 22.336 16.213 19.033 17.215 18.174 14.035 20.912 17.721 15.211 18.594 14.972 17.152 17.741 14.059 14.787 -1.883 -0.149 -1.286 3.545 0.022 1.655 0.281 2.422 0.192 14.938 15.478 17.030 12.558 13.525 18.322 13.387 15.238 15.284 14.745 16.019 14.500 15.882 19.832 15.044 13.754 18.966 23.719 18.187 19.370 15.913 17.404 14.035 18.888 16.603 13.888 16.927 14.646 16.643 16.751 15.504 13.731 -0.803 -0.205 -1.150 0.644 0.042 1.322 0.164 0.923 0.235 14.449 13.097 16.139 11.745 12.073 15.704 12.067 14.019 14.193 12.945 13.565 13.385 14.847 16.906 12.386 14.064 16.634 20.952 16.495 18.022 15.624 16.942 13.309 18.888 18.360 12.367 17.260 13.865 15.626 13.995 13.927 13.269 -1.211 -0.255 1.451 1.468 0.065 2.105 0.309 -1.757 -0.371 13.083 13.394 15.694 11.745 12.708 16.180 14.047 14.323 14.329 13.845 14.936 12.729 13.811 16.743 14.331 13.878 16.789 21.940 15.931 18.864 16.347 15.864 12.704 18.214 16.284 12.764 17.093 13.540 15.553 14.278 14.387 13.401 -0.920 0.063 1.382 0.845 0.004 1.911 -0.058 -1.271 0.087 14.059 15.478 15.583 12.468 12.527 17.489 14.707 15.847 14.875 14.607 16.091 13.910 14.018 18.288 13.164 14.064 17.256 22.138 14.662 17.854 14.322 17.250 13.309 19.226 16.364 14.285 16.760 12.889 15.044 15.762 13.402 13.203 1.445 0.432 1.314 2.088 0.187 1.726 0.625 1.898 0.568 14.059 14.387 15.694 14.456 12.981 18.917 14.330 15.034 13.647 14.814 14.576 13.319 14.294 16.337 14.720 12.267 17.411 22.336 15.508 19.707 16.347 18.174 13.188 19.563 17.162 14.351 16.927 13.540 14.754 14.843 14.321 14.061 1.036 -0.205 0.014 1.074 0.042 0.000 -0.212 0.014 -0.003 13.668 14.684 15.360 13.371 12.527 17.013 13.858 14.425 15.967 14.607 15.009 13.844 14.847 17.719 15.823 13.072 17.256 21.545 15.226 17.517 16.203 17.712 13.914 18.888 16.204 15.012 17.760 13.409 14.754 14.772 14.519 13.995 -2.000 -1.105 0.219 3.998 1.220 0.048 2.209 -0.438 -0.242 14.352 14.188 15.583 13.462 12.618 17.132 14.707 15.136 14.261 14.814 14.936 15.287 15.261 17.637 14.591 14.497 18.344 21.940 16.636 18.696 15.913 17.096 13.672 20.069 15.486 13.822 17.177 12.498 16.789 15.055 14.256 13.137 -1.912 -1.423 0.014 3.656 2.025 0.000 2.721 -0.026 -0.019 16.597 14.684 17.809 15.088 13.525 17.251 14.990 15.034 16.308 16.407 16.019 14.631 14.708 18.857 14.072 14.126 17.567 23.126 17.341 19.538 15.913 17.404 16.212 19.900 17.162 13.359 18.678 13.800 17.225 15.550 15.241 13.797 -0.190 -0.205 0.014 0.036 0.042 0.000 0.039 -0.003 -0.003 14.156 16.470 17.364 13.643 14.070 19.155 13.764 15.542 15.557 15.230 15.297 15.419 15.882 18.613 15.628 13.754 18.655 22.533 15.649 18.191 15.913 17.558 14.518 19.900 18.759 15.541 19.762 14.776 16.789 15.762 15.241 15.580 -0.073 -0.043 0.014 0.005 0.002 0.000 0.003 -0.001 -0.001 14.156 15.379 16.473 13.733 15.704 18.084 15.178 15.745 14.261 13.845 15.874 12.532 15.123 17.475 14.396 13.506 19.277 23.324 17.482 20.717 17.794 19.252 16.454 20.743 17.482 13.954 17.927 14.581 16.716 16.539 16.030 14.919 0.803 -1.635 0.014 0.644 2.674 0.000 -1.313 0.011 -0.022 16.304 15.280 17.809 15.088 14.978 19.630 15.272 17.777 13.988 14.676 15.730 15.091 14.570 18.450 14.331 15.055 19.277 23.324 17.482 20.717 17.794 19.252 16.454 20.743 17.482 13.954 17.927 14.581 16.716 16.539 16.030 14.919 0.832 -1.423 -1.971 0.692 2.025 3.884 -1.184 -1.640 2.804 14.742 14.982 17.920 15.178 14.978 19.868 15.555 15.847 15.626 14.814 16.885 13.975 16.366 18.044 15.823 14.683 18.033 23.324 15.931 20.212 16.781 20.022 14.881 20.069 16.603 14.549 17.343 15.297 15.408 13.783 14.059 14.127 0.161 -1.499 -0.534 0.026 2.248 0.285 -0.241 -0.086 0.800 17.281 16.569 18.365 14.365 14.433 18.560 15.555 17.574 14.329 14.122 16.957 14.303 15.330 17.231 14.201 15.303 20.209 23.126 17.059 20.044 18.373 18.328 15.728 21.924 15.885 15.144 18.928 14.972 15.044 15.197 15.044 14.589 -0.102 -1.529 -1.423 0.010 2.338 2.026 0.156 0.145 2.177 15.426 15.974 16.919 13.733 14.796 17.965 14.518 16.050 15.216 14.261 15.874 15.353 16.090 19.182 14.526 15.117 18.499 23.126 15.931 20.212 17.505 19.714 14.156 19.563 17.162 15.078 18.511 14.451 16.789 14.843 15.110 13.599 0.394 0.806 -1.423 0.155 0.650 2.026 0.318 -0.561 -1.147 15.914 15.676 17.030 14.275 14.615 18.798 14.141 15.441 15.762 13.845 15.947 15.419 16.435 17.475 15.044 13.692 18.655 22.533 15.790 18.528 17.071 18.020 14.035 18.551 16.204 14.086 18.261 14.321 15.044 14.843 14.650 14.259 -0.219 1.124 -1.355 0.048 1.264 1.836 -0.246 0.297 -1.523