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quad_metric_data_norng.m
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% data for learning a quadratic metric
n = 5;
N = 100;
N_test = 10;
X = [1.164954 1.696142 -1.446172 -0.360030 -0.044881 0.513478 0.375041 -0.322940 0.847649 -0.557094 -1.098195 -0.977814 -0.507700 -0.612911 1.133000 0.924159 0.394600 -0.137414 0.039885 -0.786457 -0.127443 -0.620214 -0.262681 0.499521 0.438705 0.292315 -0.759697 0.670292 -0.902031 0.846106 0.526163 0.889164 -1.010674 -1.406949 -0.165923 0.041430 -0.844414 0.336297 1.487524 0.786430 -0.702669 1.802440 -1.931134 -1.238566 1.547177 -2.526706 0.899884 -0.382918 -0.594524 1.879957 0.396727 -0.031243 0.251078 0.862500 0.968992 0.536007 1.524681 1.157783 -1.898778 -1.454749 0.418469 1.766708 -0.159448 -1.179060 -1.226502 0.658153 -0.397914 1.271743 -1.389722 -0.797533 -0.268286 1.939318 1.338814 0.420989 0.139860 -2.014986 -0.267458 0.605540 0.186747 0.434313 0.149996 1.136805 -1.378907 0.086932 -0.066596 0.642066 0.565239 -0.591204 0.393682 0.667201 -0.514013 1.289554 -0.227852 -0.904204 -1.586917 -0.047555 -0.391039 -0.956374 1.042360 -1.024905;
0.626839 0.059060 -0.701165 -0.135576 -0.798945 0.396681 1.125162 0.317988 0.268101 -0.336706 1.122648 -1.021466 0.885299 -0.209144 0.149994 -1.814115 0.639406 0.615770 -2.482843 0.634809 0.554172 0.237149 0.976490 -1.055375 -1.247344 2.565910 -0.674721 0.420146 -2.053257 -0.184538 -0.184454 -1.299152 -0.960498 1.030812 0.300907 -1.098050 -0.311630 -0.221361 -0.836821 -1.461639 0.356429 -0.642984 0.660300 -1.889236 0.644933 -0.312981 -0.200899 0.155083 0.130246 -1.003849 -0.527115 0.778212 -0.310471 -1.034706 -0.747317 0.298451 -0.195261 0.161908 1.822525 0.466546 0.247349 -0.382104 2.704026 -0.277776 0.069600 0.491314 0.864280 -0.035344 0.229328 -0.936741 -1.082140 -0.895840 1.222299 -0.433373 -0.748089 0.491717 -0.570245 -0.624481 1.594939 -0.386207 0.542038 0.391314 -0.260172 1.955674 0.373381 0.923087 -0.610781 1.691546 -0.905427 -0.067794 1.896261 -0.530575 0.376770 0.698670 -0.920783 -0.614736 -1.382045 0.451807 1.209120 -1.056846;
0.075080 1.797072 1.245982 -1.349338 -0.765172 0.756219 0.728642 -0.511172 -0.923489 0.415227 0.581667 0.317688 -0.248094 0.562148 0.703144 0.034973 0.874213 0.977894 1.158655 0.820410 -1.097344 -1.586847 0.977815 -0.450743 0.324667 -0.457816 -1.171687 -2.872751 0.089086 1.030714 0.198783 1.182573 0.691160 -0.759874 -0.322467 1.566724 0.397810 0.016649 -1.300982 1.554466 0.652636 0.109555 -1.102510 -0.973585 -2.148359 -0.593618 -0.233735 -0.964648 0.035014 -0.497446 0.344571 2.180484 -0.923004 -0.192673 -2.796024 0.284043 0.017260 1.557064 -1.518415 0.545437 0.704110 -0.911425 -0.198500 -1.581053 -0.396516 0.800734 -0.177618 -1.501329 0.271190 -0.002433 2.014134 -0.304158 -1.595978 0.706252 -0.628975 -1.554975 -0.187267 0.572228 0.321307 -0.112564 0.254409 1.605148 0.994768 0.161454 0.217314 -1.555108 1.231111 0.953356 -1.274473 -1.735660 -0.253230 -0.692971 1.221556 0.482598 -0.614274 0.240362 1.076292 -1.253778 0.780955 2.887723;
0.351607 0.264069 -0.638977 -1.270450 0.861735 0.400486 -2.377454 -0.002041 -0.070499 1.557814 -0.271354 1.516108 -0.726249 -1.063923 -0.052412 -1.807862 1.752402 -1.115348 -1.026279 -0.176027 -0.731301 -0.401485 1.170021 1.270378 0.390070 -1.610827 2.032930 1.685874 2.087099 -1.527623 1.590427 1.817472 -0.758618 0.874127 -0.368411 -1.048423 1.049786 -1.192361 1.574132 -0.597535 0.215671 -0.719038 -0.102971 0.212116 -1.028845 0.332322 1.449907 0.038756 -0.624674 -1.504397 -0.723291 0.437814 -0.384776 -1.299723 0.696732 0.959664 0.246340 -0.193544 -1.051071 1.320319 0.631939 -0.996090 -0.141405 1.049022 1.388807 -0.767269 1.874381 0.365373 -0.366360 0.396086 1.944031 0.555253 -1.067730 0.227857 1.394831 -0.140609 1.208557 -0.724410 0.866841 -0.964333 -0.307241 0.825892 1.834034 -0.628688 -0.179457 0.663594 0.994300 -1.930055 0.346546 0.806349 -0.174531 -0.859806 1.098288 0.811696 -0.334672 0.125017 1.269466 0.256435 -1.179900 -0.267744;
-0.696513 0.871673 0.577350 0.984570 -0.056225 -1.341381 -0.273782 1.606511 0.147891 -2.444299 0.414191 0.749432 -0.445040 0.351589 2.018496 1.028193 -0.320051 -0.550021 1.153487 0.562474 1.404732 -0.770692 0.159311 0.898694 -0.405138 -2.669524 0.968481 0.027925 0.365118 0.964939 0.032192 -0.584302 -0.096972 0.761127 1.147895 0.422724 -0.340796 -0.131646 1.166040 -1.210568 -0.263896 0.420628 -1.059802 0.493442 -0.141582 0.558851 1.836132 0.765458 -0.539775 -0.095449 1.268193 1.333329 1.158181 0.306596 3.206908 2.087593 -0.854485 1.651301 0.049931 -0.404494 -0.992362 1.195143 0.411268 0.302689 1.364422 0.364420 0.172400 -0.198660 1.376960 -0.508693 -1.521529 -0.324247 -0.759919 -1.016992 -1.647691 0.244944 -0.638855 1.192196 1.291844 -2.057251 -0.417112 1.470390 -1.715910 -1.438824 0.025673 -0.609500 -0.803475 0.512845 -1.195235 -0.914801 0.978788 0.529038 -0.853014 0.327883 0.080345 -0.223605 0.487268 0.421229 1.001450 -0.488540];
Y = [0.419420 -0.611729 -0.506138 -2.122378 -0.673263 -1.350292 0.202680 0.186106 1.408075 0.179925 -0.683631 0.450343 -0.201343 -0.906374 -0.179097 0.067372 1.177170 1.173296 -0.574005 -0.081630 1.662312 1.166705 -0.960461 -0.915962 0.427947 0.213963 0.261843 0.144555 -0.972946 -0.534127 -0.310909 -1.719190 -0.345134 -0.785496 -0.275569 -0.744296 2.680118 -0.583258 -2.068566 0.385524 0.610146 -0.226541 0.263481 -0.988875 -0.130638 -1.266094 -0.768533 1.100780 -0.328912 -1.555024 0.698124 1.361879 -1.159160 -1.450383 -1.304731 1.000335 0.125589 -0.260304 -1.212525 -0.265477 -1.474263 -2.366324 1.195417 1.966075 2.955089 -1.133640 -2.032843 -0.902634 -1.327697 0.323356 0.096060 -0.875772 -1.672760 -1.548104 -0.426525 1.189467 0.750603 -1.340946 -0.876102 0.982860 0.016264 -0.934128 0.660062 0.131692 1.855048 -0.835704 -1.685751 -0.632046 1.599021 -0.245918 1.132966 -0.997240 -0.242387 0.082218 0.836056 -2.938220 1.116575 0.750101 -1.146451 -0.040269;
-0.742745 0.100402 -0.983137 -0.850378 0.989850 0.092861 -0.421487 0.667174 -1.476422 0.029963 0.813277 -0.119641 -1.236394 -0.515380 0.168926 0.184150 -1.298539 1.611950 1.362962 -1.223518 -0.256088 -0.659430 0.130287 1.490409 0.357348 0.100046 -0.440424 0.810685 1.150638 0.688182 0.177537 0.090665 -1.015168 -0.242882 2.150379 -0.200403 -0.384886 -1.039926 1.674866 -0.784288 0.478515 1.329307 0.647336 1.036852 0.015360 1.299368 1.038744 -0.393357 1.739255 0.853390 0.623186 -0.105752 1.466680 0.475028 0.443241 -0.010695 1.233429 1.302974 0.593773 1.787029 0.268053 -0.869979 -1.700570 -2.301185 1.874092 0.462473 0.564390 1.279284 0.786037 0.615560 -0.395321 0.665887 -0.027883 0.612520 -0.508498 -0.363852 0.547452 0.181441 -1.256036 1.333580 -1.287073 0.035241 -1.229566 1.644603 2.084384 -1.018327 0.358190 0.783785 0.990909 1.646456 -0.492347 1.105070 -0.445072 0.732257 -1.958656 -1.104897 -1.372281 -0.728689 1.365443 -0.281505;
0.572912 -1.112905 -0.437222 -0.424095 -0.577293 1.390198 1.218891 -0.429976 -0.809376 -0.711098 0.137012 0.299881 0.576187 1.181516 0.796552 -0.056014 -0.410115 2.318210 1.148564 -1.084040 -0.807258 0.385522 0.893410 2.148636 -0.513751 0.721376 -1.816264 -0.617132 0.042902 1.722587 -0.976696 1.660189 0.805136 -0.020406 -1.161508 -0.276941 -0.057147 -1.398089 -0.582561 0.384008 0.620631 -1.655171 0.814268 -0.057835 -0.673946 0.531241 0.639814 -0.222340 -1.587151 -0.779175 0.625826 -2.359716 0.255200 -0.586808 -0.400561 -0.832345 1.059862 -1.358675 0.597249 0.034741 1.765786 -0.699984 -0.585549 -0.994563 0.109977 -0.046205 1.156908 -0.346535 1.117178 -1.723877 -1.651466 0.937835 0.438835 0.193465 0.241914 -0.228302 -1.737480 0.030161 -0.269798 -0.926771 -1.553320 1.576796 -0.570628 -0.236055 -0.227784 -0.945054 -0.671933 0.240538 0.066988 1.561130 -0.336589 -1.148196 0.748184 -0.962436 -0.779537 -1.547502 2.074836 -0.648186 -0.632439 -1.227824;
-0.143680 0.957172 1.640728 -1.029596 -1.278514 0.153271 -1.751493 -1.146584 -0.196892 0.456901 0.403788 0.643104 0.933544 0.200532 -0.464512 0.674326 -1.847284 -0.814667 -0.378804 -0.440653 -0.077400 -0.187585 0.348338 1.129853 -0.086701 0.091444 0.528719 -1.191801 0.664119 -1.273178 -0.765922 -0.653223 -1.287555 -1.440631 -0.001266 -0.975253 -1.728765 0.844010 -0.785796 0.839488 -1.770459 -0.060916 -0.709093 -0.823255 -0.525083 -0.719614 -0.661728 -0.259005 1.013978 0.844147 -1.408990 -0.777909 -0.146252 0.305144 -0.621204 -1.181208 -1.755407 0.359975 -0.294485 0.325478 -1.768180 0.859512 2.205565 0.106741 -1.372973 -1.298474 1.253641 0.081997 -0.540079 1.241964 -1.098188 1.563100 0.800308 -1.093574 -0.408954 -0.824891 -0.296406 0.381845 -0.732456 1.154125 -0.059866 -1.532254 -0.682228 -0.706986 -0.265914 -0.865398 -1.021033 -1.470454 1.993145 -0.758432 0.059077 -0.473563 -2.271209 0.876035 1.224104 -1.434385 1.485758 0.138927 1.959653 1.159358;
-0.156844 -0.577886 0.530367 -0.349036 0.281387 0.801381 2.945547 -1.873306 -1.127700 -1.077242 1.288723 -1.775968 1.131390 -0.364330 -0.814449 2.557545 -0.899062 0.853069 -2.380476 -1.522343 -1.595641 -1.598445 0.760433 -1.434479 -0.668682 -0.002400 -0.351920 -2.082037 1.577989 -1.126164 -2.372749 2.050284 2.145294 0.780599 -1.142249 0.397122 1.280767 0.248825 -0.594914 0.471760 -0.351909 -0.470341 -0.669992 1.956099 0.711471 -0.107439 -0.170603 -1.262057 1.207766 -0.643000 -1.170419 -0.059081 -0.108548 1.017417 1.200154 -0.766562 -0.554640 1.314540 -0.935959 0.565107 1.627511 -1.296415 -0.827220 1.375143 -1.354662 0.080468 0.309434 -1.756170 -0.920435 0.568060 -1.103339 -0.756307 -0.974407 0.977825 -1.021484 0.610675 -0.369597 1.463439 0.279208 2.135796 0.582646 -0.254342 0.254562 -0.588331 -0.021790 -0.808710 2.498869 0.334877 -0.633251 -0.903983 -0.991926 0.333565 -1.080591 -0.633172 0.576336 0.128015 -0.043598 -0.153634 0.431631 -1.274743];
X_test = [-0.186647 -0.636795 -0.242266 -1.000994 -1.094656 -0.088627 0.357200 1.236353 -0.657828 -1.081924;
-2.001022 0.007438 0.545292 1.134810 1.258890 -0.459909 1.365078 -1.397270 -0.864847 0.965412;
-1.028858 -0.002620 1.980639 0.758663 0.336024 -0.261001 -0.718739 -1.722115 -2.186815 0.701975;
0.545433 0.056516 0.111102 0.291716 1.496372 0.085050 0.415523 -1.234309 -0.785680 -1.487673;
0.224813 -1.022040 3.533658 2.245274 -0.665822 -0.009841 0.179097 0.494105 -0.905888 -0.197859];
Y_test = [-0.294687 -0.689915 -2.285898 -0.938975 0.035156 -0.430063 0.352267 -0.385081 -0.752931 -0.014699;
-0.222314 0.699612 -0.264101 -0.767007 -0.183959 1.502923 -0.280606 1.081048 0.391797 -0.011185;
1.801455 0.772426 -0.945537 0.322200 0.057886 0.579556 0.961475 -1.396751 0.404377 -0.063508;
-0.133797 0.497607 0.310190 0.612367 -0.926959 -0.457190 1.309079 -1.575387 -1.116767 -1.027934;
-2.243783 0.391663 0.852659 0.069602 2.284313 -0.057675 -1.306810 -0.515741 -1.484789 0.988259];
d = [3.105698 9.303920 6.834464 8.535880 6.895867 2.084421 5.802307 6.078630 7.676743 7.889291 1.747867 5.421094 8.056460 5.403059 6.134915 9.260686 11.292909 6.465282 12.659127 6.716904 8.247420 7.677115 2.345364 10.289954 7.556104 9.927747 2.885653 8.667243 10.105910 8.164997 4.403754 10.905269 6.736946 7.881454 9.098149 5.616785 13.511874 8.607833 10.158668 7.828967 6.669338 10.942197 7.102851 12.512170 1.693926 5.316018 6.161766 7.008868 8.568092 13.728702 4.080557 10.282838 6.515821 11.142170 8.083361 4.659479 7.252958 11.903167 9.148000 7.844158 7.144369 12.485157 16.621630 13.365911 10.855162 4.169473 3.658437 6.554199 5.956399 6.189959 15.132870 8.958080 11.450199 6.767207 6.598192 8.818651 8.531837 5.173845 8.337579 10.310235 6.315191 1.352438 12.100806 2.871881 5.391262 5.899694 12.221590 4.330038 5.430671 8.585915 9.817138 8.901824 9.322942 3.233721 4.747448 5.238966 4.640416 5.379597 11.164867 10.616969];
d_test = [7.600672 4.423181 9.997974 8.315172 12.786013 7.426758 11.055029 8.688143 6.585704 4.253190];
Z = X - Y;
cvx_begin
variable P(n,n) symmetric;
f = 0; %build up objective function iteratively
for i=1:N
f = f + d(i)^2 - 2*d(i)*sqrt(Z(:,i)'*P*Z(:,i)) + Z(:,i)'*P*Z(:,i);
end
minimize (f/N)
subject to
P == semidefinite(n);
cvx_end
mse = f/N
Z_test = X_test - Y_test;
mse_test = 0;
for i=1:N_test
mse_test = mse_test + d_test(i)^2 - 2*d_test(i)*sqrt(Z_test(:,i)'*P*Z_test(:,i)) + Z_test(:,i)'*P*Z_test(:,i);
end
mse_test = mse_test/N_test