update
This commit is contained in:
Morten Hjorth-Jensen
@@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output"
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Week 40: Gradient descent methods (continued) and start Neural networks
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</a>
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</li>
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<li class="toctree-l1">
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<a class="reference internal" href="exercisesweek41.html">
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Exercises week 41
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</a>
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</li>
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<li class="toctree-l1">
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<a class="reference internal" href="week41.html">
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Week 41 Neural networks and constructing a neural network code
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</a>
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</li>
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<li class="toctree-l1">
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<a class="reference internal" href="exercisesweek42.html">
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Exercises week 42
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</a>
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</li>
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<li class="toctree-l1">
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<a class="reference internal" href="week42.html">
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Week 42 Constructing a Neural Network code with introduction to Tensor flow
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</a>
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</li>
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</ul>
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<p aria-level="2" class="caption" role="heading">
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<span class="caption-text">
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@@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
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Project 1 on Machine Learning, deadline October 9 (midnight), 2023
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</a>
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</li>
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<li class="toctree-l1">
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<a class="reference internal" href="project2.html">
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Project 2 on Machine Learning, deadline November 13 (Midnight)
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</a>
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</li>
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</ul>
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@@ -726,10 +751,10 @@ covariance matrix through the <strong>np.linalg.eig()</strong> function.</p>
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</div>
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</div>
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<div class="cell_output docutils container">
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.026250840755899812
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3.9783319210079595
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[[ 1.06075426 3.40216748]
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[ 3.40216748 11.8635085 ]]
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.10776220958055382
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3.743189104728408
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[[0.82379443 2.29894362]
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[2.29894362 7.75174305]]
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</pre></div>
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</div>
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</div>
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@@ -769,10 +794,10 @@ a more brute force way. Here we scale the mean values for each column of the des
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</div>
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</div>
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<div class="cell_output docutils container">
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.08076969085177746
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1.9295763474254684
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[[1. 0.7135487]
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[0.7135487 1. ]]
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.0704374681593734
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1.3273472571412799
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[[1. 0.58076367]
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[0.58076367 1. ]]
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</pre></div>
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</div>
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</div>
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@@ -801,30 +826,30 @@ this matrix we easily see that it is a positive definite matrix.</p>
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</div>
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</div>
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<div class="cell_output docutils container">
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[ 1.52944573 4.65218729]
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[ 0.12050822 0.97069774]
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[ 0.40413036 1.80861057]
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[-0.07004211 0.30763135]
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[-1.27793476 -4.21460652]
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[-0.14670413 -1.48950243]
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[-0.41506637 -1.52573941]
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[ 1.75627883 5.73410729]
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[-0.47187428 -1.10927588]
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[-1.42874148 -5.13410999]]
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[-0.92200223 -1.78838813]
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[-0.90854751 -2.66047048]
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[ 0.83618601 2.91748202]
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[-0.88821402 -4.10035098]
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[ 0.44781662 2.48685204]
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[ 1.20493234 2.32729105]
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[ 1.02509184 2.42265837]
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[-0.84210141 -3.82012236]
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[-0.01031541 1.40111899]
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[ 0.05715377 0.81392948]]
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0 1
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0 1.529446 4.652187
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1 0.120508 0.970698
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2 0.404130 1.808611
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3 -0.070042 0.307631
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4 -1.277935 -4.214607
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5 -0.146704 -1.489502
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6 -0.415066 -1.525739
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7 1.756279 5.734107
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8 -0.471874 -1.109276
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9 -1.428741 -5.134110
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0 -0.922002 -1.788388
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1 -0.908548 -2.660470
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2 0.836186 2.917482
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3 -0.888214 -4.100351
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4 0.447817 2.486852
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5 1.204932 2.327291
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6 1.025092 2.422658
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7 -0.842101 -3.820122
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8 -0.010315 1.401119
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9 0.057154 0.813929
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0 1
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0 1.000000 0.988835
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1 0.988835 1.000000
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0 1.000000 0.920619
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1 0.920619 1.000000
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</pre></div>
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</div>
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</div>
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@@ -881,37 +906,37 @@ this matrix we easily see that it is a positive definite matrix.</p>
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<div class="cell_output docutils container">
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 0 1 2 3 4 5 6 7 \
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0 0.0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
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1 0.0 0.076825 0.078868 0.077705 0.077226 0.076504 0.071258 0.070157
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2 0.0 0.078868 0.083096 0.081976 0.082506 0.082577 0.076127 0.075513
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3 0.0 0.077705 0.081976 0.085023 0.085454 0.085391 0.081955 0.081126
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4 0.0 0.077226 0.082506 0.085454 0.086441 0.086843 0.082760 0.082255
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5 0.0 0.076504 0.082577 0.085391 0.086843 0.087642 0.083000 0.082781
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6 0.0 0.071258 0.076127 0.081955 0.082760 0.083000 0.081584 0.080933
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7 0.0 0.070157 0.075513 0.081126 0.082255 0.082781 0.080933 0.080505
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8 0.0 0.069033 0.074780 0.080163 0.081570 0.082347 0.080105 0.079878
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9 0.0 0.067915 0.073984 0.079124 0.080773 0.081772 0.079165 0.079121
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10 0.0 0.064634 0.069384 0.076833 0.077710 0.078029 0.078187 0.077613
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11 0.0 0.063407 0.068403 0.075582 0.076662 0.077171 0.076996 0.076587
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12 0.0 0.062221 0.067419 0.074327 0.075587 0.076266 0.075779 0.075521
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13 0.0 0.061084 0.066453 0.073088 0.074509 0.075342 0.074560 0.074439
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14 0.0 0.060001 0.065517 0.071879 0.073445 0.074419 0.073354 0.073362
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1 0.0 0.076527 0.079731 0.075684 0.075421 0.075030 0.066467 0.065808
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2 0.0 0.079731 0.084207 0.080233 0.080607 0.080750 0.071252 0.070964
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3 0.0 0.075684 0.080233 0.079381 0.079948 0.080284 0.072483 0.072285
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4 0.0 0.075421 0.080607 0.079948 0.080953 0.081677 0.073541 0.073640
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5 0.0 0.075030 0.080750 0.080284 0.081677 0.082746 0.074340 0.074708
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6 0.0 0.066467 0.071252 0.072483 0.073541 0.074340 0.068082 0.068257
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7 0.0 0.065808 0.070964 0.072285 0.073640 0.074708 0.068257 0.068650
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8 0.0 0.065215 0.070694 0.072098 0.073720 0.075030 0.068406 0.068997
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9 0.0 0.064696 0.070461 0.071942 0.073802 0.075331 0.068551 0.069320
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10 0.0 0.057462 0.062071 0.064444 0.065735 0.066768 0.061869 0.062273
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11 0.0 0.056898 0.061747 0.064145 0.065645 0.066870 0.061826 0.062390
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12 0.0 0.056418 0.061484 0.063905 0.065593 0.066992 0.061813 0.062523
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13 0.0 0.056019 0.061281 0.063722 0.065582 0.067139 0.061833 0.062675
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14 0.0 0.055697 0.061138 0.063597 0.065614 0.067315 0.061888 0.062852
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8 9 10 11 12 13 14
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0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
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1 0.069033 0.067915 0.064634 0.063407 0.062221 0.061084 0.060001
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2 0.074780 0.073984 0.069384 0.068403 0.067419 0.066453 0.065517
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3 0.080163 0.079124 0.076833 0.075582 0.074327 0.073088 0.071879
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4 0.081570 0.080773 0.077710 0.076662 0.075587 0.074509 0.073445
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5 0.082347 0.081772 0.078029 0.077171 0.076266 0.075342 0.074419
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6 0.080105 0.079165 0.078187 0.076996 0.075779 0.074560 0.073354
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7 0.079878 0.079121 0.077613 0.076587 0.075521 0.074439 0.073362
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8 0.079434 0.078845 0.076857 0.075984 0.075058 0.074108 0.073152
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9 0.078845 0.078412 0.075980 0.075249 0.074457 0.073630 0.072790
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10 0.076857 0.075980 0.076105 0.074970 0.073802 0.072624 0.071452
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11 0.075984 0.075249 0.074970 0.073972 0.072931 0.071872 0.070811
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12 0.075058 0.074457 0.073802 0.072931 0.072009 0.071062 0.070107
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13 0.074108 0.073630 0.072624 0.071872 0.071062 0.070220 0.069365
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14 0.073152 0.072790 0.071452 0.070811 0.070107 0.069365 0.068606
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1 0.065215 0.064696 0.057462 0.056898 0.056418 0.056019 0.055697
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2 0.070694 0.070461 0.062071 0.061747 0.061484 0.061281 0.061138
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3 0.072098 0.071942 0.064444 0.064145 0.063905 0.063722 0.063597
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4 0.073720 0.073802 0.065735 0.065645 0.065593 0.065582 0.065614
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5 0.075030 0.075331 0.066768 0.066870 0.066992 0.067139 0.067315
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6 0.068406 0.068551 0.061869 0.061826 0.061813 0.061833 0.061888
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7 0.068997 0.069320 0.062273 0.062390 0.062523 0.062675 0.062852
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8 0.069522 0.070009 0.062631 0.062894 0.063159 0.063434 0.063723
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9 0.070009 0.070645 0.062963 0.063359 0.063747 0.064134 0.064527
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10 0.062631 0.062963 0.057231 0.057361 0.057502 0.057657 0.057831
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11 0.062894 0.063359 0.057361 0.057613 0.057864 0.058121 0.058388
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12 0.063159 0.063747 0.057502 0.057864 0.058216 0.058567 0.058921
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13 0.063434 0.064134 0.057657 0.058121 0.058567 0.059004 0.059439
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14 0.063723 0.064527 0.057831 0.058388 0.058921 0.059439 0.059949
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</pre></div>
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</div>
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</div>
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@@ -1100,10 +1125,10 @@ We can write our own code or simply use either the functionaly of <strong>numpy<
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</div>
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<div class="cell_output docutils container">
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 0 1
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0 3.942604 1.984308
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1 1.984308 1.984182
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[[3.94260358 1.98430782]
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[1.98430782 1.98418221]]
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0 3.949162 1.987722
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1 1.987722 2.004480
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[[3.94916237 1.98772232]
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[1.98772232 2.00447992]]
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</pre></div>
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</div>
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</div>
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@@ -1130,8 +1155,8 @@ Our own code here is not very elegant and asks for obvious improvements. It is t
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</div>
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<div class="cell_output docutils container">
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Centered covariance using own code
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[[3.94260358 1.98430782]
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[1.98430782 1.98418221]]
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[[3.94916237 1.98772232]
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[1.98772232 2.00447992]]
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</pre></div>
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</div>
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<img alt="_images/chapter8_65_1.png" src="_images/chapter8_65_1.png" />
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@@ -1191,16 +1216,16 @@ questions.</p>
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</div>
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<div class="cell_output docutils container">
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Eigenvalues of Covariance matrix
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5.17615838052499
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0.7506274061293645
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5.189621963782685
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0.7640203256838339
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First eigenvector
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[0.84927263 0.52795454]
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[0.84835621 0.52942586]
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Second eigenvector
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[-0.52795454 0.84927263]
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[-0.52942586 0.84835621]
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</pre></div>
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</div>
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Eigenvector of largest eigenvalue
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[0.84927263 0.52795454]
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[0.84835621 0.52942586]
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</pre></div>
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</div>
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</div>
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