update
This commit is contained in:
Morten Hjorth-Jensen
@@ -34,7 +34,7 @@
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@@ -254,6 +254,9 @@
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<li class="toctree-l1"><a class="reference internal" href="week44.html">Week 44, Convolutional Neural Networks (CNN)</a></li>
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<li class="toctree-l1"><a class="reference internal" href="week45.html">Week 45, Convolutional Neural Networks (CCNs) and Recurrent Neural Networks (RNNs)</a></li>
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<li class="toctree-l1"><a class="reference internal" href="week46.html">Week 46: Decision Trees, Ensemble methods and Random Forests</a></li>
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<li class="toctree-l1"><a class="reference internal" href="week47.html">Week 47: From Decision Trees to Ensemble Methods, Random Forests and Boosting Methods</a></li>
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<li class="toctree-l1"><a class="reference internal" href="exercisesweek47.html">Exercise week 47</a></li>
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</ul>
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<p aria-level="2" class="caption" role="heading"><span class="caption-text">Projects</span></p>
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<ul class="nav bd-sidenav">
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@@ -614,10 +617,10 @@ 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>-0.10788894797253629
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3.6790874039223653
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[[ 1.18171035 3.52117449]
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[ 3.52117449 11.6382529 ]]
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.08913527419249101
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3.7127415072708665
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[[ 1.13025431 3.39215451]
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[ 3.39215451 11.15061293]]
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</pre></div>
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@@ -657,10 +660,10 @@ 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>0.08881838553924991
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1.6247013033699416
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[[1. 0.65701477]
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[0.65701477 1. ]]
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.09335279187105122
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2.2108106787032815
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[[1. 0.66771869]
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[0.66771869 1. ]]
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</pre></div>
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</div>
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</div>
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@@ -689,30 +692,30 @@ 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>[[-0.05662878 1.37467921]
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[-1.56333824 -3.5136046 ]
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[ 0.15344015 1.34849765]
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[ 0.71518529 2.50939698]
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[-0.2748515 -2.1020484 ]
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[-0.10159408 -2.63005749]
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[-0.64480719 -1.2968224 ]
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[ 0.55460489 1.06146057]
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[ 1.03970435 4.18061699]
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[ 0.1782851 -0.93211852]]
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[ 0.35582913 0.96196912]
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[ 0.20039135 1.07902642]
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[-0.47708415 -1.39752266]
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[-0.0118395 0.55664957]
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[-0.18990703 1.30646904]
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[ 0.22370063 -0.76173777]
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[-0.25925579 -1.7132548 ]
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[-0.56061802 -1.9921751 ]
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[-1.14025916 -4.44655399]
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[ 1.85904253 6.40713017]]
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0 1
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0 -0.056629 1.374679
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1 -1.563338 -3.513605
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2 0.153440 1.348498
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3 0.715185 2.509397
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4 -0.274852 -2.102048
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5 -0.101594 -2.630057
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6 -0.644807 -1.296822
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7 0.554605 1.061461
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8 1.039704 4.180617
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9 0.178285 -0.932119
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0 0.355829 0.961969
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1 0.200391 1.079026
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2 -0.477084 -1.397523
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3 -0.011839 0.556650
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4 -0.189907 1.306469
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5 0.223701 -0.761738
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6 -0.259256 -1.713255
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7 -0.560618 -1.992175
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8 -1.140259 -4.446554
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9 1.859043 6.407130
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0 1
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0 1.000000 0.845552
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1 0.845552 1.000000
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0 1.000000 0.946278
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1 0.946278 1.000000
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</pre></div>
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</div>
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</div>
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@@ -769,37 +772,37 @@ 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 0.084442 0.087416 0.085903 0.084926 0.083769 0.078992 0.077203
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2 0.0 0.087416 0.092483 0.089654 0.089681 0.089361 0.082384 0.081118
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3 0.0 0.085903 0.089654 0.093779 0.092882 0.091642 0.089976 0.087925
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4 0.0 0.084926 0.089681 0.092882 0.092595 0.091896 0.089004 0.087346
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5 0.0 0.083769 0.089361 0.091642 0.091896 0.091694 0.087651 0.086360
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6 0.0 0.078992 0.082384 0.089976 0.089004 0.087651 0.088697 0.086573
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7 0.0 0.077203 0.081118 0.087925 0.087346 0.086360 0.086573 0.084743
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8 0.0 0.075459 0.079833 0.085858 0.085639 0.084999 0.084404 0.082852
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9 0.0 0.073790 0.078582 0.083819 0.083940 0.083630 0.082237 0.080953
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10 0.0 0.071660 0.074465 0.083896 0.082819 0.081372 0.084236 0.082113
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11 0.0 0.069730 0.072833 0.081583 0.080779 0.079598 0.081839 0.079946
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12 0.0 0.067898 0.071271 0.079347 0.078801 0.077874 0.079503 0.077829
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13 0.0 0.066167 0.069798 0.077201 0.076902 0.076222 0.077241 0.075780
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14 0.0 0.064543 0.068424 0.075155 0.075095 0.074656 0.075064 0.073809
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1 0.0 0.075894 0.073179 0.073456 0.072746 0.071970 0.064485 0.064123
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2 0.0 0.073179 0.070833 0.070597 0.070031 0.069409 0.061930 0.061649
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3 0.0 0.073456 0.070597 0.076555 0.075647 0.074674 0.070295 0.069812
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4 0.0 0.072746 0.070031 0.075647 0.074821 0.073930 0.069398 0.068968
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5 0.0 0.071970 0.069409 0.074674 0.073930 0.073126 0.068445 0.068069
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6 0.0 0.064485 0.061930 0.070295 0.069398 0.068445 0.066551 0.066050
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7 0.0 0.064123 0.061649 0.069812 0.068968 0.068069 0.066050 0.065589
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8 0.0 0.063763 0.061372 0.069330 0.068539 0.067694 0.065550 0.065128
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9 0.0 0.063403 0.061097 0.068844 0.068107 0.067318 0.065047 0.064664
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10 0.0 0.055942 0.053732 0.062913 0.062085 0.061210 0.060946 0.060463
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11 0.0 0.055680 0.053525 0.062569 0.061780 0.060945 0.060582 0.060130
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12 0.0 0.055429 0.053330 0.062237 0.061487 0.060692 0.060229 0.059808
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13 0.0 0.055190 0.053147 0.061915 0.061205 0.060449 0.059887 0.059497
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14 0.0 0.054960 0.052974 0.061603 0.060933 0.060217 0.059554 0.059195
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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 0.075459 0.073790 0.071660 0.069730 0.067898 0.066167 0.064543
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2 0.079833 0.078582 0.074465 0.072833 0.071271 0.069798 0.068424
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3 0.085858 0.083819 0.083896 0.081583 0.079347 0.077201 0.075155
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4 0.085639 0.083940 0.082819 0.080779 0.078801 0.076902 0.075095
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5 0.084999 0.083630 0.081372 0.079598 0.077874 0.076222 0.074656
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6 0.084404 0.082237 0.084236 0.081839 0.079503 0.077241 0.075064
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7 0.082852 0.080953 0.082113 0.079946 0.077829 0.075780 0.073809
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8 0.081230 0.079591 0.079936 0.077991 0.076088 0.074246 0.072478
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9 0.079591 0.078208 0.077748 0.076019 0.074325 0.072688 0.071121
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10 0.079936 0.077748 0.081045 0.078681 0.076364 0.074111 0.071928
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11 0.077991 0.076019 0.078681 0.076508 0.074378 0.072303 0.070295
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12 0.076088 0.074325 0.076364 0.074378 0.072426 0.070527 0.068690
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13 0.074246 0.072688 0.074111 0.072303 0.070527 0.068798 0.067128
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14 0.072478 0.071121 0.071928 0.070295 0.068690 0.067128 0.065622
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1 0.063763 0.063403 0.055942 0.055680 0.055429 0.055190 0.054960
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2 0.061372 0.061097 0.053732 0.053525 0.053330 0.053147 0.052974
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3 0.069330 0.068844 0.062913 0.062569 0.062237 0.061915 0.061603
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4 0.068539 0.068107 0.062085 0.061780 0.061487 0.061205 0.060933
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5 0.067694 0.067318 0.061210 0.060945 0.060692 0.060449 0.060217
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6 0.065550 0.065047 0.060946 0.060582 0.060229 0.059887 0.059554
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7 0.065128 0.064664 0.060463 0.060130 0.059808 0.059497 0.059195
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8 0.064706 0.064282 0.059981 0.059679 0.059388 0.059108 0.058837
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9 0.064282 0.063898 0.059497 0.059226 0.058967 0.058718 0.058478
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10 0.059981 0.059497 0.056837 0.056475 0.056124 0.055783 0.055452
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11 0.059679 0.059226 0.056475 0.056139 0.055814 0.055499 0.055194
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12 0.059388 0.058967 0.056124 0.055814 0.055515 0.055226 0.054947
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13 0.059108 0.058718 0.055783 0.055499 0.055226 0.054963 0.054709
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14 0.058837 0.058478 0.055452 0.055194 0.054947 0.054709 0.054481
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</pre></div>
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</div>
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</div>
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@@ -988,10 +991,10 @@ 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 3.970238 1.999801
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1 1.999801 2.021273
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[[3.97023801 1.99980092]
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[1.99980092 2.02127327]]
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0 3.946263 1.971035
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1 1.971035 1.988524
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[[3.94626291 1.97103474]
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[1.97103474 1.98852413]]
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</pre></div>
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</div>
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</div>
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@@ -1018,11 +1021,11 @@ 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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[[3.97023801 1.99980092]
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[1.99980092 2.02127327]]
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[[3.94626291 1.97103474]
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[1.97103474 1.98852413]]
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</pre></div>
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</div>
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<img alt="_images/e5e6bf0c464c3e5a86a023adac1e329391745d4c31e520e53767d038a5bcf4ae.png" src="_images/e5e6bf0c464c3e5a86a023adac1e329391745d4c31e520e53767d038a5bcf4ae.png" />
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<img alt="_images/6ca0e6a8c6122c37cbb752b49917fd1e67a1de46298e8c2247a990d083fdb3c7.png" src="_images/6ca0e6a8c6122c37cbb752b49917fd1e67a1de46298e8c2247a990d083fdb3c7.png" />
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</div>
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</div>
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<p>Depending on the number of points <span class="math notranslate nohighlight">\(n\)</span>, we will get results that are close to the covariance values defined above.
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@@ -1079,16 +1082,16 @@ 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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5.220349900775413
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0.7711613838358012
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5.168112312789667
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0.7666747242371026
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First eigenvector
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[0.84795327 0.53007099]
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[0.84993979 0.52687982]
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Second eigenvector
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[-0.53007099 0.84795327]
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[-0.52687982 0.84993979]
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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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[-0.84795327 -0.53007099]
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[0.84993979 0.52687982]
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</pre></div>
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</div>
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</div>
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