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Morten Hjorth-Jensen
2024-11-03 14:50:52 +01:00
parent e9d6ea5784
commit 620d191340
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doc/LectureNotes/_build/html/chapter8.html
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@@ -353,6 +353,11 @@ const thebe_selector_output = ".output, .cell_output"
Week 44, Convolutional Neural Networks (CNN)
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="week45.html">
Week 45, Convolutional Neural Networks (CCNs) and Recurrent Neural Networks (RNNs)
</a>
</li>
</ul>
<p aria-level="2" class="caption" role="heading">
<span class="caption-text">
@@ -771,10 +776,10 @@ covariance matrix through the <strong>np.linalg.eig()</strong> function.</p>
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.0610096522011426
3.8847504075456363
[[ 1.07280604 3.11827698]
[ 3.11827698 10.20730033]]
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.07475005787902417
4.35510226157812
[[ 1.02595928 3.2527634 ]
[ 3.2527634 11.12684733]]
</pre></div>
</div>
</div>
@@ -814,10 +819,10 @@ a more brute force way. Here we scale the mean values for each column of the des
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.08699604706693358
1.8785678201327416
[[1. 0.67701729]
[0.67701729 1. ]]
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.0746776881193676
1.7289381470678358
[[1. 0.74948572]
[0.74948572 1. ]]
</pre></div>
</div>
</div>
@@ -846,32 +851,30 @@ this matrix we easily see that it is a positive definite matrix.</p>
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[-0.56439048 -1.59243304]
[ 0.34744134 -0.79671424]
[-1.55842946 -5.7693748 ]
[ 0.1084649 0.43675706]
[-0.34689964 -0.80973749]
[ 0.54581307 1.66293202]
[-0.38075194 -0.87904563]
[ 0.89964122 5.25714271]
[ 0.67258465 1.91633883]
[ 0.27652633 0.57413459]]
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 0 1
0 -0.564390 -1.592433
1 0.347441 -0.796714
2 -1.558429 -5.769375
3 0.108465 0.436757
4 -0.346900 -0.809737
5 0.545813 1.662932
6 -0.380752 -0.879046
7 0.899641 5.257143
8 0.672585 1.916339
9 0.276526 0.574135
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[-0.16405003 0.54955605]
[-0.11637304 -0.7621305 ]
[ 0.01996582 1.48906628]
[-0.79270207 -3.3173567 ]
[ 0.52745417 2.2316734 ]
[ 1.34172766 4.48299299]
[-0.60711982 -1.1103761 ]
[-1.56812901 -5.66825374]
[ 0.74859587 2.31737432]
[ 0.61063045 -0.212546 ]]
0 1
0 1.000000 0.932605
1 0.932605 1.000000
0 -0.164050 0.549556
1 -0.116373 -0.762131
2 0.019966 1.489066
3 -0.792702 -3.317357
4 0.527454 2.231673
5 1.341728 4.482993
6 -0.607120 -1.110376
7 -1.568129 -5.668254
8 0.748596 2.317374
9 0.610630 -0.212546
0 1
0 1.000000 0.933053
1 0.933053 1.000000
</pre></div>
</div>
</div>
@@ -928,37 +931,37 @@ this matrix we easily see that it is a positive definite matrix.</p>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 0 1 2 3 4 5 6 7 \
0 0.0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
1 0.0 0.079059 0.081365 0.076315 0.081270 0.086391 0.066334 0.070891
2 0.0 0.081365 0.085489 0.076059 0.081793 0.087930 0.064777 0.069667
3 0.0 0.076315 0.076059 0.078398 0.082223 0.085871 0.071052 0.075199
4 0.0 0.081270 0.081793 0.082223 0.086686 0.091074 0.073735 0.078326
5 0.0 0.086391 0.087930 0.085871 0.091074 0.096339 0.076078 0.081151
6 0.0 0.066334 0.064777 0.071052 0.073735 0.076078 0.066329 0.069696
7 0.0 0.070891 0.069667 0.075199 0.078326 0.081151 0.069696 0.073438
8 0.0 0.075831 0.075047 0.079570 0.083213 0.086609 0.073167 0.077326
9 0.0 0.081169 0.080964 0.084139 0.088383 0.092454 0.076692 0.081316
10 0.0 0.057338 0.055249 0.063213 0.065107 0.066605 0.060295 0.063007
11 0.0 0.061147 0.059192 0.066951 0.069155 0.070974 0.063515 0.066524
12 0.0 0.065303 0.063532 0.070967 0.073529 0.075723 0.066934 0.070275
13 0.0 0.069840 0.068317 0.075276 0.078251 0.080886 0.070553 0.074265
14 0.0 0.074791 0.073599 0.079886 0.083341 0.086493 0.074366 0.078493
1 0.0 0.091870 0.082074 0.092077 0.086967 0.081650 0.082936 0.079181
2 0.0 0.082074 0.074742 0.080377 0.076475 0.072462 0.071634 0.068667
3 0.0 0.092077 0.080377 0.097651 0.091384 0.084848 0.091276 0.086696
4 0.0 0.086967 0.076475 0.091384 0.085807 0.079987 0.084996 0.080907
5 0.0 0.081650 0.072462 0.084848 0.079987 0.074920 0.078475 0.074883
6 0.0 0.082936 0.071634 0.091276 0.084996 0.078475 0.087603 0.082951
7 0.0 0.079181 0.068667 0.086696 0.080907 0.074883 0.082951 0.078670
8 0.0 0.075515 0.065793 0.082200 0.076895 0.071365 0.078384 0.074464
9 0.0 0.071891 0.062978 0.077729 0.072907 0.067875 0.073847 0.070281
10 0.0 0.073837 0.063468 0.083409 0.077459 0.071310 0.081647 0.077164
11 0.0 0.070649 0.060893 0.079551 0.073998 0.068246 0.077709 0.073536
12 0.0 0.067610 0.058445 0.075858 0.070684 0.065314 0.073933 0.070055
13 0.0 0.064698 0.056110 0.072302 0.067495 0.062496 0.070295 0.066700
14 0.0 0.061891 0.053872 0.068856 0.064406 0.059771 0.066768 0.063444
8 9 10 11 12 13 14
0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
1 0.075831 0.081169 0.057338 0.061147 0.065303 0.069840 0.074791
2 0.075047 0.080964 0.055249 0.059192 0.063532 0.068317 0.073599
3 0.079570 0.084139 0.063213 0.066951 0.070967 0.075276 0.079886
4 0.083213 0.088383 0.065107 0.069155 0.073529 0.078251 0.083341
5 0.086609 0.092454 0.066605 0.070974 0.075723 0.080886 0.086493
6 0.073167 0.076692 0.060295 0.063515 0.066934 0.070553 0.074366
7 0.077326 0.081316 0.063007 0.066524 0.070275 0.074265 0.078493
8 0.081683 0.086203 0.065751 0.069590 0.073705 0.078104 0.082794
9 0.086203 0.091326 0.068471 0.072660 0.077172 0.082023 0.087227
10 0.065751 0.068471 0.055720 0.058436 0.061294 0.064287 0.067400
11 0.069590 0.072660 0.058436 0.061405 0.064542 0.067841 0.071290
12 0.073705 0.077172 0.061294 0.064542 0.067986 0.071624 0.075448
13 0.078104 0.082023 0.064287 0.067841 0.071624 0.075640 0.079883
14 0.082794 0.087227 0.067400 0.071290 0.075448 0.079883 0.084595
1 0.075515 0.071891 0.073837 0.070649 0.067610 0.064698 0.061891
2 0.065793 0.062978 0.063468 0.060893 0.058445 0.056110 0.053872
3 0.082200 0.077729 0.083409 0.079551 0.075858 0.072302 0.068856
4 0.076895 0.072907 0.077459 0.073998 0.070684 0.067495 0.064406
5 0.071365 0.067875 0.071310 0.068246 0.065314 0.062496 0.059771
6 0.078384 0.073847 0.081647 0.077709 0.073933 0.070295 0.066768
7 0.074464 0.070281 0.077164 0.073536 0.070055 0.066700 0.063444
8 0.070610 0.066774 0.072769 0.069439 0.066244 0.063164 0.060174
9 0.066774 0.063285 0.068412 0.065374 0.062458 0.059646 0.056918
10 0.072769 0.068412 0.077270 0.073441 0.069770 0.066233 0.062805
11 0.069439 0.065374 0.073441 0.069876 0.066455 0.063158 0.059960
12 0.066244 0.062458 0.069770 0.066455 0.063273 0.060204 0.057225
13 0.063164 0.059646 0.066233 0.063158 0.060204 0.057353 0.054585
14 0.060174 0.056918 0.062805 0.059960 0.057225 0.054585 0.052021
</pre></div>
</div>
</div>
@@ -1147,10 +1150,10 @@ We can write our own code or simply use either the functionaly of <strong>numpy<
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 0 1
0 4.021032 1.990843
1 1.990843 1.969959
[[4.02103235 1.99084335]
[1.99084335 1.9699594 ]]
0 4.070272 2.059136
1 2.059136 2.054311
[[4.07027208 2.05913631]
[2.05913631 2.05431096]]
</pre></div>
</div>
</div>
@@ -1177,8 +1180,8 @@ Our own code here is not very elegant and asks for obvious improvements. It is t
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Centered covariance using own code
[[4.02103235 1.99084335]
[1.99084335 1.9699594 ]]
[[4.07027208 2.05913631]
[2.05913631 2.05431096]]
</pre></div>
</div>
<img alt="_images/chapter8_65_1.png" src="_images/chapter8_65_1.png" />
@@ -1238,16 +1241,16 @@ questions.</p>
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<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Eigenvalues of Covariance matrix
5.234956145890017
0.7560356057040467
5.3549029458698545
0.7696800897647572
First eigenvector
[0.85379714 0.52060584]
[0.84842937 0.5293086 ]
Second eigenvector
[-0.52060584 0.85379714]
[-0.5293086 0.84842937]
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Eigenvector of largest eigenvalue
[-0.85379714 -0.52060584]
[-0.84842937 -0.5293086 ]
</pre></div>
</div>
</div>