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<!doctype html>
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<div id='write' class=''><h1><a name="project-2-report" class="md-header-anchor"></a><span>Project 2 Report</span></h1><h3><a name="group-x" class="md-header-anchor"></a><span>Group X:</span></h3><ul><li><span>Ziyao Wang, 320180940361</span></li><li><span>Ke Lei, 320180939861</span></li><li><span>Tao Tao, 320180940281</span></li></ul><h2><a name="1-abstract" class="md-header-anchor"></a><span>1. Abstract</span></h2><p><span>This report is used to record and present our group's work in project 2. First, we selected a data visualization chart from a very influential paper, and then we introduced and explained it (from the aspects of context, visual variables, etc.). </span></p><p><span>Next, we first reproduce this chart, and then improve it according to some basic principles and principles of visualization to make it conform to the theoretical knowledge of information visualization. Finally, we summarize the work of the whole project.</span></p><p> </p><h2><a name="2introduction" class="md-header-anchor"></a><span>2.Introduction</span></h2><h4><a name="21-influential-chart-source" class="md-header-anchor"></a><span>2.1 Influential Chart Source</span></h4><p><span>We extracted this graph from a paper on deep learning optimization methods.</span></p><pre spellcheck="false" class="md-fences md-end-block ty-contain-cm modeLoaded" lang=""><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; height: 0px; top: 0px; left: 8px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"></textarea></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"></div><div class="CodeMirror-gutter-filler" cm-not-content="true"></div><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 0px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"></div><div class="CodeMirror-measure"></div><div style="position: relative; z-index: 1;"></div><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"></div><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: 0px; width: 0px;"></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">@article{kingma2015adam,</span></pre></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">title={Adam: A Method for Stochastic Optimization},</span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">author={Kingma, P. Diederik and Ba, Lei Jimmy},</span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">journal={international conference on learning representations},</span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">year={2015}</span></pre></div></div></div></div></div><div style="position: absolute; height: 0px; width: 1px; border-bottom: 0px solid transparent; top: 136px;"></div><div class="CodeMirror-gutters" style="display: none; height: 136px;"></div></div></div></pre><p><span>You can read this paper by visiting:</span></p><p><a href='https://www.aminer.cn/pub/5550415745ce0a409eb3a739/adam-a-method-for-stochastic-optimization' target='_blank' class='url'>https://www.aminer.cn/pub/5550415745ce0a409eb3a739/adam-a-method-for-stochastic-optimization</a></p><p> </p><h4><a name="22-the-original-image" class="md-header-anchor"></a><span>2.2 The original image</span></h4><p><span>As we can see, the original chart we selected is like this:</span></p><p><img src="sourcecode/origin chart.png" referrerpolicy="no-referrer" alt="origin chart"></p><h4><a name="23-why-we-choose-it" class="md-header-anchor"></a><span>2.3 Why we choose it</span></h4><p><span>This visualization image has a deep machine learning knowledge background, the visualization structure is clear, and the data is easy to understand.The visualization in the paper we selected has fallen into several visualization pitfalls learned in class. So it is easy for us to modify and improve.</span></p><p> </p><h4><a name="24-impact-in-the-society" class="md-header-anchor"></a><span>2.4 Impact in the society</span></h4><p><span>The number of citations of the source paper for this visualization is 49516 and it has a very important influence in the field of deep learning. The paper indicates that the Adam algorithm, which combines two traditional algorithms, has advantages over traditional algorithms (Adagrad, SGD) in terms of training costs.</span></p><p><span>This information visualization result promotes the Adam algorithm with lower training cost and higher efficiency. Adam algorithm is considered to replace traditional SGD and Adagrad algorithms in many occasions.It also caused a lot of controversy between SGD algorithm and Adam algorithm</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.967ex" height="2.344ex" viewBox="0 -956.9 846.7 1009.2" role="img" focusable="false" style="vertical-align: -0.121ex;"><defs><path stroke-width="0" id="E1-MJMAIN-5B" d="M118 -250V750H255V710H158V-210H255V-250H118Z"></path><path stroke-width="0" id="E1-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="0" id="E1-MJMAIN-5D" d="M22 710V750H159V-250H22V-210H119V710H22Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(0,362)"><use transform="scale(0.707)" xlink:href="#E1-MJMAIN-5B" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E1-MJMAIN-31" x="278" y="0"></use><use transform="scale(0.707)" xlink:href="#E1-MJMAIN-5D" x="778" y="0"></use></g></g></svg></span><script type="math/tex">^{[1]}</script><span>.</span></p><p> </p><h2><a name="3-interpretation-visualization" class="md-header-anchor"></a><span>3. Interpretation Visualization</span></h2><h4><a name="31-visualization-background" class="md-header-anchor"></a><span>3.1 Visualization background</span></h4><p><span>Adam is an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments.</span></p><p><span>Our aim is to compare different algorithm to show some of Adam’s advantages.</span></p><p><span>We want to evaluate the different algorithms by using large models and datasets,and we demonstrate Adam can efficiently solve practical deep learning problems.Otherwise, we use the same parameter initialization when comparing different optimization algorithms. </span></p><h4><a name="32-the-story-of-visualization" class="md-header-anchor"></a><span>3.2 The story of visualization</span></h4><p><span>The main characters in the visualization is Adam,Adagrad and SGD Nesterov.</span></p><p><span>The main data of the visualization is logistic regression training negative log likelihood on MNIST images with 10,000 bag-of-words feature vectors.</span></p><p><span>The visualization graph uses three lines of different colors to clearly compare the training costs of the three algorithms under different (0-45) iteration times.Our aim is to compare different algorithm to show some of Adam’s advantages.</span></p><h4><a name="33-how-to-read-it" class="md-header-anchor"></a><span>3.3 how to read it</span></h4><p><span>According to the core information in the figure, readers can compare the vertical coordinate values (training cost) of three different color curves (algorithms) under the same number of iterations from the vertical direction. Readers can learn from the change trend of the three different color curves on the line chart the different decreasing trend of the training cost of the three algorithms as the number of iterations increases.</span></p><p><span>We can understand the data about the result of logistic regression training negative log likelihood on MNIST images with 10,000 bag-of-words feature vectors. We can find some important contents. For example, the Adam yields similar convergence as SGD with momentum and both converge faster than Adagrad.From the different downward trend of training costs of the three curves, we can find the advantages of Adam's algorithm compared to the other two algorithms.</span></p><h4><a name="34-visual-variables" class="md-header-anchor"></a><span>3.4 visual variables</span></h4><p><span>The curve in the figure represents that changing value of training cost because of different iterations over entire dataset.Different curve colors represent different algorithm types.</span></p><p><span>X-axis represents iterations over the entire data set,y-axis represents the training cost.</span></p><h4><a name="35-the-analysis-of-the-information-visualization" class="md-header-anchor"></a><span>3.5 the analysis of the information visualization</span></h4><p><span>We compare Adam to accelerated SGD with Nesterov momentum and Adagrad using mini batch size of 128. According to the figure, we found that the Adam yields similar convergence as SGD with momentum and both converge faster than Adagrad. Adagrad can efficiently deal with sparse features and gradients as one of its main theoretical results whereas SGD is low at learning rare features. Adam with1/√t decay on its step size match the performance of Adagrad. </span></p><p><span> In the figure, Adagrad outperforms SGD with Nesterov momentum by a large margin both with and without dropout noise. Adam converges as fast as Adagrad. Similar to Adagrad, Adam can take advantage of sparse features and obtain faster convergence rate than normal SGD with momentum.</span></p><h4><a name="36-cognitive-theory-of-the-visualization-and-its-context" class="md-header-anchor"></a><span>3.6 cognitive theory of the visualization and its context</span></h4><p><span>According to the core information of the figure, the training cost difference of the three algorithms under the same number of iterations can be compared vertically. </span></p><p><span>The context requires readers to understand the advantages of the Adam algorithm in terms of training costs through the rapid decline of the red curve in the line chart. The line chart in the visualization can better help readers compare the different decreasing trends of the training costs of the three different algorithms as the number of iterations increases.</span></p><p><span>The curve has flaws in cognitive theory , such as insufficient data clarity. </span>
<span>The visualiztion uses red curves and green curves at the same time.This will make it difficult for red-green color blindness to compare the changing trends of the red curve and the green curve. Therefore, it is difficult for them to find the advantage of Adam algorithm over SGD algorithm.</span></p><p><span>There are redundant grid lines, etc. So we need to improve the curve.</span></p><h2><a name="4replicate-the-information-visualization" class="md-header-anchor"></a><span>4.Replicate the information visualization</span></h2><p><span>We use Matplotlib in Python to reproduce the image. The specific code is in X</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.967ex" height="2.344ex" viewBox="0 -956.9 846.7 1009.2" role="img" focusable="false" style="vertical-align: -0.121ex;"><defs><path stroke-width="0" id="E2-MJMAIN-5B" d="M118 -250V750H255V710H158V-210H255V-250H118Z"></path><path stroke-width="0" id="E2-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path stroke-width="0" id="E2-MJMAIN-5D" d="M22 710V750H159V-250H22V-210H119V710H22Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(0,362)"><use transform="scale(0.707)" xlink:href="#E2-MJMAIN-5B" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E2-MJMAIN-32" x="278" y="0"></use><use transform="scale(0.707)" xlink:href="#E2-MJMAIN-5D" x="778" y="0"></use></g></g></svg></span><script type="math/tex">^{[2]}</script><span>.</span></p><center>
<figure>
<img src="sourcecode/origin chart.png" alt="origin chart" style="zoom:90%;">
<img src="sourcecode/replicate.png" alt="replicate">
</figure>
</center><p> </p><p> </p><p><span>In the figure above, the chart on the left is origin chart and the right is our replicated chart.</span></p><p> </p><h2><a name="5improvement-and-implement" class="md-header-anchor"></a><span>5.Improvement and implement</span></h2><h4><a name="51-proposal-improvements" class="md-header-anchor"></a><span>5.1 Proposal improvements</span></h4><p><span>There are changes we have improved.</span></p><ul><li><span>Change the color of the line</span></li><li><span>Remove the grid</span></li><li><span>Remove the top and right border </span></li></ul><p> </p><p><span>Please let me have a easy statement for these improvements. First, we change the three line color from red-green to blue-yellow legend. This is because the red-green can lead confusion to some people according to cognitive theory. In addition, too much grid will take away people's attention, which can take information overload. What's more, we turn off the top and right box to provide the minimum amount of information to make sure reader can concentrate on the graph itself.</span></p><p><span>It's need to take attention to the color we choose to improve. The blue and yellow are contrast color that can give reader a more obvious sight to the contrast of different method in graph. It also intensify the advantage of AdaGrad method in comparison.</span></p><h4><a name="52-implement" class="md-header-anchor"></a><span>5.2 implement</span></h4><p><span>The specific code is in X</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.967ex" height="2.344ex" viewBox="0 -956.9 846.7 1009.2" role="img" focusable="false" style="vertical-align: -0.121ex;"><defs><path stroke-width="0" id="E3-MJMAIN-5B" d="M118 -250V750H255V710H158V-210H255V-250H118Z"></path><path stroke-width="0" id="E3-MJMAIN-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path><path stroke-width="0" id="E3-MJMAIN-5D" d="M22 710V750H159V-250H22V-210H119V710H22Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(0,362)"><use transform="scale(0.707)" xlink:href="#E3-MJMAIN-5B" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E3-MJMAIN-33" x="278" y="0"></use><use transform="scale(0.707)" xlink:href="#E3-MJMAIN-5D" x="778" y="0"></use></g></g></svg></span><script type="math/tex">^{[3]}</script><span>.</span></p> <center>
<figure>
<img src="sourcecode/replicate.png" alt="replicate">
<img src="sourcecode/Improment_360.png" alt="Improment">
</figure>
</center><h2><a name="6conclusion" class="md-header-anchor"></a><span>6.Conclusion</span></h2><p><span>We have gained a lot from this project. We not only read a lot of papers on deep learning, but also practice the realization and improvement of visualization.</span></p><p><span>We are surprised to find that even very important academic papers violate some principles of information visualization.If these important papers follow the relevant visualization principles, it will be easier for people to understand.</span></p><p><span>This work will remind us to follow the principles of visualization when writing academic papers in the future.</span></p><h2><a name="references" class="md-header-anchor"></a><span>References</span></h2><p><span>[1] </span><a href='https://www.aminer.cn/pub/5550415745ce0a409eb3a739/adam-a-method-for-stochastic-optimization'><strong><span>Adam: A Method for Stochastic Optimization</span></strong></a></p><p><span>[2] </span><a href='sourcecode/replicate.ipynb'><span>replicaate code</span></a></p><p><span>[3] </span><a href='sourcecode/Improment.ipynb'><span>Improment code</span></a></p><p><span>[4] </span><a href='https://medium.com/@jiajingguo/how-is-data-visualization-inflfluenced-by-our-cognitive-processes-281d8486abfe'><span>How Is Data Visualization Inflfluenced By Our Cognitive Processes?</span></a></p></div>
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