Comments - Why Topological Data Analysis Works - Data Science Central2021-09-22T04:45:28Zhttps://www.datasciencecentral.com/profiles/comment/feed?attachedTo=6448529%3ABlogPost%3A239312&xn_auth=noComplex network theory is now…tag:www.datasciencecentral.com,2015-01-18:6448529:Comment:2416842015-01-18T01:52:04.058ZSione Paluhttps://www.datasciencecentral.com/profile/SioneKPalu
<p>Complex network theory is now a multi-disciplinary efforts (physics, biology, mathematics, computer-science, sociology, etc.) but it is still dominant in Physics research (in complex system theory). Most highly cited papers in "Complex Network" theory were published in scientific literatures like the prestigious journals Nature , Modern Physics or PRL (Physical Review Letters), etc...</p>
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<p>One of the leading researcher's in this field is physicist, Albert Barabasi &…</p>
<p>Complex network theory is now a multi-disciplinary efforts (physics, biology, mathematics, computer-science, sociology, etc.) but it is still dominant in Physics research (in complex system theory). Most highly cited papers in "Complex Network" theory were published in scientific literatures like the prestigious journals Nature , Modern Physics or PRL (Physical Review Letters), etc...</p>
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<p>One of the leading researcher's in this field is physicist, Albert Barabasi & colleagues proposed <span dir="auto">Barabasi–Albert model (<a href="http://en.wikipedia.org/wiki/Barab%C3%A1si%E2%80%93Albert_model" target="_blank">http://en.wikipedia.org/wiki/Barab%C3%A1si%E2%80%93Albert_model</a>)</span> which they published a paper in the late 1990s with title "Emergence of scaling in random networks" which appeared in "Reviews of Modern Physics" and it is highly cited by work of other authors.</p>
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<p>Barabasi & colleagues followed up with another paper in early 2000 which is highly cited as well :</p>
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<p>"Statistical Mechanics of Complex Networks" (appeared in "Reviews of modern physics" )</p>
<p><a href="http://arxiv.org/pdf/cond-mat/0106096v1.pdf" target="_blank">http://arxiv.org/pdf/cond-mat/0106096v1.pdf</a></p>
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<p>Another highly cited paper on the topic was published by Strogatz, et al in the late 1990s as well with the title:</p>
<p>"Collective dynamics of 'small-world' networks" which appeared in Nature (<a href="http://www.nature.com/nature/journal/v393/n6684/abs/393440a0.html" target="_blank">http://www.nature.com/nature/journal/v393/n6684/abs/393440a0.html</a>).</p>
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<p>The power in predictive analytics in the domain of complex network theory is developing model to predict how the network evolves over time (dynamic & temporal predictions) because network nodes changes as time progresses, new nodes enter the network and form connections with others and certain old nodes disconnected themselves & leave the network. This dynamic analysis of complex networks is a hot topic today in many disciplines (from physics, biological networks, neuronal networks, business entity networks, social networks, and so forth).</p>
<p></p> Interesting article.
Just an…tag:www.datasciencecentral.com,2015-01-18:6448529:Comment:2414932015-01-18T01:11:04.216ZSione Paluhttps://www.datasciencecentral.com/profile/SioneKPalu
<p>Interesting article.</p>
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<p>Just an add on, in higher dimensional data analysis, which is data that requires more than two or three dimensions to represent, can be difficult to interpret. One simplified approach is to assume that the data of interest lie on an embedded non-linear manifold within the higher-dimensional space. Manifold (<a href="http://en.wikipedia.org/wiki/Manifold">http://en.wikipedia.org/wiki/Manifold</a>) is a topological space that resembles Euclidean space near…</p>
<p>Interesting article.</p>
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<p>Just an add on, in higher dimensional data analysis, which is data that requires more than two or three dimensions to represent, can be difficult to interpret. One simplified approach is to assume that the data of interest lie on an embedded non-linear manifold within the higher-dimensional space. Manifold (<a href="http://en.wikipedia.org/wiki/Manifold">http://en.wikipedia.org/wiki/Manifold</a>) is a topological space that resembles Euclidean space near each point.</p>
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<p>There are algorithms that exist today (especially for non-linear dimensional reduction - PCA is a linear-dimensional reduction method) that the data is sampled from a submanifold which is embedded in high dimensional space.</p>