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POUnderstanding algorithms for measuring trends
 

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    <p>What's the rationale behind the formula used in the <code>hive_trend_mapper.py</code> program of <a href="http://www.cloudera.com/blog/2009/07/tracking-trends-with-hadoop-and-hive-on-ec2/" rel="nofollow noreferrer">this Hadoop tutorial</a> on calculating Wikipedia trends?</p> <p>There are actually two components: a monthly trend and a daily trend. I'm going to focus on the daily trend, but similar questions apply to the monthly one.</p> <p>In the daily trend, <code>pageviews</code> is an array of number of page views per day for this topic, one element per day, and <code>total_pageviews</code> is the sum of this array:</p> <pre><code># pageviews for most recent day y2 = pageviews[-1] # pageviews for previous day y1 = pageviews[-2] # Simple baseline trend algorithm slope = y2 - y1 trend = slope * log(1.0 +int(total_pageviews)) error = 1.0/sqrt(int(total_pageviews)) return trend, error </code></pre> <p>I know what it's doing superficially: it just looks at the change over the past day (<code>slope</code>), and scales this up to the log of <code>1+total_pageviews</code> (<code>log(1)==0</code>, so this scaling factor is non-negative). It can be seen as treating the month's total pageviews as a weight, but tempered as it grows - this way, the total pageviews stop making a difference for things that are "popular enough," but at the same time big changes on insignificant don't get weighed as much.</p> <p>But <em>why</em> do this? Why do we want to discount things that were initially unpopular? Shouldn't big deltas matter <em>more</em> for items that have a low constant popularity, and <em>less</em> for items that are already popular (for which the big deltas might fall well within a fraction of a standard deviation)? As a strawman, why not simply take <code>y2-y1</code> and be done with it?</p> <p>And what would the <code>error</code> be useful for? The tutorial doesn't really use it meaningfully again. Then again, it doesn't tell us how <code>trend</code> is used either - this is what's plotted in the end product, correct?</p> <p>Where can I read up for a (preferably introductory) background on the theory here? Is there a name for this madness? Is this a textbook formula somewhere?</p> <p>Thanks in advance for any answers (or discussion!).</p>
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