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PO
 

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    <p>Everyone keeps saying that you can't do the mode in an online manner but that is simply not true. Here is an <a href="http://www.americanscientist.org/issues/pub/the-britney-spears-problem/4" rel="nofollow">article</a> describing an algorithm to do just this very problem invented in 1982 by Michael E. Fischer and Steven L. Salzberg of Yale University. From the article: </p> <blockquote> <p>The majority-finding algorithm uses one of its registers for temporary storage of a single item from the stream; this item is the current candidate for majority element. The second register is a counter initialized to 0. For each element of the stream, we ask the algorithm to perform the following routine. If the counter reads 0, install the current stream element as the new majority candidate (displacing any other element that might already be in the register). Then, if the current element matches the majority candidate, increment the counter; otherwise, decrement the counter. At this point in the cycle, if the part of the stream seen so far has a majority element, that element is in the candidate register, and the counter holds a value greater than 0. What if there is no majority ele­ment? Without making a second pass through the data—which isn't possible in a stream environment—the algorithm cannot always give an unambiguous answer in this circumstance. It merely promises to correctly identify the majority element if there is one.</p> </blockquote> <p>It can also be extended to find the top N with more memory but this should solve it for the mode.</p>
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    1. PO"On-line" (iterator) algorithms for estimating statistical median, mode, skewness, kurtosis?
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    1. UShackartist
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    1. COThat is an interesting algorithm, but unless I'm missing something, while all majority values will be modes, not all modes will be majority values.
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      1. USjkebinger
 

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