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From Lance Norskog <goks...@gmail.com>
Subject Re: Map/Reduce algorithm needed- histogram
Date Tue, 08 Mar 2011 08:31:01 GMT
Really it is to support an arbitrary number of buckets. But thank you,
TeraSort does some interesting things with the M/R Hadoop framework.

One use for this is to find and remove the 5% most and least common
terms from a Lucene index, as part of vectorizing, or making spelling
dictionaries.

Lance

On Mon, Mar 7, 2011 at 10:10 PM, Chris Schilling <chris@cellixis.com> wrote:
> What about running terrasort map/reduce?  I am not sure on the run-time complexity differences,
but if you want to find the median of a large set, it gets the job done
>
>
> On Mar 7, 2011, at 9:55 PM, Lance Norskog wrote:
>
>> And now for some real machine learning. I would like to make a
>> histogram of values in a dataset. For simplicity let's just find the
>> median.
>>
>> I would like to find the median value in a dataset via Map/Reduce. The
>> basic idea is distributed error estimation and reduction:
>>    start with a guess for the median.
>>    map each value to one side of the median.
>>    when the mapper finishes, also emit metadata to all reducers.
>>        this metadata is the largest or smallest value in this sample.
>>
>>    the receiver gets the metadata from all mappers for the 'guessed' median.
>>    It also takes the boundary for the items it receives. It then
>> combines all of the boundary values into a new guess of the median.
>>    The job driver combines all of the reducer's boundaries and
>> creates a new composite guess.
>>    And repeat with some end condition. One can demand complete
>> accuracy, or a percentage of misclassified items.
>>
>> --------------------------------------------------
>> More detail
>>
>> This is an iterative design. Between each pass, there is a 'current
>> median' value passed as metadata. At the start, pick an arbitrary
>> value.
>> Key/value pair: ('upper'/'lower', (purpose='value'/boundary, item)
>> In the key/value pair, there is a special boolean/enum type called
>> 'purpose=value or boundary'. This is one of two values: an entry to be
>> classified, or metadata giving the boundary values that the mapper
>> found and emitted.
>>
>>    Start of map phase:
>>        Start with 'current median'.
>>    Mapper:
>>        The key is a boolean
>>        However, 4 kinds of output.
>>        key: boolean type: < current median or >= current median
>>        value: (boolean purpose, number value)
>>        loop(number):
>>            map number to upper/lower bin for key
>>            emit (key, (purpose = data, number) )
>>            track maximum & minimum values
>>        end
>>        emit (! key, (purpose = boundary, maximum))
>>    end Mapper
>>
>>    Reducer:
>>        Receives all (key = boolean, (purpose = boundary, number)) first.
>>        This will receive the boundary values for the other bin,
>> because the mapper wrote the boundary to !('upper' v.s. 'lower')
>>        Calculates the mean of the boundary values as the new current median.
>>        Receives and assigns all (purpose = number) tuples.
>>
>> There is a problem with this: the Reducer has to cache all of the
>> value tuples until it gets all of the boundary tuples. Thus it is
>> memory-bound. The Mapper is not memory-bound.
>>
>> A hack to fix this is to create a custom sorter that causes each
>> reducer to receive the boundary tuples first.
>>
>>
>> --
>> Lance Norskog
>> goksron@gmail.com
>
>



-- 
Lance Norskog
goksron@gmail.com

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