mongo db Standard deviation calculation with map reduce using the Welford algoritm.

map_reduce_stddev.js

/*
* (The MIT License)
* 
* Copyright (c) 2011 Peter Magnusson <kmpm@birchroad.net>
* 
* Permission is hereby granted, free of charge, to any person obtaining
* a copy of this software and associated documentation files (the
* 'Software'), to deal in the Software without restriction, including
* without limitation the rights to use, copy, modify, merge, publish,
* distribute, sublicense, and/or sell copies of the Software, and to
* permit persons to whom the Software is furnished to do so, subject to
* the following conditions:
* 
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
* 
* THE SOFTWARE IS PROVIDED 'AS IS', WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*
*/

/**
* References
* http://www.johndcook.com/standard_deviation.html
* http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#On-line_algorithm
*/

/**
* The RunningStat Class/Object is the actual heavy worker in this and the only thing you really want.
*/
var RunningStat = function(){
	this.count=0; //counter for the number of samples
	
	//use .push to add values to be calculated
	this.push = function(x){
		this.count++;
		if(this.count==1){
			this.old_mean = x;
			this.new_mean = x;
			this.old_sum = 0.0;
		}
		else{
			this.new_mean = this.old_mean + (x - this.old_mean)/this.count;
            this.new_sum = this.old_sum + (x - this.old_mean)*(x - this.new_mean);

            this.old_mean = this.new_mean; 
            this.old_sum = this.new_sum;
		}
	};

	//returns the mean 
	this.mean = function(){
		return (this.count >0) ? this.new_mean : 0.0;
	};

	//returns the variance of the data
	this.variance = function(){
		return  (this.count > 1) ? (this.new_sum/(this.count -1)) : 0.0;
	};

	//returns the standard deviation
	this.standardDeviation = function(){
		return Math.sqrt(this.variance());
	};
}

//to be able to use a function within map/reduce and have it declared externally
//then you have to save it in the database first
db.system.js.save({_id:'RunningStat', value:RunningStat});


// map+reduce sample implementation

// sample data
{ "_id" : ObjectId("4caf19200d282159bf000001"), "date" : "2010-10-06", "seq" : "00:00:00,000", "method" : "getUserByScbeId", "duration" : 3 }
{ "_id" : ObjectId("4caf19200d282159bf000002"), "date" : "2010-10-06", "seq" : "00:00:00,116", "method" : "createTicket", "duration" : 116 }
{ "_id" : ObjectId("4caf19200d282159bf000003"), "date" : "2010-10-06", "seq" : "00:00:00,131", "method" : "getCollectionMetadata", "duration" : 11 }
{ "_id" : ObjectId("4caf19200d282159bf000004"), "date" : "2010-10-06", "seq" : "00:00:00,137", "method" : "getParticipation", "duration" : 6 }
{ "_id" : ObjectId("4caf19200d282159bf000005"), "date" : "2010-10-06", "seq" : "00:00:00,139", "method" : "updateSocialObjectModified", "duration" : 371 }
{ "_id" : ObjectId("4caf19200d282159bf000006"), "date" : "2010-10-06", "seq" : "00:00:00,143", "method" : "getUserByScbeId", "duration" : 4 }


map = function() { 
	emit(this.method, { duration : this.duration, count : 1}); 
}

var reduce = function(key,emits) { 
	var n = { count : 0, duration : 0, min : Number.MAX_VALUE, max : Number.MIN_VALUE };
	var rs = new RunningStat();

	for(var i in emits) {
		var x = emits[i].duration;
		n.count += emits[i].count;
		n.duration += x;
		n.max = (x>n.max) ? x: n.max;
		n.min = (x<n.min) ? x: n.min;
		rs.push(x);
	}

	n.avg=rs.mean();
	n.variance=rs.variance();
	n.stddv=rs.standardDeviation();
	return n;
}
//since 1.7+ something you have to provide a output collection 
db.logs.mapReduce(map, reduce, { out: "methods_stat"});
db.methods_stat.find();

thanks :)

Thanks for publishing this. The reduce function is not idempotent, however, which is one of the requirements for a valid MapReduce operation. (The object structure of emit and reduce are not the same, and passing the results of reduce back into reduce does not return the same result.) In theory that will cause incorrect results for large data sets. Have you run into problems with that?

Followup - this seems to be a good alternative: https://gist.github.com/1886960
It passes the idempotence test and returns the same results.

@newleafdigital Thanks for the tip... when I did this one I couldn't find any stddev at all so I cooked this one up but you are correct, it's not idempotent and with the alternative you gave... I might not bother fixig this.... :)

@bebuckman I've made improvements to that alternative: https://gist.github.com/Pyrolistical/8139958