Variance, Mean, Normalizing Functions, Euclidean and other Distances

dustinsmith (dustin smith) — Sat, 10 Feb 2007 02:14:52 GMT

Here sum, mean and variance were inspired by the Peter's inline sum code:



class Array; def sum; inject( nil ) { |sum,x| sum ? sum+x : x }; end; end

class Array; def mean; self.sum/self.size.to_f; end; end

class Array; def variance; mean = self.mean; Math.sqrt(inject( nil ) { |var,x| var ? var+((x-mean)**2) : ((x-mean)**2)}/self.size.to_f); end; end

If you want to normalize a random variable (array) so that mean = 0 and variance = 1, you can transform your array x by calling:



# inputs a random variable, sets mean = 0 and variance = 1

def standardize_random_variable(x)

  mean = x.mean

  variance = x.variance

  x.map!{|a| (a-mean)/variance }

end

If you want to compute distance, call these functions between two arrays of data, a and b.



## Distance Functions



# Sum of (x-y)^2

def euclidean_squared_distance(a,b)

  b = b.to_a

  a = a.to_a

  sum_of_diff_sq = 0

  (0...a.size).each { |i| sum_of_diff_sq+=((a[i].to_f-b[i].to_f)**2)}

  sum_of_diff_sq 

end



# Square root of sum of (x-y)^2

def euclidean_distance(neighbor,xq)

  Math.sqrt(euclidean_squared_distance(neighbor,xq))

end



# Sum of abs(x,y)

def cityblock_distance(neighbor,xq)

  xq = xq.to_a

  abs_diff = 0

  (0...xq.size).each { |i| abs_diff+=(Math.abs(xq[i].to_f-neighbor[i].to_f)}

  abs_diff

end

DZone Snippets: ruby code

Variance, Mean, Normalizing Functions, Euclidean and other Distances