This module provides classical distance functions
Euclidean distance, or L2 norm. Parameters a and b are vectors with continuous attributes. Euclidean distance tends to form hyperspherical clusters(Clustering, Xu and Wunsch, 2009). Translations and rotations do not cause a distortion in distance relation (Duda et al, 2001) If attributes are measured with different units, attributes with larger values and variance will dominate the metric.
# File lib/ai4r/data/proximity.rb, line 36 def self.euclidean_distance(a, b) Math.sqrt(squared_euclidean_distance(a, b)) end
The Hamming distance between two attributes vectors of equal length is the number of attributes for which the corresponding vectors are different This distance function is frequently used with binary attributes, though it can be used with other discrete attributes.
# File lib/ai4r/data/proximity.rb, line 69 def self.hamming_distance(a,b) count = 0 a.each_index do |i| count += 1 if a[i] != b[i] end return count end
city block, Manhattan distance, or L1 norm. Parameters a and b are vectors with continuous attributes.
# File lib/ai4r/data/proximity.rb, line 43 def self.manhattan_distance(a, b) sum = 0.0 a.each_with_index do |item_a, i| item_b = b[i] sum += (item_a - item_b).abs end return sum end
The "Simple matching" distance between two attribute sets is given by the number of values present on both vectors. If sets a and b have lengths da and db then:
S = 2/(da + db) * Number of values present on both sets D = 1.0/S - 1
Some considerations:
a and b must not include repeated items
all attributes are treated equally
all attributes are treated equally
# File lib/ai4r/data/proximity.rb, line 88 def self.simple_matching_distance(a,b) similarity = 0.0 a.each {|item| similarity += 2 if b.include?(item)} similarity /= (a.length + b.length) return 1.0/similarity - 1 end
This is a faster computational replacement for eclidean distance. Parameters a and b are vectors with continuous attributes.
# File lib/ai4r/data/proximity.rb, line 18 def self.squared_euclidean_distance(a, b) sum = 0.0 a.each_with_index do |item_a, i| item_b = b[i] sum += (item_a - item_b)**2 end return sum end
Sup distance, or L-intinity norm Parameters a and b are vectors with continuous attributes.
# File lib/ai4r/data/proximity.rb, line 54 def self.sup_distance(a, b) distance = 0.0 a.each_with_index do |item_a, i| item_b = b[i] diff = (item_a - item_b).abs distance = diff if diff > distance end return distance end
Generated with the Darkfish Rdoc Generator 2.