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# The MIT License
#
### Copyright (c) 2007 Ilya Grigorik <ilya AT igvita DOT com>
### Modifed at 2007 by José Ignacio Fernández <joseignacio.fernandez AT gmail DOT com>
begin
require 'graph/graphviz_dot'
rescue LoadError
STDERR.puts "graph/graphviz_dot not installed, graphing functionality not included."
end
class Object
def save_to_file(filename)
File.open(filename, 'w+' ) { |f| f << Marshal.dump(self) }
end
def self.load_from_file(filename)
Marshal.load( File.read( filename ) )
end
end
class Array
def classification; collect { |v| v.last }; end
# calculate information entropy
def entropy
return 0 if empty?
info = {}
total = 0
each {|i| info[i] = !info[i] ? 1 : (info[i] + 1); total += 1}
result = 0
info.each do |symbol, count|
result += -count.to_f/total*Math.log(count.to_f/total)/Math.log(2.0) if (count > 0)
end
result
end
end
module DecisionTree
Node = Struct.new(:attribute, :threshold, :gain)
class ID3Tree
def initialize(attributes, data, default, type)
@used, @tree, @type = {}, {}, type
@data, @attributes, @default = data, attributes, default
end
def train(data=@data, attributes=@attributes, default=@default)
initialize(attributes, data, default, @type)
# Remove samples with same attributes leaving most common classification
data2 = data.inject({}) {|hash, d| hash[d.slice(0..-2)] ||= Hash.new(0); hash[d.slice(0..-2)][d.last] += 1; hash }.map{|key,val| key + [val.sort_by{ |k, v| v }.last.first]}
@tree = id3_train(data2, attributes, default)
end
def id3_train(data, attributes, default, used={})
# Choose a fitness algorithm
case @type
when :discrete; fitness = proc{|a,b,c| id3_discrete(a,b,c)}
when :continuous; fitness = proc{|a,b,c| id3_continuous(a,b,c)}
end
return default if data.empty?
# return classification if all examples have the same classification
return data.first.last if data.classification.uniq.size == 1
# Choose best attribute (1. enumerate all attributes / 2. Pick best attribute)
performance = attributes.collect { |attribute| fitness.call(data, attributes, attribute) }
max = performance.max { |a,b| a[0] <=> b[0] }
best = Node.new(attributes[performance.index(max)], max[1], max[0])
best.threshold = nil if @type == :discrete
@used.has_key?(best.attribute) ? @used[best.attribute] += [best.threshold] : @used[best.attribute] = [best.threshold]
tree, l = {best => {}}, ['>=', '<']
case @type
when :continuous
data.partition { |d| d[attributes.index(best.attribute)] >= best.threshold }.each_with_index { |examples, i|
tree[best][String.new(l[i])] = id3_train(examples, attributes, (data.classification.mode rescue 0), &fitness)
}
when :discrete
values = data.collect { |d| d[attributes.index(best.attribute)] }.uniq.sort
partitions = values.collect { |val| data.select { |d| d[attributes.index(best.attribute)] == val } }
partitions.each_with_index { |examples, i|
tree[best][values[i]] = id3_train(examples, attributes-[values[i]], (data.classification.mode rescue 0), &fitness)
}
end
tree
end
# ID3 for binary classification of continuous variables (e.g. healthy / sick based on temperature thresholds)
def id3_continuous(data, attributes, attribute)
values, thresholds = data.collect { |d| d[attributes.index(attribute)] }.uniq.sort, []
return [-1, -1] if values.size == 1
values.each_index { |i| thresholds.push((values[i]+(values[i+1].nil? ? values[i] : values[i+1])).to_f / 2) }
thresholds.pop
#thresholds -= used[attribute] if used.has_key? attribute
gain = thresholds.collect { |threshold|
sp = data.partition { |d| d[attributes.index(attribute)] >= threshold }
pos = (sp[0].size).to_f / data.size
neg = (sp[1].size).to_f / data.size
[data.classification.entropy - pos*sp[0].classification.entropy - neg*sp[1].classification.entropy, threshold]
}.max { |a,b| a[0] <=> b[0] }
return [-1, -1] if gain.size == 0
gain
end
# ID3 for discrete label cases
def id3_discrete(data, attributes, attribute)
values = data.collect { |d| d[attributes.index(attribute)] }.uniq.sort
partitions = values.collect { |val| data.select { |d| d[attributes.index(attribute)] == val } }
remainder = partitions.collect {|p| (p.size.to_f / data.size) * p.classification.entropy}.inject(0) {|i,s| s+=i }
[data.classification.entropy - remainder, attributes.index(attribute)]
end
def predict(test)
return (@type == :discrete ? descend_discrete(@tree, test) : descend_continuous(@tree, test))
end
def graph(filename)
dgp = DotGraphPrinter.new(build_tree)
dgp.write_to_file("#{filename}.png", "png")
end
def ruleset
rs = Ruleset.new(@attributes, @data, @default, @type)
rs.rules = build_rules
rs
end
def build_rules(tree=@tree)
attr = tree.to_a.first
cases = attr[1].to_a
rules = []
cases.each do |c,child|
if child.is_a?(Hash) then
build_rules(child).each do |r|
r2 = r.clone
r2.premises.unshift([attr.first, c])
rules << r2
end
else
rules << Rule.new(@attributes, [[attr.first, c]], child)
end
end
rules
end
private
def descend_continuous(tree, test)
attr = tree.to_a.first
return @default if !attr
return attr[1]['>='] if !attr[1]['>='].is_a?(Hash) and test[@attributes.index(attr.first.attribute)] >= attr.first.threshold
return attr[1]['<'] if !attr[1]['<'].is_a?(Hash) and test[@attributes.index(attr.first.attribute)] < attr.first.threshold
return descend_continuous(attr[1]['>='],test) if test[@attributes.index(attr.first.attribute)] >= attr.first.threshold
return descend_continuous(attr[1]['<'],test) if test[@attributes.index(attr.first.attribute)] < attr.first.threshold
end
def descend_discrete(tree, test)
attr = tree.to_a.first
return @default if !attr
return attr[1][test[@attributes.index(attr[0].attribute)]] if !attr[1][test[@attributes.index(attr[0].attribute)]].is_a?(Hash)
return descend_discrete(attr[1][test[@attributes.index(attr[0].attribute)]],test)
end
def build_tree(tree = @tree)
return [] unless tree.is_a?(Hash)
return [["Always", @default]] if tree.empty?
attr = tree.to_a.first
links = attr[1].keys.collect do |key|
parent_text = "#{attr[0].attribute}\n(#{attr[0].object_id})"
if attr[1][key].is_a?(Hash) then
child = attr[1][key].to_a.first[0]
child_text = "#{child.attribute}\n(#{child.object_id})"
else
child = attr[1][key]
child_text = "#{child}\n(#{child.to_s.clone.object_id})"
end
label_text = "#{key} #{@type == :continuous ? attr[0].threshold : ""}"
[parent_text, child_text, label_text]
end
attr[1].keys.each { |key| links += build_tree(attr[1][key]) }
return links
end
end
class Rule
attr_accessor :premises
attr_accessor :conclusion
attr_accessor :attributes
def initialize(attributes,premises=[],conclusion=nil)
@attributes, @premises, @conclusion = attributes, premises, conclusion
end
def to_s
str = ''
@premises.each do |p|
str += "#{p.first.attribute} #{p.last} #{p.first.threshold}" if p.first.threshold
str += "#{p.first.attribute} = #{p.last}" if !p.first.threshold
str += "\n"
end
str += "=> #{@conclusion} (#{accuracy})"
end
def predict(test)
verifies = true;
@premises.each do |p|
if p.first.threshold then # Continuous
if !(p.last == '>=' && test[@attributes.index(p.first.attribute)] >= p.first.threshold) && !(p.last == '<' && test[@attributes.index(p.first.attribute)] < p.first.threshold) then
verifies = false; break
end
else # Discrete
if test[@attributes.index(p.first.attribute)] != p.last then
verifies = false; break
end
end
end
return @conclusion if verifies
return nil
end
def get_accuracy(data)
correct = 0; total = 0
data.each do |d|
prediction = predict(d)
correct += 1 if d.last == prediction
total += 1 if !prediction.nil?
end
(correct.to_f + 1) / (total.to_f + 2)
end
def accuracy(data=nil)
data.nil? ? @accuracy : @accuracy = get_accuracy(data)
end
end
class Ruleset
attr_accessor :rules
def initialize(attributes, data, default, type)
@attributes, @default, @type = attributes, default, type
mixed_data = data.sort_by {rand}
cut = (mixed_data.size.to_f * 0.67).to_i
@train_data = mixed_data.slice(0..cut-1)
@prune_data = mixed_data.slice(cut..-1)
end
def train(train_data=@train_data, attributes=@attributes, default=@default)
dec_tree = DecisionTree::ID3Tree.new(attributes, train_data, default, @type)
dec_tree.train
@rules = dec_tree.build_rules
@rules.each { |r| r.accuracy(train_data) } # Calculate accuracy
prune
end
def prune(data=@prune_data)
@rules.each do |r|
(1..r.premises.size).each do
acc1 = r.accuracy(data)
p = r.premises.pop
if acc1 > r.get_accuracy(data) then
r.premises.push(p); break
end
end
end
@rules = @rules.sort_by{|r| -r.accuracy(data)}
end
def to_s
str = ''; @rules.each { |rule| str += "#{rule}\n\n" }
str
end
def predict(test)
@rules.each do |r|
prediction = r.predict(test)
return prediction, r.accuracy unless prediction.nil?
end
return @default, 0.0
end
end
class Bagging
attr_accessor :classifiers
def initialize(attributes, data, default, type)
@classifiers, @type = [], type
@data, @attributes, @default = data, attributes, default
end
def train(data=@data, attributes=@attributes, default=@default)
@classifiers = []
10.times { @classifiers << Ruleset.new(attributes, data, default, @type) }
@classifiers.each do |c|
c.train(data, attributes, default)
end
end
def predict(test)
predictions = Hash.new(0)
@classifiers.each do |c|
p, accuracy = c.predict(test)
predictions[p] += accuracy unless p.nil?
end
return @default, 0.0 if predictions.empty?
winner = predictions.sort_by {|k,v| -v}.first
return winner[0], winner[1].to_f / @classifiers.size.to_f
end
end
end
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