Class: Entropy::ProbabilityMetricSpace

Inherits:
ProbabilitySpace show all
Defined in:
lib/entropy/metric_space.rb

Overview

Entropy::ProbabilityMetricSpace defines a finite probability metric space

Instance Attribute Summary collapse

Attributes inherited from ProbabilitySpace

#prob_space

Instance Method Summary collapse

Methods inherited from ProbabilitySpace

#surprise

Constructor Details

#initialize ⇒ ProbabilityMetricSpace

Returns a new instance of ProbabilityMetricSpace.



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# File 'lib/entropy/metric_space.rb', line 10

def initialize
  @distance_matrix = nil
  @density = nil
  super
end

Instance Attribute Details

#distance_function ⇒ Object (readonly)

Returns the value of attribute distance_function.



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# File 'lib/entropy/metric_space.rb', line 8

def distance_function
  @distance_function
end

#distance_matrix ⇒ Object (readonly)

Returns the value of attribute distance_matrix.



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# File 'lib/entropy/metric_space.rb', line 8

def distance_matrix
  @distance_matrix
end

Instance Method Details

#add_stream(stream) ⇒ Object

Adds a set of elements (char, bit) to the space



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# File 'lib/entropy/metric_space.rb', line 17

def add_stream(stream)
  super(stream)
end

#cardinality(alpha) ⇒ Object

Computes the α-Cardinality of the space



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# File 'lib/entropy/metric_space.rb', line 87

def cardinality(alpha)
  raise "Warning: distance metric not defined..." if @distance_matrix.nil?
  card = 0
  if alpha == 1
    card = 1
    @prob_space.each_index do |i| 
      card = card * (@density[i] ** (-@prob_space[i]))
    end
  elsif alpha == :infinite
    card = 1.0/@density.max
  else
    @prob_space.each_index do |i| 
      card += @prob_space[i] * (@density[i]**(alpha - 1))
    end
    card = card ** (1.0 / (1 - alpha)) if card != 0
  end
  card
end

#define_distance(*args, &blk) ⇒ Object

Defines the distance among the elements of the set. The method accepts a block, so you can use your function to calculate the distance. The function should accept two parameters, viz. the ordinals i,j of the elements and should return a decimal number, the distance between element i and j. In alternative you could pass a matrix of numbers defining the distances among i’s and j’s.



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# File 'lib/entropy/metric_space.rb', line 29

def define_distance(*args, &blk)
  if !blk.nil?
    @distance_function = blk
    update_distance_matrix
  else
    mat = args[0]
    raise "distance matrix is not a matrix object" if !mat.respond_to?("square?") 
    raise "distance matrix is not square" if !mat.square?
    raise "distance matrix has wrong dimensions" if mat.to_a.size != @prob_space.size
    @distance_matrix = mat
  end
  z = @distance_matrix.map { |d| d == :infinite ? 0 : Math.exp(-d) }
  @density = z * Matrix.column_vector(@prob_space)
  @density = @density.column(0).to_a
end

#diversity(alpha) ⇒ Object

Computes the α-Diversity of the space



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# File 'lib/entropy/metric_space.rb', line 76

def diversity(alpha)
  raise "Warning: distance metric not defined..." if @distance_matrix.nil?
  div = []
  @prob_space.each_index do |i| 
    p = @prob_space[i]
    div[i] = p *  surprise(alpha, @density[i])
  end
  div.inject(:+)
end

#rao_entropy ⇒ Object

Computes the Rao Entropy of the space



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# File 'lib/entropy/metric_space.rb', line 51

def rao_entropy
  diversity(2)
end

#renyi_entropy(alpha) ⇒ Object

Computes the Renyi Entropy (α-Entropy) of the space



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# File 'lib/entropy/metric_space.rb', line 57

def renyi_entropy(alpha)
  raise "Warning: distance metric not defined..." if @distance_matrix.nil?
  h = 0
    if alpha == 1
      @prob_space.each_index do |i| 
        h += -@prob_space[i] * Math.log(@density[i])
      end
    elsif alpha == :infinite
      h = -Math.log(@density.max)
    else
      @prob_space.each_index do |i| 
        h += @prob_space[i] * (@density[i]**(alpha - 1))
      end
      h = 1.0 / (1 - alpha) * Math.log(h)
    end
  h
end

#shannon_entropy ⇒ Object

Computes the Shannon Entropy of the space



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# File 'lib/entropy/metric_space.rb', line 46

def shannon_entropy
  diversity(1)
end