gaussian_naive_bayes.py

import numpy as np
import math
import operator

trainingSet = np.array([
  [5.1, 3.5, 1.4, 0.2],
  [4.9, 3.0, 1.4, 0.2],
  [4.7, 3.2, 1.3, 0.2],
  [7.0, 3.2, 4.7, 1.4],
  [6.4, 3.2, 4.5, 1.5],
  [6.9, 3.1, 4.9, 1.5],
  [6.3, 3.3, 6.0, 2.5],
  [5.8, 2.7, 5.1, 1.9],
  [7.1, 3.0, 5.9, 2.1]])

classTypes = np.array([
  'Iris-setosa', 'Iris-setosa', 'Iris-setosa',
  'Iris-versicolor','Iris-versicolor','Iris-versicolor',
  'Iris-virginica','Iris-virginica','Iris-virginica'])
testVals = [[6.1, 3.0, 4.6, 1.4]]

def organizeData(trainingArr, classTypes):
  dict = {}
  for i in range(classTypes.size):
    if classTypes[i] in dict:
      dict[classTypes[i]] = np.append(dict[classTypes[i]], [trainingArr[i]], axis = 0)
    else:
      dict[classTypes[i]] = np.array([trainingArr[i]])
  return dict

def mean(arr):
  sum = 0.0
  count = 0.0
  for v in arr:
    sum += v
    count += 1
  return sum/count

def standardDeviation(arr, avg):
  count = 0
  sum = 0.0
  for v in arr:
    sum += (v - avg)**2
    count += 1
  t1 = 1.0/count * sum
  t2 = math.sqrt(t1)
  return t2

def gaussianNB(val, avg, std):
  exp = math.exp(-(val - avg)**2/(2 * std**2))
  g = 1.0/(math.sqrt(2 * math.pi) * std) * exp
  return g

def classProbability(arr):
  classTypes = {}
  probs = {}
  count = 0.0
  for val in arr:
    count += 1
    if val in classTypes:
      classTypes[val] += 1
    else:
      classTypes[val] = 1
  for val in classTypes.keys():
    probs[val] = classTypes[val]/count
  return probs

def getStats(data):
  stats = {}
  for classType in data:
    dataArr = data[classType]
    statsArr = []
    for i in range(dataArr.shape[1]):
      arr = dataArr[:,i]
      varMean = mean(arr)
      varStandardDeviation = standardDeviation(arr, varMean)
      statsArr.append((varMean, varStandardDeviation))
    stats[classType] = statsArr
  return stats

def calculateGaussianNB(testVals, stats):
  gaussianNBs = {}
  arr = []
  for classType in stats:
    for i in range(len(testVals[0])):
      g = gaussianNB(testVals[0][i], stats[classType][i][0], stats[classType][i][1])
      arr.append(g)
    gaussianNBs[classType] = arr
    arr = []

  return gaussianNBs

def posteriorNumerator(classProbs, gaussianNBs):
  arr = []
  for classType in classProbs:
    total = 1.0
    for g in gaussianNBs[classType]:
      total *= g
    arr.append((classType, classProbs[classType] * total))
    total = 1.0
  print arr
  arr.sort(key=operator.itemgetter(1), reverse = True)
  return arr

data = organizeData(trainingSet, classTypes)
stats = getStats(data)
classProbs = classProbability(classTypes)
gaussianNBs = calculateGaussianNB(testVals, stats)
numerator = posteriorNumerator(classProbs, gaussianNBs)
print numerator[0][0]