naive bayes classifier calculating sigma

# Naive Bayes On The Iris Dataset
from csv import reader
from random import seed
from random import randrange
from math import sqrt
from math import exp
from math import pi

# Load a CSV file
def load_csv(filename):
	dataset = list()
	with open(filename, 'r') as file:
		csv_reader = reader(file)
		for row in csv_reader:
			if not row:
				continue
			dataset.append(row)
	return dataset

# Convert string column to float
def str_column_to_float(dataset, column):
	for row in dataset:
		row[column] = float(row[column].strip())

# Convert string column to integer
def str_column_to_int(dataset, column):
	class_values = [row[column] for row in dataset]
	unique = set(class_values)
	lookup = dict()
	for i, value in enumerate(unique):
		lookup[value] = i
	for row in dataset:
		row[column] = lookup[row[column]]
	return lookup

# Split a dataset into k folds
def cross_validation_split(dataset, n_folds):
	dataset_split = list()
	dataset_copy = list(dataset)
	fold_size = int(len(dataset) / n_folds)
	for _ in range(n_folds):
		fold = list()
		while len(fold) < fold_size:
			index = randrange(len(dataset_copy))
			fold.append(dataset_copy.pop(index))
		dataset_split.append(fold)
	return dataset_split

# Calculate accuracy percentage
def accuracy_metric(actual, predicted):
	correct = 0
	for i in range(len(actual)):
		if actual[i] == predicted[i]:
			correct += 1
	return correct / float(len(actual)) * 100.0

# Evaluate an algorithm using a cross validation split
def evaluate_algorithm(dataset, algorithm, n_folds, *args):
	folds = cross_validation_split(dataset, n_folds)
	scores = list()
	for fold in folds:
		train_set = list(folds)
		train_set.remove(fold)
		train_set = sum(train_set, [])
		test_set = list()
		for row in fold:
			row_copy = list(row)
			test_set.append(row_copy)
			row_copy[-1] = None
		predicted = algorithm(train_set, test_set, *args)
		actual = [row[-1] for row in fold]
		accuracy = accuracy_metric(actual, predicted)
		scores.append(accuracy)
	return scores

# Split the dataset by class values, returns a dictionary
def separate_by_class(dataset):
	separated = dict()
	for i in range(len(dataset)):
		vector = dataset[i]
		class_value = vector[-1]
		if (class_value not in separated):
			separated[class_value] = list()
		separated[class_value].append(vector)
	return separated

# Calculate the mean of a list of numbers
def mean(numbers):
	return sum(numbers)/float(len(numbers))

# Calculate the standard deviation of a list of numbers
def stdev(numbers):
	avg = mean(numbers)
	variance = sum([(x-avg)**2 for x in numbers]) / float(len(numbers)-1)
	return sqrt(variance)

# Calculate the mean, stdev and count for each column in a dataset
def summarize_dataset(dataset):
	summaries = [(mean(column), stdev(column), len(column)) for column in zip(*dataset)]
	del(summaries[-1])
	return summaries

# Split dataset by class then calculate statistics for each row
def summarize_by_class(dataset):
	separated = separate_by_class(dataset)
	summaries = dict()
	for class_value, rows in separated.items():
		summaries[class_value] = summarize_dataset(rows)
	return summaries

# Calculate the Gaussian probability distribution function for x
def calculate_probability(x, mean, stdev):
	exponent = exp(-((x-mean)**2 / (2 * stdev**2 )))
	return (1 / (sqrt(2 * pi) * stdev)) * exponent

# Calculate the probabilities of predicting each class for a given row
def calculate_class_probabilities(summaries, row):
	total_rows = sum([summaries[label][0][2] for label in summaries])
	probabilities = dict()
	for class_value, class_summaries in summaries.items():
		probabilities[class_value] = summaries[class_value][0][2]/float(total_rows)
		for i in range(len(class_summaries)):
			mean, stdev, _ = class_summaries[i]
			probabilities[class_value] *= calculate_probability(row[i], mean, stdev)
	return probabilities

# Predict the class for a given row
def predict(summaries, row):
	probabilities = calculate_class_probabilities(summaries, row)
	best_label, best_prob = None, -1
	for class_value, probability in probabilities.items():
		if best_label is None or probability > best_prob:
			best_prob = probability
			best_label = class_value
	return best_label

# Naive Bayes Algorithm
def naive_bayes(train, test):
	summarize = summarize_by_class(train)
	predictions = list()
	for row in test:
		output = predict(summarize, row)
		predictions.append(output)
	return(predictions)

# Test Naive Bayes on Iris Dataset
seed(1)
filename = 'iris.csv'
dataset = load_csv(filename)
for i in range(len(dataset[0])-1):
	str_column_to_float(dataset, i)
# convert class column to integers
str_column_to_int(dataset, len(dataset[0])-1)
# evaluate algorithm
n_folds = 5
scores = evaluate_algorithm(dataset, naive_bayes, n_folds)
print('Scores: %s' % scores)
print('Mean Accuracy: %.3f%%' % (sum(scores)/float(len(scores))))