## Tutorial To Implement k-Nearest Neighbors in Python From Scratch

http://machinelearningmastery.com/tutorial-to-implement-k-nearest-neighbors-in-python-from-scratch/

The k-Nearest Neighbors algorithm (or kNN for short) is an easy algorithm to understand and to implement, and a powerful tool to have at your disposal.

In this tutorial you will implement the k-Nearest Neighbors algorithm from scratch in Python (2.7). The implementation will be specific for classification problems and will be demonstrated using the Iris flowers classification problem.

This tutorial is for you if you are a Python programmer, or a programmer who can pick-up python quickly, and you are interested in how to implement the k-Nearest Neighbors algorithm from scratch.

What is k-Nearest NeighborsThe model for kNN is the entire training dataset. When a prediction is required for a unseen data instance, the kNN algorithm will search through the training dataset for the k-most similar instances. The prediction attribute of the most similar instances is summarized and returned as the prediction for the unseen instance.

The similarity measure is dependent on the type of data. For real-valued data, the Euclidean distance can be used. Other other types of data such as categorical or binary data, Hamming distance can be used.

In the case of regression problems, the average of the predicted attribute may be returned. In the case of classification, the most prevalent class may be returned.

How does k-Nearest Neighbors WorkThe kNN algorithm is belongs to the family of instance-based, competitive learning and lazy learning algorithms.

Instance-based algorithms are those algorithms that model the problem using data instances (or rows) in order to make predictive decisions. The kNN algorithm is an extreme form of instance-based methods because all training observations are retained as part of the model.

It is a competitive learning algorithm, because it internally uses competition between model elements (data instances) in order to make a predictive decision. The objective similarity measure between data instances causes each data instance to compete to “win” or be most similar to a given unseen data instance and contribute to a prediction.

Lazy learning refers to the fact that the algorithm does not build a model until the time that a prediction is required. It is lazy because it only does work at the last second. This has the benefit of only including data relevant to the unseen data, called a localized model. A disadvantage is that it can be computationally expensive to repeat the same or similar searches over larger training datasets.

Finally, kNN is powerful because it does not assume anything about the data, other than a distance measure can be calculated consistently between any two instances. As such, it is called non-parametric or non-linear as it does not assume a functional form.

Classify Flowers Using MeasurementsThe test problem we will be using in this tutorial is iris classification.

The problem is comprised of 150 observations of iris flowers from three different species. There are 4 measurements of given flowers: sepal length, sepal width, petal length and petal width, all in the same unit of centimeters. The predicted attribute is the species, which is one of setosa, versicolor or virginica.

It is a standard dataset where the species is known for all instances. As such we can split the data into training and test datasets and use the results to evaluate our algorithm implementation. Good classification accuracy on this problem is above 90% correct, typically 96% or better.

How to implement k-Nearest Neighbors in PythonThis tutorial is broken down into the following steps:

1. Handle Data: Open the dataset from CSV and split into test/train datasets.
2. Similarity: Calculate the distance between two data instances.
3. Neighbors: Locate k most similar data instances.
4. Response: Generate a response from a set of data instances.
5. Accuracy: Summarize the accuracy of predictions.
6. Main: Tie it all together.

1. Handle DataThe first thing we need to do is load our data file. The data is in CSV format without a header line or any quotes. We can open the file with the open function and read the data lines using the reader function in the csv module.

import csv with open('iris.data', 'rb') as csvfile: lines = csv.reader(csvfile) for row in lines: print ', '.join(row)

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import csv

with open('iris.data', 'rb') as csvfile:

for row in lines:

print ', '.join(row)

Next we need to split the data into a training dataset that kNN can use to make predictions and a test dataset that we can use to evaluate the accuracy of the model.

We first need to convert the flower measures that were loaded as strings into numbers that we can work with. Next we need to split the data set randomly into train and datasets. A ratio of 67/33 for train/test is a standard ratio used.

Pulling it all together, we can define a function called loadDataset that loads a CSV with the provided filename and splits it randomly into train and test datasets using the provided split ratio.

import csv import random def loadDataset(filename, split, trainingSet=[] , testSet=[]): with open(filename, 'rb') as csvfile: lines = csv.reader(csvfile) dataset = list(lines) for x in range(len(dataset)-1): for y in range(4): dataset[x][y] = float(dataset[x][y]) if random.random() < split: trainingSet.append(dataset[x]) else: testSet.append(dataset[x])

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import csv

import random

def loadDataset(filename, split, trainingSet=[] , testSet=[]):

with open(filename, 'rb') as csvfile:

dataset = list(lines)

for x in range(len(dataset)-1):

for y in range(4):

dataset[x][y] = float(dataset[x][y])

if random.random() < split:

trainingSet.append(dataset[x])

else:

testSet.append(dataset[x])

Download the iris flowers dataset CSV file to the local directory. We can test this function out with our iris dataset, as follows:

trainingSet=[] testSet=[] loadDataset('iris.data', 0.66, trainingSet, testSet) print 'Train: ' + repr(len(trainingSet)) print 'Test: ' + repr(len(testSet))

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trainingSet=[]

testSet=[]

print 'Train: ' + repr(len(trainingSet))

print 'Test: ' + repr(len(testSet))

2. SimilarityIn order to make predictions we need to calculate the similarity between any two given data instances. This is needed so that we can locate the k most similar data instances in the training dataset for a given member of the test dataset and in turn make a prediction.

Given that all four flower measurements are numeric and have the same units, we can directly use the Euclidean distance measure. This is defined as the square root of the sum of the squared differences between the two arrays of numbers (read that again a few times and let it sink in).

Additionally, we want to control which fields to include in the distance calculation. Specifically, we only want to include the first 4 attributes. One approach is to limit the euclidean distance to a fixed length, ignoring the final dimension.

Putting all of this together we can define the euclideanDistance function as follows:

import math def euclideanDistance(instance1, instance2, length): distance = 0 for x in range(length): distance += pow((instance1[x] - instance2[x]), 2) return math.sqrt(distance)

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import math

def euclideanDistance(instance1, instance2, length):

distance = 0

for x in range(length):

distance += pow((instance1[x] - instance2[x]), 2)

return math.sqrt(distance)

We can test this function with some sample data, as follows:

data1 = [2, 2, 2, 'a'] data2 = [4, 4, 4, 'b'] distance = euclideanDistance(data1, data2, 3) print 'Distance: ' + repr(distance)

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data1 = [2, 2, 2, 'a']

data2 = [4, 4, 4, 'b']

distance = euclideanDistance(data1, data2, 3)

print 'Distance: ' + repr(distance)

3. NeighborsNow that we have a similarity measure, we can use it collect the k most similar instances for a given unseen instance.

This is a straight forward process of calculating the distance for all instances and selecting a subset with the smallest distance values.

Below is the getNeighbors function that returns k most similar neighbors from the training set for a given test instance (using the already defined euclideanDistance function)

import operator def getNeighbors(trainingSet, testInstance, k): distances = [] length = len(testInstance)-1 for x in range(len(trainingSet)): dist = euclideanDistance(testInstance, trainingSet[x], length) distances.append((trainingSet[x], dist)) distances.sort(key=operator.itemgetter(1)) neighbors = [] for x in range(k): neighbors.append(distances[x][0]) return neighbors

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import operator

def getNeighbors(trainingSet, testInstance, k):

distances = []

length = len(testInstance)-1

for x in range(len(trainingSet)):

dist = euclideanDistance(testInstance, trainingSet[x], length)

distances.append((trainingSet[x], dist))

distances.sort(key=operator.itemgetter(1))

neighbors = []

for x in range(k):

neighbors.append(distances[x][0])

return neighbors

We can test out this function as follows:

trainSet = [[2, 2, 2, 'a'], [4, 4, 4, 'b']] testInstance = [5, 5, 5] k = 1 neighbors = getNeighbors(trainSet, testInstance, 1) print(neighbors)

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trainSet = [[2, 2, 2, 'a'], [4, 4, 4, 'b']]

testInstance = [5, 5, 5]

k = 1

neighbors = getNeighbors(trainSet, testInstance, 1)

print(neighbors)

4. ResponseOnce we have located the most similar neighbors for a test instance, the next task is to devise a predicted response based on those neighbors.

We can do this by allowing each neighbor to vote for their class attribute, and take the majority vote as the prediction.

Below provides a function for getting the majority voted response from a number of neighbors. It assumes the class is the last attribute for each neighbor.

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import operator

def getResponse(neighbors):

for x in range(len(neighbors)):

response = neighbors[x][-1]

else:

We can test out this function with some test neighbors, as follows:

neighbors = [[1,1,1,'a'], [2,2,2,'a'], [3,3,3,'b']] response = getResponse(neighbors) print(response)

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neighbors = [[1,1,1,'a'], [2,2,2,'a'], [3,3,3,'b']]

response = getResponse(neighbors)

print(response)

This approach returns one response in the case of a draw, but you could handle such cases in a specific way, such as returning no response or selecting an unbiased random response.

5. AccuracyWe have all of the pieces of the kNN algorithm in place. An important remaining concern is how to evaluate the accuracy of predictions.

An easy way to evaluate the accuracy of the model is to calculate a ratio of the total correct predictions out of all predictions made, called the classification accuracy.

Below is the getAccuracy function that sums the total correct predictions and returns the accuracy as a percentage of correct classifications.

def getAccuracy(testSet, predictions): correct = 0 for x in range(len(testSet)): if testSet[x][-1] is predictions[x]: correct += 1 return (correct/float(len(testSet))) * 100.0

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def getAccuracy(testSet, predictions):

correct = 0

for x in range(len(testSet)):

if testSet[x][-1] is predictions[x]:

correct += 1

return (correct/float(len(testSet))) * 100.0

We can test this function with a test dataset and predictions, as follows:

testSet = [[1,1,1,'a'], [2,2,2,'a'], [3,3,3,'b']] predictions = ['a', 'a', 'a'] accuracy = getAccuracy(testSet, predictions) print(accuracy)

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testSet = [[1,1,1,'a'], [2,2,2,'a'], [3,3,3,'b']]

predictions = ['a', 'a', 'a']

accuracy = getAccuracy(testSet, predictions)

print(accuracy)

6. MainWe now have all the elements of the algorithm and we can tie them together with a main function.

Below is the complete example of implementing the kNN algorithm from scratch in Python.

# Example of kNN implemented from Scratch in Python

import csv import random import math import operator

def loadDataset(filename, split, trainingSet=[] , testSet=[]): with open(filename, 'rb') as csvfile: lines = csv.reader(csvfile) dataset = list(lines) for x in range(len(dataset)-1): for y in range(4): dataset[x][y] = float(dataset[x][y]) if random.random() < split: trainingSet.append(dataset[x]) else: testSet.append(dataset[x])

def euclideanDistance(instance1, instance2, length): distance = 0 for x in range(length): distance += pow((instance1[x] - instance2[x]), 2) return math.sqrt(distance)

def getNeighbors(trainingSet, testInstance, k): distances = [] length = len(testInstance)-1 for x in range(len(trainingSet)): dist = euclideanDistance(testInstance, trainingSet[x], length) distances.append((trainingSet[x], dist)) distances.sort(key=operator.itemgetter(1)) neighbors = [] for x in range(k): neighbors.append(distances[x][0]) return neighbors

def getAccuracy(testSet, predictions): correct = 0 for x in range(len(testSet)): if testSet[x][-1] == predictions[x]: correct += 1 return (correct/float(len(testSet))) * 100.0 def main(): # prepare data trainingSet=[] testSet=[] split = 0.67 loadDataset('iris.data', split, trainingSet, testSet) print 'Train set: ' + repr(len(trainingSet)) print 'Test set: ' + repr(len(testSet)) # generate predictions predictions=[] k = 3 for x in range(len(testSet)): neighbors = getNeighbors(trainingSet, testSet[x], k) result = getResponse(neighbors) predictions.append(result) print('> predicted=' + repr(result) + ', actual=' + repr(testSet[x][-1])) accuracy = getAccuracy(testSet, predictions) print('Accuracy: ' + repr(accuracy) + '%') main()

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# Example of kNN implemented from Scratch in Python

import csv

import random

import math

import operator

def loadDataset(filename, split, trainingSet=[] , testSet=[]):

with open(filename, 'rb') as csvfile:

dataset = list(lines)

for x in range(len(dataset)-1):

for y in range(4):

dataset[x][y] = float(dataset[x][y])

if random.random() < split:

trainingSet.append(dataset[x])

else:

testSet.append(dataset[x])

def euclideanDistance(instance1, instance2, length):

distance = 0

for x in range(length):

distance += pow((instance1[x] - instance2[x]), 2)

return math.sqrt(distance)

def getNeighbors(trainingSet, testInstance, k):

distances = []

length = len(testInstance)-1

for x in range(len(trainingSet)):

dist = euclideanDistance(testInstance, trainingSet[x], length)

distances.append((trainingSet[x], dist))

distances.sort(key=operator.itemgetter(1))

neighbors = []

for x in range(k):

neighbors.append(distances[x][0])

return neighbors

def getResponse(neighbors):

for x in range(len(neighbors)):

response = neighbors[x][-1]

else:

def getAccuracy(testSet, predictions):

correct = 0

for x in range(len(testSet)):

if testSet[x][-1] == predictions[x]:

correct += 1

return (correct/float(len(testSet))) * 100.0

def main():

# prepare data

trainingSet=[]

testSet=[]

split = 0.67

print 'Train set: ' + repr(len(trainingSet))

print 'Test set: ' + repr(len(testSet))

# generate predictions

predictions=[]

k = 3

for x in range(len(testSet)):

neighbors = getNeighbors(trainingSet, testSet[x], k)

result = getResponse(neighbors)

predictions.append(result)

print('> predicted=' + repr(result) + ', actual=' + repr(testSet[x][-1]))

accuracy = getAccuracy(testSet, predictions)

print('Accuracy: ' + repr(accuracy) + '%')

main()

Running the example, you will see the results of each prediction compared to the actual class value in the test set. At the end of the run, you will see the accuracy of the model. In this case, a little over 98%.

... > predicted='Iris-virginica', actual='Iris-virginica' > predicted='Iris-virginica', actual='Iris-virginica' > predicted='Iris-virginica', actual='Iris-virginica' > predicted='Iris-virginica', actual='Iris-virginica' > predicted='Iris-virginica', actual='Iris-virginica' Accuracy: 98.0392156862745%

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...

> predicted='Iris-virginica', actual='Iris-virginica'

> predicted='Iris-virginica', actual='Iris-virginica'

> predicted='Iris-virginica', actual='Iris-virginica'

> predicted='Iris-virginica', actual='Iris-virginica'

> predicted='Iris-virginica', actual='Iris-virginica'

Accuracy: 98.0392156862745%

Ideas For ExtensionsThis section provides you with ideas for extensions that you could apply and investigate with the Python code you have implemented as part of this tutorial.

• Regression: You could adapt the implementation to work for regression problems (predicting a real-valued attribute). The summarization of the closest instances could involve taking the mean or the median of the predicted attribute.
• Normalization: When the units of measure differ between attributes, it is possible for attributes to dominate in their contribution to the distance measure. For these types of problems, you will want to rescale all data attributes into the range 0-1 (called normalization) before calculating similarity. Update the model to support data normalization.
• Alternative Distance Measure: There are many distance measures available, and you can even develop your own domain-specific distance measures if you like. Implement an alternative distance measure, such as Manhattan distance or the vector dot product.

There are many more extensions to this algorithm you might like to explore. Two additional ideas include support for distance-weighted contribution for the k-most similar instances to the prediction and more advanced data tree-based structures for searching for similar instances.

Resource To Learn MoreThis section will provide some resources that you can use to learn more about the k-Nearest Neighbors algorithm in terms of both theory of how and why it works and practical concerns for implementing it in code.

ProblemIris flowers dataset on Wikipedia UCI Machine Learning Repository Iris Dataset CodeThis section links to open source implementations of kNN in popular machine learning libraries. Review these if you are considering implementing your own version of the method for operational use.

BooksYou may have one or more books on applied machine learning. This section highlights the sections or chapters in common applied books on machine learning that refer to k-Nearest Neighbors.

Tutorial SummaryIn this tutorial you learned about the k-Nearest Neighbor algorithm, how it works and some metaphors that you can use to think about the algorithm and relate it to other algorithms. You implemented the kNN algorithm in Python from scratch in such a way that you understand every line of code and can adapt the implementation to explore extensions and to meet your own project needs.

Below are the 5 key learnings from this tutorial:

• k-Nearest Neighbor: A simple algorithm to understand and implement, and a powerful non-parametric method.
• Instanced-based method: Model the problem using data instances (observations).
• Competitive-learning: Learning and predictive decisions are made by internal competition between model elements.
• Lazy-learning: A model is not constructed until it is needed in order to make a prediction.
• Similarity Measure: Calculating objective distance measures between data instances is a key feature of the algorithm.

Did you implement kNN using this tutorial? How did you go? What did you learn?

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