KNN algorithm: Introduction to K-Nearest Neighbors Algorithm for Regression

Aishwarya Singh 13 Feb, 2024 • 9 min read

Introduction

Out of all the machine learning algorithms I have come across, the KNN algorithm has easily been the simplest to pick up. Despite its simplicity, it has proven to be incredibly effective at certain tasks (as you will see in this article).

What’s even better? It finds utility in both classification and regression problems! However, the KNN algorithm predominantly garners popularity for classification tasks. In my experience, I rarely see people using the KNN algorithm for regression tasks.

My aim here is to illustrate and emphasize how KNN can be equally effective when the target variable is continuous in nature.

knn algorithm


Learning Objectives

  • Understand the intuition behind KNN algorithms.
  • Learn different ways to calculate distances between points.
  • Practice implementing the algorithm in Python on the Big Mart Sales dataset.

If you want to understand the KNN algorithm in a course format, here is the link to our free course- K-Nearest Neighbors (KNN) Algorithm in Python and R

Understanding the Intuition Behind the KNN Algorithm

Let us start with a simple example. Consider the following table – it consists of the height, age, and weight (target) values for 10 people. As you can see, the weight value of ID11 is missing. We need to predict the weight of this person based on their height and age, utilizing the kNN algorithm.

Note: The data in this table does not represent actual values. We’re simply employing it as an example to illustrate this concept.
Sample dataset table | knn algorithm

For a clearer understanding of this, below is the plot of height versus age from the above table:

sample datapoints plotted | knn algorithm

In the above graph, the y-axis represents the height of a person (in feet) and the x-axis represents the age (in years). The points are numbered according to the ID values. The yellow point (ID 11) is our test point.

If I ask you to identify the weight of ID11 based on the plot, what would be your answer? You would likely say that since ID11 is closer to points 5 and 1, so it must have a weight similar to these IDs, probably between 72-77 kgs (weights of ID1 and ID5 from the table). That actually makes sense, but how do you think the algorithm predicts the values? We will find that out in this article.

Here is a free video-based course to help you understand the KNN algorithm – K-Nearest Neighbors (KNN) Algorithm in Python and R

How Does the KNN Algorithm Work?

As we saw above, the KNN algorithm can be used for both classification and regression problems. The KNN algorithm uses ‘feature similarity’ to predict the values of any new data points. This means that the new point is assigned a value based on how closely it resembles the points in the training set. From our example, we know that ID11 has height and age similar to ID1 and ID5, so the weight would also approximately be the same.

Had it been a classification problem, we would have taken the mode as the final prediction. In this case, we have two values of weight – 72 and 77. Any guesses on how the final value will be calculated? The average of the values is taken to be the final prediction.

Below is a stepwise explanation of the algorithm:

1. First, the distance between the new point and each training point is calculated.

distance calculation knn algorithm

2. The closest k data points are selected (based on the distance). In this example, points 1, 5, and 6 will be selected if the value of k is 3. We will further explore the method to select the right value of k later in this article.

clustering | knn algorithm

3. The average of these data points is the final prediction for the new point. Here, we have the weight of ID11 = (77+72+60)/3 = 69.66 kg.

In the next few sections, we will discuss each of these three steps in detail.

How to Calculate the Distance Between Points?

The first step is to calculate the distance between the new point and each training point. There are various methods for calculating this distance, of which the most commonly known methods are – Euclidian, Manhattan (for continuous), and Hamming distance (for categorical).

  1. Euclidean Distance: Euclidean distance is calculated as the square root of the sum of the squared differences between a new point (x) and an existing point (y).
  2. Manhattan Distance: This is the distance between real vectors using the sum of their absolute difference.Euclidean and Manhattan Distance Formulae
  3. Hamming Distance: It is used for categorical variables. If the value (x) and the value (y) are the same, the distance D will be equal to 0. Otherwise D=1.
Hamming Distance Formula

There is also Minkowski distance which is a generalized form of Euclidean and manhattan distances.

After measuring the distance of a new observation from the points in our training set, we proceed to select the closest points. The number of points to be considered is determined by the value of k.

How to Choose the K-factor?

The second step is to select the k value. This determines the number of neighbors we look at when we assign a value to any new observation.

In our example, for a value k = 3, the closest points are ID1, ID5, and ID6.

Closest points in knn algorithm
closest points table

The prediction of weight for ID11 will be:

ID11 = (77+72+60)/3 

ID11 = 69.66 kg

For the value of k=5, the closest point will be ID1, ID4, ID5, ID6, and ID10.

closest points in knn algorithm
Table of clustered points

The prediction for ID11 will be:

ID 11 =  (77+59+72+60+58)/5 

ID 11 = 65.2 kg

We notice that based on the k value, the final result tends to change. Then how can we figure out the optimum value of k? Let us decide based on the error calculation for our train and validation set (after all, minimizing the error is our final goal!).

Have a look at the below graphs for training error and validation error for different values of k.

training error graph | knn algorithm
validation error graph | knn algorithm

For a very low value of k (suppose k=1), the model is overfitting the training data, which leads to a high error rate on the validation set. On the other hand, for a high value of k, the model performs poorly on both the train and validation sets. If you observe closely, the validation error curve reaches a minimum at a value of k = 9. This value of k is the optimum value of the model (it will vary for different datasets). Researchers typically use the elbow curve, named for its resemblance to an elbow, to determine the k value.

Implementation of KNN Algorithm Using Python

By now, you must have a clear understanding of the algorithm. If you have any questions regarding the same, please use the comments section below, and I will be happy to answer them. We will now go ahead and implement the algorithm on a dataset. I have used the Big Mart sales dataset to show the implementation; you can download it from this link.

The full Python code is below, but we have a really cool coding window here where you can code your own k-Nearest Neighbor model in Python:

Step 1: Read the file

import pandas as pd
df = pd.read_csv('train.csv')
df.head()

Step 2: Impute missing values

df.isnull().sum()
#missing values in Item_weight and Outlet_size needs to be imputed
mean = df['Item_Weight'].mean() #imputing item_weight with mean
df['Item_Weight'].fillna(mean, inplace =True)

mode = df['Outlet_Size'].mode() #imputing outlet size with mode
df['Outlet_Size'].fillna(mode[0], inplace =True)

Step 3: Deal with categorical variables and drop the id columns

df.drop(['Item_Identifier', 'Outlet_Identifier'], axis=1, inplace=True)
df = pd.get_dummies(df)

Step 4: Create a train and a test set

from sklearn.model_selection import train_test_split
train , test = train_test_split(df, test_size = 0.3)

x_train = train.drop('Item_Outlet_Sales', axis=1)
y_train = train['Item_Outlet_Sales']

x_test = test.drop('Item_Outlet_Sales', axis = 1)
y_test = test['Item_Outlet_Sales']

Step 5: Preprocessing – Scaling the features

from sklearn.preprocessing import MinMaxScaler
scaler = MinMaxScaler(feature_range=(0, 1))

x_train_scaled = scaler.fit_transform(x_train)
x_train = pd.DataFrame(x_train_scaled)

x_test_scaled = scaler.fit_transform(x_test)
x_test = pd.DataFrame(x_test_scaled)

Step 6: Let’s examine the error rate for different k values.

#import required packages
from sklearn import neighbors
from sklearn.metrics import mean_squared_error 
from math import sqrt
import matplotlib.pyplot as plt
%matplotlib inline
rmse_val = [] #to store rmse values for different k
for K in range(20):
    K = K+1
    model = neighbors.KNeighborsRegressor(n_neighbors = K)

    model.fit(x_train, y_train)  #fit the model
    pred=model.predict(x_test) #make prediction on test set
    error = sqrt(mean_squared_error(y_test,pred)) #calculate rmse
    rmse_val.append(error) #store rmse values
    print('RMSE value for k= ' , K , 'is:', error)

Output:

RMSE value for k = 1 is: 1579.8352322344945
RMSE value for k = 2 is: 1362.7748806138618
RMSE value for k = 3 is: 1278.868577489459
RMSE value for k = 4 is: 1249.338516122638
RMSE value for k = 5 is: 1235.4514224035129
RMSE value for k = 6 is: 1233.2711649472913
RMSE value for k = 7 is: 1219.0633086651026
RMSE value for k = 8 is: 1222.244674933665
RMSE value for k = 9 is: 1219.5895059285074
RMSE value for k = 10 is: 1225.106137547365
RMSE value for k = 11 is: 1229.540283771085
RMSE value for k = 12 is: 1239.1504407152086
RMSE value for k = 13 is: 1242.3726040709887
RMSE value for k = 14 is: 1251.505810196545
RMSE value for k = 15 is: 1253.190119191363
RMSE value for k = 16 is: 1258.802262564038
RMSE value for k = 17 is: 1260.884931441893
RMSE value for k = 18 is: 1265.5133661294733
RMSE value for k = 19 is: 1269.619416217394
RMSE value for k = 20 is: 1272.10881411344
#plotting the rmse values against k values
curve = pd.DataFrame(rmse_val) #elbow curve 
curve.plot()
RMSE graph | knn algorithm

As we discussed, when we take k=1, we get a very high RMSE value. The RMSE value decreases as we increase the k value. At k= 7, the RMSE is approximately 1219.06 and shoots upon further increasing the k value. We can safely say that k=7 will give us the best result in this case.

These are the predictions using our training dataset. Let us now predict the values for test data and make a submission.

Step 7: Make predictions on the test dataset

#reading test and submission files
test = pd.read_csv('test.csv')
submission = pd.read_csv('SampleSubmission.csv')
submission['Item_Identifier'] = test['Item_Identifier']
submission['Outlet_Identifier'] = test['Outlet_Identifier']

#preprocessing test dataset
test.drop(['Item_Identifier', 'Outlet_Identifier'], axis=1, inplace=True)
test['Item_Weight'].fillna(mean, inplace =True)
test = pd.get_dummies(test)
test_scaled = scaler.fit_transform(test)
test = pd.DataFrame(test_scaled)

#predicting on the test set and creating submission file
predict = model.predict(test)
submission['Item_Outlet_Sales'] = predict
submission.to_csv('submit_file.csv',index=False)

On submitting this file, I get an RMSE of 1279.5159651297.

Step 8: Implementing GridsearchCV 

For deciding the value of k, plotting the elbow curve every time is a cumbersome and tedious process. You can simply use grid search to find the best parameter value.

from sklearn.model_selection import GridSearchCV
params = {'n_neighbors':[2,3,4,5,6,7,8,9]}

knn = neighbors.KNeighborsRegressor()

model = GridSearchCV(knn, params, cv=5)
model.fit(x_train,y_train)
model.best_params_

Output:

{'n_neighbors': 7}

Conclusion

In this article, we covered the workings of the KNN algorithm and its implementation in Python. It’s one of the most basic yet effective machine-learning models. For KNN implementation in R, you can go through this tutorial: kNN Algorithm using R. You can also go for our free course – K-Nearest Neighbors (KNN) Algorithm in Python and R, to further your foundations of KNN.

In this article, we used the KNN model directly from the scikit-learn library. If you think you know KNN well and have a solid grasp of the technique, test your skills in this MCQ quiz: 30 questions on kNN Algorithm. Good luck!

Key Takeaways

  • We have learned how to implement KNN in Python.
  • We have learned to compute the optimum value of the K hyper-parameter.
  • We have learned that the KNN regression model is useful in many regression problems.

Frequently Asked Questions

Q1. What is the purpose of the K nearest neighbor algorithm?

A. The K nearest neighbors supervised machine learning algorithm performs classification and regression tasks effectively. In this, we calculate the distance between features of test data points against those of train data points. We calculate prediction values by taking the mode or mean.

Q2. Can you use K Nearest Neighbors for regression?

A. Yes, we can use KNN for regression. Here, we take the k nearest values of the target variable and compute the mean of those values. Those k nearest values act like regressors of linear regression.

Q3. How do you calculate the K nearest neighbors?

A. We can use the elbow method where we plot the test data set error vs. k-value for different k-values. We can choose K, where the improvement in error is negligible.

Q4. What is KNN Classifier?

A. KNN (K-Nearest Neighbors) Classifier is a type of machine learning algorithm used for classification tasks. It is a non-parametric algorithm, which means it does not make any assumptions about the underlying distribution of the data.
In KNN Classifier, a new data point is classified based on its proximity to the K nearest neighbors in the training set. We calculate proximity using a distance metric, such as Euclidean distance or Manhattan distance. Then, we determine the predicted class of the new data point based on the majority class among its K nearest neighbors.

Aishwarya Singh 13 Feb 2024

An avid reader and blogger who loves exploring the endless world of data science and artificial intelligence. Fascinated by the limitless applications of ML and AI; eager to learn and discover the depths of data science.

Frequently Asked Questions

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Responses From Readers

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Paren Kansara
Paren Kansara 23 Aug, 2018

Hi Aishwarya, your explanation on KNN is really helpful. I have a doubt though. KNN suffers from the dimensionality curse i.e. Euclidean distance is not helpful when subjected to high dimensions as it is equidistant for different vectors. What was your viewpoint while using the KNN despite this fact ? Curious to know. Thank you.

Osman
Osman 23 Aug, 2018

Hi. I have been following you now for a while. Love your post. I wish you cold provide a pdf format also, because it is hard to archive and read web posts when you are offline.

Abin Singh Rajan
Abin Singh Rajan 23 Aug, 2018

Hi thanks for the explanations. Can you explain the intuition behind categorical variable calculations. For example, assume data set has height,age,gender as independent variable and weight as dependent variable. Now if an unseen data comes with male as gender, then how it works? how it predicts the weight?

Steffen
Steffen 23 Aug, 2018

cannot find the data on https://datahack.analyticsvidhya.com/contest/practice-problem-big-mart-sales-iii/

Mukul MIshra
Mukul MIshra 29 Aug, 2018

please provide the code for R as well

Akshay
Akshay 03 Sep, 2018

First of all, thank you for such a nice explanation. I have couple of questions about the methods for calculating the distance. 1) Are Manhattan distance and Hamming Distance are same? Because by looking at the formulas, it looks like the same. 2) For Hamming Distance the article says 'If the predicted value (x) and the real value (y) are same, the distance D will be equal to 0 . Otherwise D=1." But the the formula itself will be use in the process of calculation of predicted value so how can we use the predicted value in Hamming Distance formula, I hope you got my question. Thank you.

Rajiv S
Rajiv S 10 Sep, 2018

Hi Aishwarya, This is the first time I have read one of your blogs. You are doing a fantastic job of explaining concepts in a lucid yet simple language. Keep it up!!! It will help if you in the End notes section you can include limitations of the model usage like the one explained in response to Abin's question. Further would it be possible for you to publish a series on other models too? Thanks.

Ranganath
Ranganath 16 Oct, 2018

Hi, How did you calculate the RMSE for the test data. Did you build model on entire training data and then predicted on the test data (which included submission['Item_Outlet_Sales']) to calculate RMSE? Ranganath

Ashish
Ashish 14 Nov, 2018

HI Aishwarya Nice article. Explained very well. Couple of questions: * The best K value i get is 8 as per the elbow curve however when i ran GridSearchCV function it returned 9 Dont they have to match ? I am a bit unclear on this * You mentioned that after submission you got RMSE of 1279.52. Plz can you help understand how did you calculate it ? ~~Ashish

geeta
geeta 23 Nov, 2018

In which format i should use data if i have a user profile and i want to show doctors near you and also is KNN beneficial for this?

Merav
Merav 16 Dec, 2018

Where can I download the dataset?

Noah
Noah 21 Dec, 2018

Hi Aishwarya! Great article. I tried this code on my own data set and it seemed to work fine. On the last part of the code where you are using GridSearch, nothing output for me. Are we supposed to add print to "model.best_params_"

Sharan
Sharan 04 Jan, 2022

Hi Aishwarya, Thanks for posting this. I have a question. I am using the Knn algorithm in my project to detect anomalies for each day comparing against last 120 days & it doesn't seem to work well with a dataset that changes everyday. Example: Let's say there is a query to pull and track top 25 pages (out of 100 pages on a website) with most number of visits on a given day. Now let's say if there was a problem with a page the next day or if there was a promotion then the visits can increase/decrease & with that the top 25 list of pages will change. So when a page goes out of the top 25 list & I compare this new list with the last 120 days of data (120 days of top25) the KNN algorithm defaults that page going out as zero & it gives a false anomaly alert that there is no visits to the page but in fact it just went out of top25. Is this a limitation/problem on the Knn algorithm or is it to do with the sql query that pulls top 25 which is not static everyday?

S SIVARAMAKRISHNAN
S SIVARAMAKRISHNAN 08 Jan, 2022

After we find best params using grid serach search cv and applying this to the model , what are the further steps to come to a conclusion of the model and it's output

Micah
Micah 16 Jun, 2022

Thanks very much for this express explanations. I wish to ask how the dataset can be gotten from a database instead of using a predefined set of data.

Matthew Leichter
Matthew Leichter 11 Aug, 2022

Wonderful article. Just wanted to point out there is an error in your preprocessing for MinMax. The test set should only fit not fit_transform, as it needs to be fit to the same scale as the training set or you create bias.

Steven
Steven 15 Jan, 2023

Hi Aishwarya. Thank you so very much for this article. Is there a way I can plot a KNN regression line, quickly? similar to sns.regplot(x, y, ci=None) function for regular linear regression? Thank so much

Chad Druck
Chad Druck 16 Jun, 2023

What is the best method to get the predictions into a production dataset? If I start with a csv file, how can I merge predictions back into the original file or create a new file.

Amit
Amit 17 Jan, 2024

Hi Aishwarya, Thanks for this blog article. I have a couple of questions here, like: 1. Can you please share the explanation for using Pandas "get_dummies"? 2. Why did you drop "Item_Outlet_Sales" from the train and test datasets? 3. Why did you use MinMaxScaler? 4. Why did you choose fit_transform? 5. Why do we require mean squared error?

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