In this blog, we will learn about the KNN algorithm, why we need it, and the types of distance metrics used. Along with these topics, we will also cover the implementation and know the facts behind “why the KNN algorithm is a lazy algorithm”.
Table of Contents
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What is KNN Algorithm in Machine Learning?
The K-Nearest Neighbors (KNN) algorithm is a versatile supervised learning approach used for classification and regression tasks. In KNN, data points are classified based on the majority class of their nearest neighbors. The “k” represents the number of clusters. KNN’s simplicity and effectiveness make it valuable in various applications, although it may be sensitive to outliers and requires careful selection of the optimal k value for optimal performance.
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Why do we need KNN Algorithm?
KNN is easy to understand and implement, making it a valuable tool for both beginners and experienced practitioners. Overall, KNN provides a flexible and effective approach for making predictions based on the similarity of data points.
Imagine having two categories, say A and B, and you encounter a new data point, let’s call it x. The challenge is determining which category x belongs to. This is where the K-Nearest Neighbors (KNN) algorithm comes into play. KNN is a powerful tool for classification tasks like this. By assessing the proximity of the new data point to its neighbors, KNN helps identify the category or class to which it likely belongs. Essentially, KNN uses the collective influence of its closest data points, making it an intuitive algorithm for categorizing or labeling unknown data based on its proximity to known data points.
Some of the other reasons why the KNN algorithm is essential are given below:
- Firstly, KNN is a multifunctional and simple classification algorithm that can be applied to both classification and regression tasks. It’s particularly useful when the underlying data distribution is not well-defined or linear.
- Secondly, KNN doesn’t require assumptions about the underlying data, making it applicable in various scenarios.
- Thirdly, it excels in cases where the decision boundaries are complex and non-linear.
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Types of Distance Metrics Used in KNN Algorithm
In the KNN algorithm, we measure the distance between data points to decide which ones are similar. This helps us group similar points together. Imagine it as measuring how far or close things are in a neighborhood. The distance could be like the blocks between houses. This is important because it helps us figure out which group, or “cluster,” a new point belongs to. So, if a new house is close to many others, it joins their cluster. Distance measurement in KNN is like figuring out who your closest neighbors are, making it easier to group similar things together.
Euclidean distance measures straight-line distance, and Manhattan distance measures the sum of absolute differences along each dimension. However, Minkowski distance is a generalized form with a parameter (p) that allows you to adjust the sensitivity to different dimensions. The choice between these metrics depends on the nature of the data and the problem being solved. Let’s step into explanations for the three distance metrics: Euclidean Distance, Manhattan Distance, and Minkowski Distance.
Euclidean Distance
Formula:
Explanation: Euclidean distance measures the straight-line distance between two points in Euclidean space. In a two-dimensional space (for simplicity), if you have two points (x1, y1) and (x2, y2), the Euclidean distance (d) between them is given by the Pythagorean theorem: (d = sqrt{(x2 – x1)^2 + (y2 – y1)^2}). This distance metric is sensitive to both the magnitude and direction of the vectors.
Manhattan Distance
Formula:
Explanation: Manhattan distance, also known as the L1 norm or Taxicab distance, measures the sum of the absolute differences between the corresponding coordinates of two points. Imagine navigating a city grid: the distance traveled to reach a destination is the sum of the horizontal and vertical distances traveled along the grid lines. Similarly, the Manhattan distance is the sum of the absolute differences along each dimension.
Minkowski Distance
Formula:
Explanation: Minkowski distance is a generalization of both Euclidean and Manhattan distances. The parameter (p) allows you to adjust the formula. When (p = 2), it becomes the Euclidean distance; when (p = 1), it becomes the Manhattan distance. For other values of (p), it represents a more general form. Minkowski distance is used when you want to control the sensitivity to different dimensions based on the problem requirements.
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How to Choose “k” for KNN
Choosing the right value for k in the k-Nearest Neighbors (k-NN) algorithm is a critical step that significantly influences its performance. The selection of k involves finding a balance between overfitting and underfitting.
A smaller value of k, such as 1 or 3, tends to make the algorithm more sensitive to noise and outliers, potentially leading to overfitting. On the other hand, a larger k, such as 10 or 20, may smooth out the decision boundaries, possibly resulting in underfitting.
To determine the optimal k:
- Consider Dataset Characteristics
Assess the nature of the dataset. For noisy or small datasets, a smaller k may be suitable, while larger datasets may benefit from a larger k.
- Odd Values for Binary Classification
For binary classification problems, consider using an odd value for k to avoid ties when voting for the majority class.
Employ cross-validation techniques, such as k-fold cross-validation, to evaluate the model’s performance with different values of k. This helps identify the k that provides the best balance between bias and variance.
Perform a grid search over a range of k values, testing each value’s impact on the model’s performance. Choose the k that results in the highest accuracy or the desired evaluation metric.
Visualize decision boundaries for different k values to observe how they affect the model’s ability to capture the underlying patterns in the data.
Working of KNN Algorithm in Machine Learning
The K-Nearest Neighbors algorithm classifies or predicts a new data point based on the majority class or average of its k-nearest neighbors. Here’s a step-by-step explanation of how the KNN algorithm works:
Step 1: Choose the Value of k
Decide the number of neighbors (k) to consider. This is a crucial parameter that can impact the algorithm’s performance.
Step 2: Calculate Distances
Measure the distance between the new data point and every point in the training dataset. Common distance metrics include Euclidean distance, Manhattan distance, or other distance measures based on the problem at hand.
Step 3: Identify Neighbors
Select the k data points from the training set that are closest to the new data point based on the calculated distances.
Step 4: Majority Voting (Classification) or Weighted Averaging (Regression)
For classification tasks, determine the majority class among the k neighbors. The new data point is assigned to this class.
For regression tasks, calculate the average of the target values of the k neighbors. This average becomes the predicted value for the new data point.
Step 5: Make Prediction
Assign the predicted class or value to the new data point based on the results of the majority voting or averaging.
Step 6: Output
The KNN algorithm provides the final classification or prediction for the new data point.
Step 7: Evaluate Performance
If working with a labeled dataset, evaluate the performance of the algorithm using metrics such as accuracy, precision, recall, or F1 score.
Why is KNN a Lazy Algorithm?
The KNN algorithm is considered a “lazy” algorithm because it doesn’t make any generalizations during the training phase. In a lazy algorithm, the model is not explicitly trained on the dataset, but instead, it memorizes the entire dataset. The algorithm delays the processing of the training data until a new, unseen data point needs to be classified or predicted.
In the case of KNN, during the training phase, the algorithm simply stores the training dataset in memory. When a prediction is required for a new data point, the algorithm calculates the distances between that point and all points in the training set. It then selects the k-nearest neighbors based on these distances and makes predictions based on the majority class or average of the target values of these neighbors.
The term “lazy” is used to highlight that the algorithm doesn’t actively learn a model during the training phase; it defers the learning until the prediction phase, when the specific instance needs to be classified. This characteristic makes KNN simple and flexible but can also lead to higher computational costs during prediction, especially with large datasets.
Implementation of KNN Algorithm in Machine Learning
Refer to the code below to understand the implementation of KNN algorithm in machine learning:
# Import necessary libraries
from sklearn.model_selection import train_test_split
from sklearn.neighbors import KNeighborsClassifier
from sklearn.metrics import accuracy_score
# Sample dataset (replace this with your own dataset)
# X represents features, and y represents labels
X = [[1, 2], [2, 3], [3, 1], [6, 5], [7, 7], [8, 6]]
y = ['A', 'A', 'A', 'B', 'B', 'B']
# Split the dataset into training and testing sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)
# Create a KNN classifier with k=3 (you can adjust this parameter)
knn_classifier = KNeighborsClassifier(n_neighbors=3)
# Fit the model on the training set
knn_classifier.fit(X_train, y_train)
# Make predictions on the test set
y_pred = knn_classifier.predict(X_test)
# Evaluate the accuracy of the model
accuracy = accuracy_score(y_test, y_pred)
print(f'Accuracy: {accuracy}')
# Example of making a prediction for a new data point
new_data_point = [[4, 4]]
predicted_class = knn_classifier.predict(new_data_point)
print(f'Predicted class for {new_data_point}: {predicted_class}')
Output:
Accuracy: 0.0
Predicted class for [[4, 4]]: [‘B’]
In this example, the KNN algorithm is used for classification. You can replace the sample dataset with your own dataset, ensuring that you have corresponding features (X) and labels (y). The “n_neighbors” parameter in “KNeighborsClassifier” specifies the number of neighbors to consider, and you can adjust it based on your specific needs.
Advantages and Disadvantages of KNN Algorithm
Understanding these pros and cons is essential when deciding whether KNN is suitable for a particular task and dataset or not. Below are some of the pros and cons of the KNN algorithm.
Advantages
- KNN is straight forward and easy to understand, making it accessible for beginners.
- As a lazy learning algorithm, KNN does not involve a training phase. The model simply memorizes the entire dataset, making it quick to implement.
- KNN is non-parametric, meaning it makes no assumptions about the underlying data distribution. It can be versatile in various types of datasets.
- The algorithm can adapt to changes in the data during runtime, making it suitable for dynamic environments where the data distribution may shift.
- It tends to perform well when the dataset is small or has a relatively simple structure.
Disadvantages
- The algorithm memorizes the entire dataset, leading to high memory usage, which may become impractical for large datasets.
- Outliers or noise in the dataset can significantly impact predictions because KNN relies on the majority class or average of the k-nearest neighbors.
- KNN’s performance can be affected by the scale of the features, as features with larger scales may dominate the distance calculations.
- The choice of the parameter k (number of neighbors) is crucial, and selecting an inappropriate value can lead to suboptimal results. Cross-validation may be needed to find the best k for a given dataset.
Conclusion
The KNN algorithm stands as an intuitive tool in the field of machine learning. Its simplicity, interpretability, and effectiveness in classification and regression tasks make it a valuable asset for both beginners and experts. KNN’s adaptability to various domains, from healthcare to finance, underscores its relevance. Moreover, its non-parametric nature allows it to excel in dynamic environments. Looking forward, KNN’s role is to expand with the increasing complexity of datasets, emphasizing its enduring significance in shaping the future of machine learning, where interpretable and adaptable models remain important.
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