Explain K-Nearest Neighbour (K-NN) classification algorithm with the help of a suitable example

The K-Nearest Neighbour (K-NN) classification algorithm is a type of supervised learning algorithm used for classification and regression tasks. It is one of the simplest and most intuitive machine learning algorithms, which makes it popular for both theoretical and practical applications. Despite its simplicity, K-NN can be highly effective in many real-world applications, particularly in pattern recognition, data mining, and intrusion detection systems.

At the heart of the K-NN algorithm lies the principle of similarity. It operates under the assumption that similar data points exist in close proximity in feature space. Hence, it classifies new data points based on the class labels of their nearest neighbors in the training dataset.

Working of K-NN Algorithm

The K-NN algorithm follows these steps:

1. Choose the number of neighbors (K):
   This is a user-defined constant that represents the number of nearest neighbors to consider for classification.

2. Calculate the distance between the new point and all the training points:
   Common distance metrics include:

   • Euclidean Distance

   • Manhattan Distance

   • Minkowski Distance

3. Identify the K nearest neighbors:
   After calculating the distances, the K data points in the training set that are closest to the new data point are selected.

4. Vote for the most frequent class:
   The most frequent class among the K neighbors is selected as the predicted class for the new data point.

5. Return the predicted class.

Mathematical Formulation

The Euclidean distance between two points x=(x1,x2,...,xn)x = (x_1, x_2, ..., x_n) and y=(y1,y2,...,yn)y = (y_1, y_2, ..., y_n) is given by:

d(x,y)=(x1−y1)2+(x2−y2)2+…+(xn−yn)2d(x, y) = \sqrt{(x_1 - y_1)^2 + (x_2 - y_2)^2 + \ldots + (x_n - y_n)^2}

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