K-nearest neighbors – “Classifying with neighbors in a feature space.”

K-nearest neighbors (KNN) is a machine learning algorithm used for classification and regression tasks. It is a type of instance-based or lazy learning algorithm that makes predictions based on the similarity of instances in a feature space.

The basic idea behind the KNN algorithm is to classify or predict the target variable of a new data point by examining the K nearest neighbors to that point in the feature space. The feature space is a multi-dimensional space where each data point is represented by its feature values.

Here’s a general overview of the KNN algorithm for classification:

1. Training Phase: The algorithm starts by training on a labelled dataset, where each data point is associated with a class or label. The training data is used to build a representation of the feature space.
2. Calculating Similarity: To classify a new data point, the algorithm calculates the similarity between the new point and all the training data points. The similarity is typically measured using distance metrics, such as Euclidean distance or Manhattan distance.
3. Selecting Neighbors: The K nearest neighbours to the new data point are determined based on their similarity scores. The value of K is a user-defined parameter, representing the number of neighbours to consider.
4. Voting or Weighted Voting: Once the neighbours are identified, the algorithm assigns the class label to the new data point based on the class labels of its neighbours. In the case of classification, the majority class among the K neighbours is assigned to the new data point. Alternatively, a weighted voting scheme can be used, where closer neighbours have a higher influence on the final prediction.

KNN can also be used for regression tasks, where the algorithm predicts a continuous target variable. In this case, instead of assigning a class label, the algorithm calculates the average or weighted average of the target variable among the K nearest neighbors to make the prediction.

KNN is a simple and intuitive algorithm that doesn’t require explicit training. However, its performance can be sensitive to the choice of K and the distance metric used. It is also computationally expensive for large datasets, as it requires calculating distances between the new data point and all training instances. Despite its limitations, KNN can be effective for certain classification and regression problems, especially when there is sufficient training data and the feature space is well-defined.