K-nearest neighbors (KNN) is a supervised learning algorithm used for classification and regression. The algorithm works by finding the k closest data points (neighbors) to a given test data point and making a prediction based on their labels/values. The prediction is typically the average (for regression) or the majority class label (for classification) among the k nearest neighbors.
In mathematical terms, KNN is a non-parametric method. Given a training dataset of N labeled points in a d-dimensional feature space, where each point is represented by its d feature values and a class label, the KNN algorithm works as follows:
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For a new test data point with feature values x, the Euclidean or other distance metric is used to calculate the distance between x and each of the N training data points.
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The K nearest neighbors are selected based on the distances, where K is a user-defined parameter.
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For a classification problem, the K nearest neighbors are assigned to their…