Description: The computational complexity of the K-nearest neighbors (K-NN) algorithm refers to the amount of computational resources required to execute this algorithm, which is widely used in classification and regression tasks. This algorithm is based on the idea that similar data points tend to be close to each other in the feature space. The complexity of K-NN can be divided into two main phases: the training phase and the prediction phase. During the training phase, the algorithm stores the training data, which implies a complexity of O(n), where n is the number of examples in the dataset. However, the prediction phase is where the complexity becomes more significant, as to classify a new point, the algorithm must calculate the distance between this point and all training points, resulting in a complexity of O(n * d), where d is the dimensionality of the feature space. This can become inefficient with large datasets and high dimensionality. To optimize the performance of K-NN, techniques such as dimensionality reduction, the use of efficient data structures like k-d trees, or the implementation of approximate search algorithms can significantly reduce search time and improve the algorithm’s efficiency in practical applications.
