1Nearest

1nearest, more commonly referred to as the 1-nearest neighbor (1NN) algorithm, is a simple non-parametric method used for classification and regression in machine learning. It belongs to the family of instance-based or lazy learning techniques, in which the model stores the training data and defers computation until a query is made.

In classification, 1NN assigns to a new instance the label of the single closest training example according to a chosen distance metric. For regression, the predicted value is the target value of that nearest neighbor. The distance metric commonly used is Euclidean distance, but others such as Manhattan, cosine, or Hamming distance may be employed depending on the data type and feature space.

Key characteristics of 1NN include the absence of a distinct training phase and the reliance on the entire training dataset at prediction time. This results in low training cost but high prediction cost and memory usage, as every query requires computing distances to all training samples in general. The method is particularly sensitive to feature scaling and irrelevant or redundant features, since the distance measure directly influences the outcome. It also suffers from the curse of dimensionality in high-dimensional spaces, where distances become less informative.

Advantages of 1NN are its simplicity, interpretability, and ability to model complex decision boundaries without assuming a parametric form. Limitations include poor scalability to large datasets, vulnerability to noisy data, and potential ties when two or more instances are equally near. To mitigate these issues, practitioners use indexing structures (such as KD-trees or ball trees), distance weighting, or switch to k-nearest neighbors with k greater than one.

Extensions include weighted 1NN, where closer neighbors contribute more to the prediction, and ensemble or kernelized variants that blend 1NN with other methods. 1NN remains a foundational baseline in many classification and regression tasks.