k-NN works well with a small number of input variables (p), but struggles when the number of inputs is very largeReview LaterTrueFalse

Understanding the k-NN Algorithm

The k-Nearest Neighbors (k-NN) algorithm is a simple, yet effective supervised learning method used for classification and regression. It makes predictions based on the 'k' closest training examples in the feature space.

Impact of High Dimensionality

1. Curse of Dimensionality: As the number of input variables (or dimensions) increases, the volume of the feature space grows exponentially. This phenomenon is known as the 'curse of dimensionality.' In high-dimensional spaces, data points become sparse, making it hard for k-NN to find meaningful neighbors.

2. Distance Metrics: k-NN relies on distance metrics (like Euclidean distance) to calculate how close data points are. In high dimensions, distances between points tend to become more uniform, which diminishes the algorithm's effectiveness because distinguishing between neighbors becomes challenging.

3. Computational Complexity: The search for nearest neighbors becomes computationally expensive as dimensionality increases, leading to slower performance.

Summary of Findings

Therefore, the statement is True. k-NN works well when the number of input variables is small but struggles significantly when the number of inputs becomes very large due to the curse of dimensionality and the challenges associated with distance calculations.