Specifying the number of nearest neighbors, $K$, is a critical step in configuring a K-Nearest Neighbors (K-NN) algorithm:

• Constraint: $K \ge 1$.
• Small $K$: A value that is too small (e.g., $K=1$) makes the model overly sensitive to local noise, resulting in jagged decision boundaries, high variance, and overfitting.
• Large $K$: A value that is too large produces overly smoothed decision boundaries, leading to lower variance but increased bias (underfitting). It also increases computational cost.
• Heuristic: A common rule of thumb is setting $K = \sqrt{N}$, where $N$ is the total number of training samples.
• Cross-Validation: A more robust method is evaluating different $K$ values on a validation dataset and selecting the $K$ that minimizes the validation error.
• Elbow Method: This approach involves plotting the validation error rates for different $K$ values to visually identify the "elbow" or optimal point of diminishing returns.