Since the algorithm assigns the test/query data point to the class that is most common among its k-nearest neighbors, in the case you just describe, every query data point will be assigned to the majority class.

In a K-Nearest Neighbors (KNN) classifier, setting k equal to the total number of training points means the algorithm will consider every single data point in the training set when making a prediction. As a result, it essentially performs a majority vote across the entire dataset, regardless of how close or far the neighbors actually are from the query point.

This leads to a very generalized and biased model. Instead of predicting based on local patterns or nearby neighbors, the classifier just assigns the most frequent class label in the whole training data. In practice, this means the model will often ignore the structure or distribution of the data and might always predict the majority class, especially in imbalanced datasets.

So, while it avoids overfitting, it also loses the main strength of KNN — local decision-making. That’s why choosing the right value of k is important: too small and the model may overfit; too large and it may underfit or generalize too much.

Dear Joseph Isdory ,

A K-Nearest Neighbor Classifier is a simple algorithm used in computer science that classifies a data point based on the majority class of its nearest neighbors, where the value of 'k' represents the number of neighboring data points considered for classification.

https://www.sciencedirect.com/topics/computer-science/k-nearest-neighbor-classifier

Regards,

Shafagat

If we set "k" to be the total number of points in your training data for a KNN classifier:

-> The algorithm will treat every training point as a neighbour of any new data point. This implies that the majority class across all of our training examples will be the prediction.

-> KNN essentially becomes a "global majority vote" classifier. This is typically detrimental since it negates the purpose of KNN, which is to use local information.

-> No complex patterns will be captured by your model, which will have a high bias and probably only predict the most common class. For classification in the real world, it becomes overly simplistic and essentially useless.

The model will be biased toward the most frequent class because it considers all training points when making predictions, leading to predictions based solely on the majority class.

Joseph Isdory

If k equals the total number of training points in a KNN classifier, the prediction is based on a global majority vote, not the local neighborhood. This causes the model to:

• Lose local sensitivity, ignoring patterns in nearby data.
• Bias toward the majority class, especially in imbalanced datasets.
• Underfit, resulting in high bias and poor generalization.

In essence, KNN becomes a simplistic majority classifier, defeating its core purpose.

In a KNN classifier, setting *k* equal to the number of training data points causes the algorithm to predict the most frequent class in the entire dataset, ignoring local patterns and leading to poor classification accuracy due to oversmoothing.