Question

How does the curse of dimensionality affect the performance of the K-Nearest Neighbours (K-NN) algorithm?

• A. K-NN performs better with an increasing number of input variables.
• B. K-NN struggles to predict the output accurately with an increasing number of input variables.
• C. K-NN becomes faster with more input variables due to increased computational power.
• D. K-NN becomes less sensitive to outliers with an increasing number of input variables.

Hint:

High dimensions make distance metrics unreliable — keep K-NN features limited.

Answer 1

The Correct Option is B

The curse of dimensionality refers to problems that arise when the number of input features increases.
In K-NN, distance calculations between points become less meaningful in high-dimensional space.
As dimensions increase, data points spread out and become equally distant from each other.
This makes it hard for K-NN to find true nearest neighbours, which reduces accuracy.
Also, more dimensions mean more computation and storage requirements, which can make K-NN slower, not faster.
Options (A), (C), and (D) are incorrect because they suggest improvements or benefits that do not occur.
Therefore, K-NN struggles with prediction accuracy when dealing with too many input variables due to the curse of dimensionality.