What is the most widely used distance metric in KNN?Euclidean distanceManhattan distancePerpendicular distanceAll of the aboveClear selection

Break Down the Problem

1. Identify the distance metrics listed.
2. Determine which one is the most widely used in K-Nearest Neighbors (KNN).

Relevant Concepts

1. Euclidean Distance: Measures the straight-line distance between two points in Euclidean space.
2. Manhattan Distance: Measures the distance between two points based on a strictly horizontal and vertical path.
3. Perpendicular Distance: Typically used in a geometric context; not commonly applied in KNN.
4. All of the Above: Suggests that multiple metrics might be widely used.

Analysis and Detail

1. Euclidean Distance: Frequently used in KNN due to its effectiveness in measuring the “as-the-crow-flies” distance, making it ideal for most applications.
2. Manhattan Distance: Also used, especially in high-dimensional spaces or when working with grid-like data.
3. Perpendicular Distance: Not a standard term associated with KNN distance metrics.
4. While all these metrics have their applications, Euclidean distance is typically preferred for KNN for its simplicity and performance with continuous variables.

Verify and Summarize

Based on the analysis, Euclidean distance is the most popular metric used in KNN due to its straightforward mathematical interpretation and effective distance measurement in multi-dimensional space.

Final Answer

Euclidean distance is the most widely used distance metric in KNN.