Discussion Overview
The discussion revolves around whether the distance functions used in the K-nearest neighbors (KNN) algorithm in machine learning must satisfy the properties of a mathematical metric. Participants explore the implications of these properties on the performance of KNN in binary classification tasks.
Discussion Character
- Debate/contested
- Technical explanation
- Conceptual clarification
Main Points Raised
- One participant questions if distance functions in KNN must satisfy metric properties such as non-negativity, identity of indiscernibles, symmetry, and the triangle inequality.
- Another participant suggests that while many metrics used in machine learning do satisfy the triangle inequality, some, like cosine distance, do not.
- A participant proposes that the requirement for distance functions may not be strict, as functions that perform well could still be valid even if they do not meet all metric criteria.
- Examples of distance functions commonly used in KNN, such as Pythagorean distance, taxicab distance, and Minkowski distance, are mentioned, with some noted to satisfy the corrected metric criteria.
- There is a discussion about the implications of modifying Euclidean distance (e.g., adding 1) on the algorithm's performance, despite it not satisfying the triangle inequality.
- Cosine similarity is highlighted as another distance measure that does not satisfy the triangle inequality but retains certain properties beneficial for clustering similar points.
Areas of Agreement / Disagreement
Participants express differing views on the necessity of distance functions meeting all metric properties, with some arguing that certain functions may still be effective despite not being true metrics. The discussion remains unresolved regarding the strict requirements for distance functions in KNN.
Contextual Notes
Participants note that some distance functions may not adhere to all metric properties, such as those used in boolean spaces or modifications of traditional metrics. The implications of these deviations on the algorithm's effectiveness are not fully explored.
