When to use Cosine Similarity over Euclidean Similarity?

Answer: Use Cosine Similarity over Euclidean Similarity when you want to measure the similarity between two vectors regardless of their magnitude and focus on the direction of the vectors in a high-dimensional space.

Cosine Similarity and Euclidean Similarity are two distinct metrics used for measuring similarity between vectors, each with its own strengths and weaknesses. The choice between them depends on the characteristics of the data and the specific requirements of the application. Below is a detailed comparison with a table highlighting key considerations:

Criteria	Cosine Similarity	Euclidean Similarity
Definition	Measures the cosine of the angle between two vectors.	Measures the distance between two vectors.
Magnitude Sensitivity	Insensitive to the magnitude of vectors.	Sensitive to the magnitude of vectors.
Dimensionality	Well-suited for high-dimensional spaces.	Works better in lower-dimensional spaces.
Data Sparsity	Effective for sparse data, such as text data.	May not perform well with sparse data.
Orthogonality	Handles orthogonality well, distinguishing between similar vectors even if their magnitudes vary.	Tends to struggle with orthogonality, as it considers the direct distance.
Normalization	Requires normalized vectors for accurate results.	Normalization is not required.
Application	Commonly used in natural language processing, document similarity, and recommendation systems.	Commonly used in clustering, classification, and dimensionality reduction.
Computation Complexity	Generally less computationally intensive.	Can be computationally intensive in high dimensions due to the square root operation.

Conclusion:

In summary, use Cosine Similarity when dealing with high-dimensional data, text analysis, or situations where the magnitude of vectors is not crucial. On the other hand, choose Euclidean Similarity when working in lower-dimensional spaces, and the magnitude of vectors plays a significant role in determining similarity. The choice also depends on the specific characteristics of the data and the goals of the analysis.