About Cosine Similarity

Cosine similarity is a measure of similarity between two non-zero vectors of an inner product space. It measures the cosine of the angle between two vectors projected in a multi-dimensional space.

Key Concepts:

• Vectors: Ordered lists of numbers representing points in space
• Dot Product: Sum of products of corresponding elements
• Magnitude: Length of a vector (square root of sum of squared elements)
• Angle: The angle between two vectors determines their similarity

Properties of Cosine Similarity:

• Range: -1 to 1 (1 = identical, 0 = orthogonal, -1 = opposite)
• Invariant to scaling
• Measures orientation, not magnitude
• Widely used in text analysis and machine learning

Applications:

• Text similarity and document comparison
• Recommendation systems
• Image similarity
• Clustering and classification

Tips:

• Vectors must have the same dimension
• Higher values indicate greater similarity
• Useful for comparing documents regardless of their length
• Consider normalizing vectors for better results