What method is commonly used to measure similarity between two items in an embedding space?

Measuring similarity in an embedding space is crucial for many applications in machine learning, particularly in areas like natural language processing, computer vision, and recommendation systems. The commonly used method in this context is cosine similarity.

Cosine similarity quantifies the cosine of the angle between two non-zero vectors in a multi-dimensional space. When two vectors point in similar directions (even if they have different magnitudes), the cosine similarity approaches 1, indicating high similarity. This property makes cosine similarity particularly effective in identifying items that are similar based on their directionality rather than their magnitude.

In contrast, counting common features may not adequately capture the nuances of relationships in complex data structures, and while Manhattan distance is a valid measure of distance, it may not effectively represent similarity in high-dimensional spaces where the vectors can be sparsely populated. Applying linear regression is unrelated as it pertains to predictive modeling rather than measuring similarity between items. Thus, the use of cosine similarity in the embedding space stands out as the optimal choice for analyzing similarity based on orientation and directional context within the data.