Dot Product Similarity

In the context of machine learning and AI, dot product similarity (also known as the inner product or scalar product) is a fundamental mathematical operation used to determine the cosine of the angle between two vectors in a high-dimensional space. This measure is particularly useful in various applications such as information retrieval, natural language processing, and recommendation systems, where it helps quantify the similarity between feature vectors. A higher dot product value indicates greater similarity, while a lower or negative value indicates dissimilarity. In normalized vectors (unit vectors), the dot product directly provides the cosine of the angle between the vectors, thereby simplifying the calculation of cosine similarity.

The concept of the dot product was introduced in the 19th century, with foundational work by Josiah Willard Gibbs and Oliver Heaviside in vector calculus. The term "dot product similarity" gained traction in the mid to late 20th century as computer science and AI fields started leveraging vector mathematics for various applications, particularly in the 1960s and 1970s with the advent of information retrieval systems.

Significant contributors to the development and application of dot product similarity include Josiah Willard Gibbs and Oliver Heaviside for their work in vector calculus. In the realm of computer science and AI, researchers such as Gerard Salton, who developed the vector space model for information retrieval in the 1970s, played a crucial role in popularizing the use of vector-based similarity measures.