Cosine Similarity is a measure of the similarity between two vectors of an inner product space.
For two vectors, A and B, the Cosine Similarity is calculated as:
Cosine Similarity = ΣAiBi / (√ΣAi2√ΣBi2)
This tutorial explains how to calculate the Cosine Similarity between vectors in Excel.
Cosine Similarity Between Two Vectors in Excel
Suppose we have the following two vectors in Excel:
We can use the following formula to calculate the Cosine Similarity between the two vectors in Excel:
=SUMPRODUCT(A$2:A$9,B2:B9)/(SQRT(SUMSQ(B2:B9))*SQRT(SUMSQ($A$2:$A$9)))
The following screenshot shows how to use this formula:
The Cosine Similarity between the two vectors turns out to be 0.965195.
Note that we interpret the value for Cosine Similarity as follows:
- A value of -1 indicates maximum dissimilarity
- A value of 0 indicates that the two vectors are orthogonal
- A value of 1 indicates maximum similarity
A value of 0.965195 indicates a high level of similarity between the two vectors in our example.
Additional Resources
The following tutorials explain how to calculate Cosine Similarity in other statistical software:
For an in-depth explanation of Cosine Similarity, refer to the following Wikipedia article:
