Calculate Cosine Similarity
An interactive tool to calculate the cosine similarity between two vectors, a key metric in data science and machine learning.
Interactive Calculator
Enter two vectors (comma-separated values) to calculate the cosine similarity:
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Cosine Similarity Formula
The Cosine Similarity Formula is:
Where:
- $A_i$ = elements of vector A
- $B_i$ = elements of vector B
Cosine Similarity Table Example
| Vector A | Vector B | Cosine Similarity |
|---|---|---|
| (1, 2, 3) | (1, 2, 3) | 1.0000 |
| (1, 0, 0) | (0, 1, 0) | 0.0000 |
| (2, 3, 4) | (4, 5, 6) | 0.9926 |
| (1, -1, 0) | (1, 1, 0) | 0.0000 |
Cosine Similarity Chart
How It Works
The Cosine Similarity Calculator works by:
- Taking two vectors from the user.
- Computing the dot product of both vectors.
- Finding the magnitude (length) of each vector.
- Dividing the dot product by the product of magnitudes.
- Returning a value between 0 and 1 (1 means identical, 0 means no similarity).
This method is widely used in Data Science, Machine Learning, Natural Language Processing (NLP), and Recommendation Systems.
User Guide
- Enter numeric values separated by commas (e.g., 1,2,3).
- The vectors must have the same length.
- Press Calculate to see the cosine similarity value.
- A result close to 1 means high similarity, while a result near 0 means very low similarity.
Frequently Asked Questions (FAQs)
Q1: What is Cosine Similarity in Data Science?
It is a metric used to measure how similar two vectors are, regardless of their magnitude.
Q2: How is Cosine Similarity used in Machine Learning?
It is used in clustering, classification, and recommendation systems to compare text, users, or product features.
Q3: What is the difference between Cosine Similarity and Cosine Distance?
Cosine Distance = $1 - \text{Cosine Similarity}$.
Q4: Can Cosine Similarity be negative?
Yes, in cases where vectors point in opposite directions.