Cosine Similarity Calculator
The Cosine Similarity Calculator helps measure the similarity between two vectors in multidimensional space. By calculating the cosine of the angle between the vectors, it provides insights into their orientation relative to each other. This is useful in various fields such as text analysis, clustering, and recommendation systems.
The formula for cosine similarity is:
SC(a, b) = (a · b) / (‖a‖ × ‖b‖),
where a · b is the dot product of vectors a and b, and ‖a‖ and ‖b‖ are the magnitudes (norms) of the vectors.
To use the Cosine Similarity Calculator, input the values for vectors a and b. Fill in the boxes with the components of each vector, then click "Calculate" to get the cosine similarity, the angle between vectors, and cosine distance. Use the "Clear" button to reset the fields.
Vector A
Vector B
| Metric | Value |
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| Step | Description |
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What is cosine similarity?
Cosine similarity measures the cosine of the angle between two vectors. It quantifies how similar two vectors are, regardless of their magnitude. Values range from -1 (opposite) to 1 (identical), with 0 indicating orthogonality.
How is cosine similarity useful?
It is widely used in text analysis to compare documents or terms, in recommendation systems to find similar items, and in clustering to group similar data points. It helps in determining the orientation similarity of data vectors.
What is the formula for cosine similarity?
The formula is SC(a, b) = (a · b) / (‖a‖ × ‖b‖). Here, a · b is the dot product of vectors, and ‖a‖ and ‖b‖ are their magnitudes.
How do I calculate cosine similarity?
Input the components of two vectors. Compute the dot product and magnitudes of each vector. Divide the dot product by the product of the magnitudes to get the cosine similarity value.
What is cosine distance?
Cosine distance is 1 minus cosine similarity. It measures dissimilarity between vectors, with values ranging from 0 (identical) to 2 (opposite).
How is the angle between vectors calculated?
The angle θ between vectors is calculated using θ = arccos(SC(a, b)). It shows how aligned or different the two vectors are.
Can this calculator handle higher-dimensional vectors?
This example handles 2D vectors. For higher-dimensional vectors, extend the inputs and calculations accordingly.
Why is cosine similarity important?
It helps in comparing documents or data points based on their orientation, making it crucial for similarity measures in various applications such as information retrieval and machine learning.
What units are used in cosine similarity calculations?
Cosine similarity is unitless. It measures the angle between vectors, so it’s independent of the magnitude or units of the vectors.
How do I interpret the result of cosine similarity?
A value close to 1 indicates high similarity, 0 indicates orthogonality (no similarity), and a value close to -1 indicates high dissimilarity. It reflects how aligned or opposite the vectors are.
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