Cosine Similarity Calculator
Cosine Similarity Calculator: Cosine similarity measures the cosine of the angle between two non-zero vectors in a multi-dimensional space. It is used to assess how similar the vectors are, regardless of their magnitude. This is particularly useful in various fields such as text analysis, data science, and machine learning. The value of cosine similarity ranges from -1 (completely dissimilar) to 1 (completely similar), with 0 indicating no similarity.
How to Use the Cosine Similarity Calculator
To use the Cosine Similarity Calculator, input the components of two vectors (Vector a and Vector b). Fill in the values for a₁, a₂, b₁, and b₂. Click the "Calculate" button to compute the cosine similarity, the angle between the vectors, and the cosine distance. The results will be displayed in a table format, and a distribution chart will visualize the results. Click "Clear" to reset the fields and start a new calculation.
Vector A
| a₁ | a₂ |
|---|---|
Vector B
| b₁ | b₂ |
|---|---|
Frequently Asked Questions (FAQ)
1. What is cosine similarity?
Cosine similarity is a metric used to measure how similar two vectors are by calculating the cosine of the angle between them. It ranges from -1 to 1, where 1 means the vectors are identical, -1 means they are diametrically opposed, and 0 means they are orthogonal or unrelated.
2. How is cosine similarity calculated?
Cosine similarity is calculated using the formula: SC(a, b) = (a·b) / (‖a‖ × ‖b‖). This involves computing the dot product of the vectors and dividing it by the product of their magnitudes.
3. What is the cosine distance?
Cosine distance is a measure derived from cosine similarity. It is calculated as 1 minus the cosine similarity value. It helps quantify how dissimilar two vectors are.
4. Why use cosine similarity?
Cosine similarity is often used in text analysis and machine learning to determine the similarity between documents or features, regardless of their size. It is useful when comparing vectors of different magnitudes.
5. Can cosine similarity handle vectors of different dimensions?
No, cosine similarity requires vectors to be of the same dimension. If vectors are of different dimensions, they need to be adjusted or padded to match before calculating similarity.
6. What if the vectors are zero vectors?
Cosine similarity is undefined for zero vectors, as they do not have a direction or magnitude. Ensure that both vectors have non-zero values to obtain valid results.
7. How accurate is this calculator?
The calculator provides accurate results based on the input values. Ensure that all vector components are entered correctly to get precise cosine similarity, angle, and distance.
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