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Cosine Similarity
conceptdistance metric
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Overview
Use casemeasuring similarity between vectors by computing the cosine of the angle between them
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Last updatedUpdated 19 days ago
WikidataQ2997395
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Cosine Similarity

concept

Measure of similarity between vectors based on cosine of angle between them

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based on

ValueTrustConfidenceFreshnessSources
dot product of two vectors divided by product of their magnitudes○UnverifiedHighFresh1
dot product of vectors divided by product of their magnitudes○UnverifiedHighFresh1
dot product and Euclidean norm calculations○UnverifiedHighFresh1
dot product and vector magnitudes○UnverifiedHighFresh1
geometric interpretation of angle between vectors○UnverifiedHighFresh1
Dot product of vectors normalized by their magnitudes○UnverifiedHighFresh1
dot product and vector norms○UnverifiedHighFresh1
dot product and Euclidean norms of vectors○UnverifiedHighFresh1
dot product and vector magnitude calculations○UnverifiedHighFresh1

output range

ValueTrustConfidenceFreshnessSources
values between -1 and 1○UnverifiedHighFresh1

primary use case

ValueTrustConfidenceFreshnessSources
measuring similarity between vectors by computing the cosine of the angle between them○UnverifiedHighFresh1
natural language processing text similarity○UnverifiedHighFresh1
measuring similarity between vectors in high-dimensional spaces○UnverifiedHighFresh1
document similarity in information retrieval○UnverifiedHighFresh1
measuring similarity between vectors in multidimensional space○UnverifiedHighFresh1
measuring similarity between vectors in machine learning and information retrieval○UnverifiedHighFresh1
measuring similarity between vectors by calculating cosine of angle between them○UnverifiedHighFresh1
measuring similarity between vectors in high-dimensional space○UnverifiedHighFresh1
measuring similarity between vectors by calculating the cosine of the angle between them○UnverifiedHighFresh1
recommendation systems○UnverifiedHighFresh1
clustering algorithms○UnverifiedHighFresh1
information retrieval and document clustering○UnverifiedHighFresh1
recommendation systems for collaborative filtering○UnverifiedHighFresh1
text similarity measurement in natural language processing○UnverifiedHighFresh1
image similarity measurement in computer vision○UnverifiedModerateFresh1
recommendation systems for finding similar items○UnverifiedModerateFresh1

range of values

ValueTrustConfidenceFreshnessSources
-1 to 1○UnverifiedHighFresh1
-1 to 1 for general vectors, 0 to 1 for non-negative vectors○UnverifiedHighFresh1
-1 to 1 for normalized vectors○UnverifiedHighFresh1

mathematical property

ValueTrustConfidenceFreshnessSources
measures angle between vectors○UnverifiedHighFresh1
produces values between -1 and 1○UnverifiedHighFresh1
invariant to scaling of input vectors○UnverifiedHighFresh1
ranges from -1 to 1○UnverifiedHighFresh1
invariant to vector magnitude scaling○UnverifiedHighFresh1
invariant to vector magnitude○UnverifiedHighFresh1

mathematical domain

ValueTrustConfidenceFreshnessSources
linear algebra○UnverifiedHighFresh1
linear algebra and vector mathematics○UnverifiedHighFresh1
Linear algebra and vector analysis○UnverifiedHighFresh1

implemented in

ValueTrustConfidenceFreshnessSources
scikit-learn library○UnverifiedHighFresh1
NumPy library○UnverifiedHighFresh1
PyTorch○UnverifiedHighFresh1
scikit-learn Python library○UnverifiedHighFresh1
scikit-learn○UnverifiedHighFresh1
NumPy Python library○UnverifiedHighFresh1
TensorFlow library○UnverifiedHighFresh1
TensorFlow framework○UnverifiedHighFresh1
TensorFlow machine learning framework○UnverifiedHighFresh1
NumPy○UnverifiedHighFresh1
TensorFlow○UnverifiedModerateFresh1
SciPy○UnverifiedModerateFresh1

mathematical range

ValueTrustConfidenceFreshnessSources
values between -1 and 1○UnverifiedHighFresh1
-1 to 1 for similarity scores○UnverifiedHighFresh1
-1 to 1 for any dimensional vectors○UnverifiedHighFresh1

computational property

ValueTrustConfidenceFreshnessSources
invariant to vector magnitude○UnverifiedHighFresh1

requires

ValueTrustConfidenceFreshnessSources
vector representation of data○UnverifiedHighFresh1
vector representation of data objects○UnverifiedHighFresh1
normalized vectors for optimal performance○UnverifiedModerateFresh1

value range

ValueTrustConfidenceFreshnessSources
negative one to positive one○UnverifiedHighFresh1

advantage over alternatives

ValueTrustConfidenceFreshnessSources
invariant to vector magnitude○UnverifiedHighFresh1

commonly used with

ValueTrustConfidenceFreshnessSources
word embeddings○UnverifiedHighFresh1
TF-IDF vectors○UnverifiedHighFresh1

commonly used for

ValueTrustConfidenceFreshnessSources
document similarity comparison○UnverifiedHighFresh1
document similarity in text analysis○UnverifiedHighFresh1
document similarity in search engines○UnverifiedHighFresh1
recommendation systems○UnverifiedHighFresh1

commonly used in

ValueTrustConfidenceFreshnessSources
machine learning applications○UnverifiedHighFresh1
text mining applications○UnverifiedHighFresh1
text mining and document similarity○UnverifiedHighFresh1
machine learning and natural language processing○UnverifiedHighFresh1
natural language processing for document similarity○UnverifiedHighFresh1
natural language processing and text mining○UnverifiedHighFresh1
information retrieval systems○UnverifiedHighFresh1
information retrieval○UnverifiedHighFresh1
machine learning○UnverifiedHighFresh1
information retrieval and text mining○UnverifiedHighFresh1
text mining and information retrieval○UnverifiedHighFresh1
machine learning feature comparison○UnverifiedHighFresh1
natural language processing○UnverifiedModerateFresh1
recommendation systems○UnverifiedModerateFresh1

integrates with

ValueTrustConfidenceFreshnessSources
scikit-learn○UnverifiedHighFresh1
scikit-learn machine learning library○UnverifiedHighFresh1
NumPy scientific computing library○UnverifiedHighFresh1
TensorFlow machine learning framework○UnverifiedHighFresh1
NumPy○UnverifiedHighFresh1
TensorFlow○UnverifiedHighFresh1
PyTorch○UnverifiedModerateFresh1
Apache Spark MLlib machine learning library○UnverifiedModerateFresh1

supported by

ValueTrustConfidenceFreshnessSources
scikit-learn Python library○UnverifiedHighFresh1
scikit-learn○UnverifiedHighFresh1
NumPy○UnverifiedHighFresh1
NumPy Python library○UnverifiedHighFresh1
TensorFlow○UnverifiedHighFresh1
TensorFlow machine learning framework○UnverifiedModerateFresh1

mathematical basis

ValueTrustConfidenceFreshnessSources
dot product of vectors divided by product of their magnitudes○UnverifiedHighFresh1

advantage

ValueTrustConfidenceFreshnessSources
invariant to vector magnitude○UnverifiedHighFresh1
normalized similarity measure independent of vector magnitude○UnverifiedModerateFresh1

application area

ValueTrustConfidenceFreshnessSources
Document similarity in information retrieval○UnverifiedHighFresh1

invariant to

ValueTrustConfidenceFreshnessSources
vector magnitude○UnverifiedHighFresh1
vector magnitude scaling○UnverifiedHighFresh1

property

ValueTrustConfidenceFreshnessSources
invariant to vector magnitude○UnverifiedHighFresh1

measures

ValueTrustConfidenceFreshnessSources
angular similarity between vectors○UnverifiedHighFresh1

commonly implemented in

ValueTrustConfidenceFreshnessSources
scikit-learn library○UnverifiedHighFresh1
NumPy library○UnverifiedHighFresh1

property type

ValueTrustConfidenceFreshnessSources
invariant to vector magnitude scaling○UnverifiedHighFresh1

alternative to

ValueTrustConfidenceFreshnessSources
Euclidean distance for vector similarity○UnverifiedHighFresh1
Euclidean distance for high-dimensional data○UnverifiedModerateFresh1
Euclidean distance for vector similarity measurement○UnverifiedModerateFresh1
Euclidean distance for high-dimensional spaces○UnverifiedModerateFresh1
Pearson correlation coefficient for similarity measurement○UnverifiedModerateFresh1
Euclidean distance for similarity measurement○UnverifiedModerateFresh1
Manhattan distance for similarity measurement○UnverifiedModerateFresh1
Jaccard similarity coefficient○UnverifiedModerateFresh1
Euclidean distance○UnverifiedModerateFresh1
Manhattan distance○UnverifiedModerateFresh1
Jaccard similarity○UnverifiedModerateFresh1
Pearson correlation coefficient○UnverifiedModerateFresh1

computational complexity

ValueTrustConfidenceFreshnessSources
O(n) time complexity for n-dimensional vectors○UnverifiedHighFresh1
O(n) where n is vector dimensionality○UnverifiedHighFresh1
O(n) where n is vector dimension○UnverifiedHighFresh1
O(n) for n-dimensional vectors○UnverifiedModerateFresh1

key property

ValueTrustConfidenceFreshnessSources
magnitude invariant○UnverifiedHighFresh1

related concept

ValueTrustConfidenceFreshnessSources
dot product○UnverifiedHighFresh1
Pearson correlation coefficient○UnverifiedModerateFresh1

originated from

ValueTrustConfidenceFreshnessSources
vector space model in information retrieval○UnverifiedModerateFresh1

supports model

ValueTrustConfidenceFreshnessSources
TF-IDF vectors○UnverifiedModerateFresh1
word embeddings○UnverifiedModerateFresh1

suitable for

ValueTrustConfidenceFreshnessSources
high-dimensional sparse data○UnverifiedModerateFresh1

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Pearson correlation coefficient for similarity measurement
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Euclidean distance for similarity measurement
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Manhattan distance for similarity measurement
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Jaccard similarity coefficient
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Euclidean distance
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Jaccard similarity
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Commonly Used With

scikit-learnscikit-learn machine learning libraryNumPy scientific computing libraryTensorFlow machine learning frameworkNumPyTensorFlowPyTorchApache Spark MLlib machine learning library

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Claim count: 129Last updated: 4/23/2026Edit history