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2024年4月16日发(作者：遍历二叉树算法)
两个样本之间的余弦相似度
English Answer:
Cosine Similarity between Two Samples.
Cosine similarity is a measure of similarity between
two vectors. It is calculated by dividing the dot product
of the two vectors by the product of their magnitudes. The
cosine similarity ranges from -1 to 1. A cosine similarity
of 1 indicates that the two vectors are identical, a cosine
similarity of 0 indicates that the two vectors are
orthogonal, and a cosine similarity of -1 indicates that
the two vectors are pointing in opposite directions.
Cosine similarity can be used to measure the similarity
between two documents, images, or other types of data. It
is a popular metric for text analysis, where it is used to
measure the similarity between two documents based on their
word frequencies. Cosine similarity can also be used to
measure the similarity between two images based on their
pixel values.
Here is an example of how to calculate the cosine
similarity between two vectors:
vector1 = [1, 2, 3]
vector2 = [4, 5, 6]
dot_product = vector1[0] vector2[0] + vector1[1]
vector2[1] + vector1[2] vector2[2]
magnitude1 = (vector1[0]2 + vector1[1]2 +
vector1[2]2)。
magnitude2 = (vector2[0]2 + vector2[1]2 +
vector2[2]2)。
cosine_similarity = dot_product / (magnitude1
magnitude2)。
The cosine similarity between vector1 and vector2 is
0.985. This indicates that the two vectors are very similar.
Chinese Answer:
两个样本之间的余弦相似度。
余弦相似度是衡量两个向量之间相似性的指标。它是通过将两
个向量的点积除以它们的幅值的乘积来计算的。余弦相似度范围从
-1 到 1。1 的余弦相似度表示两个向量相同，0 的余弦相似度表示
两个向量正交，-1 的余弦相似度表示两个向量指向相反的方向。
余弦相似度可用于衡量两个文档、图像或其他类型数据之间的
相似性。它是文本分析的流行指标，用于根据单词频率衡量两个文
档之间的相似性。余弦相似度还可以根据像素值衡量两个图像之间
的相似性。
以下是如何计算两个向量之间的余弦相似度的示例：
vector1 = [1, 2, 3]
vector2 = [4, 5, 6]
dot_product = vector1[0] vector2[0] + vector1[1]
vector2[1] + vector1[2] vector2[2]
magnitude1 = (vector1[0]2 + vector1[1]2 +
vector1[2]2)。
magnitude2 = (vector2[0]2 + vector2[1]2 +
vector2[2]2)。
cosine_similarity = dot_product / (magnitude1
magnitude2)。
vector1 和 vector2 之间的余弦相似度为 0.985。这表明两个
向量非常相似。
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