Dot Product
The Dot Product shows how much one vector projects onto another. It gives us insight into their directional relationship:
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Negative: Opposite directions
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Zero: Perpendicular vectors
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Positive: Same direction
The bigger the dot product, the more similar the vectors.
Euclidean Distance
Imagine drawing a straight line between two points in space. That's basically what Euclidean Distance is – it measures how far apart two vectors are. The shorter the distance, the more similar they are. This is super useful in things like clustering, image processing, and more.
Vector distances
Vector similarity can be measured using:
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Euclidean Distance: calculates the straight-line distance between two vectors.
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Cosine Similarity: measures the cosine of the angle between two vectors, indicating directional similarity.
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Dot Product: calculates the sum of the products of corresponding elements, indicating both magnitude and directional similarity.
Cosine Similarity
Cosine Similarity checks if two vectors are heading in the same direction, regardless of their size.
The score ranges from -1 (opposite directions) to 1 (same direction). Here's how it breaks down:
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-1: Opposite directions
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0: Perpendicular vectors
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+1: Same direction