Three ways to be near

Why

Three indexes, one rgb attribute, three distance functions. The vectors are identical in all three, so every difference in the results is the metric and nothing else.

Cosine measures the angle between two vectors and throws away their length. For colours that means hue without brightness. Euclidean measures the straight-line gap, so brightness is distance. Dot product combines direction and magnitude, which is why a pale mint green beats a crimson against a red query: it is simply a longer vector.

Read the scores carefully, because they do not all run the same way. Cosine and Euclidean are distances: lower is nearer, and a vector against itself scores about zero. Dot product is a similarity: higher is nearer, and it can go negative. Sorting a dot-product result the way you would sort a cosine result gives you a ranking that is exactly inverted, and it still returns TopK rows and still looks like it worked.

You choose the function when you create the index and you cannot change it afterwards; changing your mind means a new index. A table holds at most five vector indexes, and two indexes over the same attribute have to agree on dimensions. Which to pick depends on your model: most sentence embedding models are normalised to unit length, and once every vector is the same length cosine and dot product rank identically.

Cosine ignores magnitude, Euclidean does not, and dot product rewards it; the choice is fixed at index creation, and lower-is-nearer for two of them and higher-is-nearer for the third.