turicreate.toolkits.distances.squared_euclidean

turicreate.toolkits.distances.squared_euclidean(x, y)

Compute the squared Euclidean distance between two dictionaries or two lists of equal length. Suppose x and y each contain \(d\) variables:

\[D(x, y) = \sum_i^d (x_i - y_i)^2\]

Parameters:

x : dict or list

First input vector.

y : dict or list

Second input vector.

Returns:

out : float

Squared Euclidean distance between x and y.

Notes

• If the input vectors are in dictionary form, keys missing in one of the two dictionaries are assumed to have value 0.
• Squared Euclidean distance does not satisfy the triangle inequality, so it is not a metric. This means the ball tree cannot be used to compute nearest neighbors based on this distance.

References

• Wikipedia - Euclidean distance

Examples

>>> tc.distances.squared_euclidean([1, 2, 3], [4, 5, 6])
27.0
...
>>> tc.distances.squared_euclidean({'a': 2, 'c': 4},
...                                {'b': 3, 'c': 12})
77.0