quaterion.distances.euclidean module

class Euclidean

Bases: BaseDistance

Compute Euclidean distances (and its interpretation as similarities).

Note

Interpretation of Euclidean distances as similarities is based on the trick in the book “Collective Intelligence” by Toby Segaran, and it’s in the range of 0 -> 1.

Note

The distance matrix computation is based on a trick explained by Samuel Albanie.

static distance(x: Tensor, y: Tensor) → Tensor

Calculate distances, i.e., the lower the value, the more similar the samples.

Parameters:

• x – shape: (batch_size, embedding_dim)

• y – shape: (batch_size, embedding_dim)

Returns:

Distances - shape – (batch_size,)

static distance_matrix(x: Tensor, y: Tensor | None = None) → Tensor

Calculate a distance matrix, i.e., distances between all possible pairs in x and y.

Parameters:

• x – shape: (batch_size, embedding_dim)

• y – shape: (batch_size, embedding_dim). If y is None, it assigns x to y.

Returns:

Distance matrix - shape – (batch_size, batch_size)

static similarity(x: Tensor, y: Tensor) → Tensor

Calculate similarities, i.e., the higher the value, the more similar the samples.

Parameters:

• x – shape: (batch_size, embedding_dim)

• y – shape: (batch_size, embedding_dim)

Returns:

Similarities - shape – (batch_size,)

static similarity_matrix(x: Tensor, y: Tensor | None = None) → Tensor

Calculate a similarity matrix, i.e., similarities between all possible pairs in x and y.

Parameters:

• x – shape: (batch_size, embedding_dim)

• y – shape: (batch_size, embedding_dim). If y is None, it assigns x to y.

Returns:

Similarity matrix - shape – (batch_size, batch_size)