Calculates Jaccard similarity based on binary attributes. It assumes that inputs have the same shape.

$$ J(X, Y) = \frac{M\_{11}}{M\_{01} + M\_{10} + M\_{11}} $$

Where:

• $M_{11}$ is the total number of attributes, for which both $X$ and $Y$ have 1.
• $M_{10}$ is the total number of attributes, for which $X$ has 1 and $Y$ has 0.
• $M_{01}$ is the total number of attributes, for which $X$ has 0 and $Y$ has 1.

Options

• :axis - Axis over which the distance will be calculated. By default the distance is calculated between the whole tensors.

Examples

iex> x = Nx.tensor([1,0,0,1,1,1])
iex> y = Nx.tensor([0,0,1,1,1,0])
iex> Scholar.Metrics.Similarity.binary_jaccard(x, y)
#Nx.Tensor<
  f32
  0.4000000059604645
>

iex> x = Nx.tensor([[1,1,0,1], [1,1,0,1]])
iex> y = Nx.tensor([[1,1,0,1], [1,0,0,1]])
iex> Scholar.Metrics.Similarity.binary_jaccard(x, y)
#Nx.Tensor<
  f32
  0.8333333134651184
>

iex> x = Nx.tensor([[1,1,0,1], [1,1,0,1]])
iex> y = Nx.tensor([[1,1,0,1], [1,0,0,1]])
iex> Scholar.Metrics.Similarity.binary_jaccard(x, y, axis: 1)
#Nx.Tensor<
  f32[2]
  [1.0, 0.6666666865348816]
>

iex> x = Nx.tensor([1, 1])
iex> y = Nx.tensor([1, 0, 0])
iex> Scholar.Metrics.Similarity.binary_jaccard(x, y)
** (ArgumentError) expected tensor to have shape {2}, got tensor with shape {3}

Calculates Dice coefficient.

It is a statistic used to gauge the similarity of two samples. Mathematically, it is defined as:

$$ Dice(A, B) = \frac{2 \mid A \cap B \mid}{\mid A \mid + \mid B \mid} $$

where A and B are sets.

Options

• :axis - Axis over which the distance will be calculated. By default the distance is calculated between the whole tensors.

Examples

iex> x = Nx.tensor([1.0, 5.0, 3.0, 6.7])
iex> y = Nx.tensor([5.0, 2.5, 3.1, 9.0])
iex> Scholar.Metrics.Similarity.dice_coefficient(x, y)
#Nx.Tensor<
  f32
  0.25
>

iex> x = Nx.tensor([1, 2, 3, 5, 7])
iex> y = Nx.tensor([1, 2, 4, 8, 9])
iex> Scholar.Metrics.Similarity.dice_coefficient(x, y)
#Nx.Tensor<
  f32
  0.4000000059604645
>

iex> x = Nx.iota({2,3})
iex> y = Nx.tensor([[0, 3, 4], [3, 4, 8]])
iex> Scholar.Metrics.Similarity.dice_coefficient(x, y, axis: 1)
#Nx.Tensor<
  f32[2]
  [0.3333333134651184, 0.6666666865348816]
>

iex> x = Nx.tensor([1, 2])
iex> y = Nx.tensor([1, 2, 3])
iex> Scholar.Metrics.Similarity.dice_coefficient(x, y)
#Nx.Tensor<
  f32
  0.800000011920929
>

Calculates Dice coefficient based on binary attributes. It assumes that inputs have the same shape.

Options

• :axis - Axis over which the distance will be calculated. By default the distance is calculated between the whole tensors.

Examples

iex> x = Nx.tensor([1,0,0,1,1,1])
iex> y = Nx.tensor([0,0,1,1,1,0])
iex> Scholar.Metrics.Similarity.dice_coefficient_binary(x, y)
#Nx.Tensor<
  f32
  0.5714285969734192
>

iex> x = Nx.tensor([[1,1,0,1], [1,1,0,1]])
iex> y = Nx.tensor([[1,1,0,1], [1,0,0,1]])
iex> Scholar.Metrics.Similarity.dice_coefficient_binary(x, y)
#Nx.Tensor<
  f32
  0.9090909361839294
>

iex> x = Nx.tensor([[1,1,0,1], [1,1,0,1]])
iex> y = Nx.tensor([[1,1,0,1], [1,0,0,1]])
iex> Scholar.Metrics.Similarity.dice_coefficient_binary(x, y, axis: 1)
#Nx.Tensor<
  f32[2]
  [1.0, 0.800000011920929]
>

iex> x = Nx.tensor([1, 1])
iex> y = Nx.tensor([1, 0, 0])
iex> Scholar.Metrics.Similarity.dice_coefficient_binary(x, y)
** (ArgumentError) expected tensor to have shape {2}, got tensor with shape {3}

Calculates Jaccard similarity (also known as Jaccard similarity coefficient, or Jaccard index).

Jaccard similarity is a statistic used to measure similarities between two sets. Mathematically, the calculation of Jaccard similarity is the ratio of set intersection over set union.

$$ J(A, B) = \frac{\mid A \cap B \mid}{\mid A \cup B \mid} $$

where A and B are sets.

Options

• :axis - Axis over which the distance will be calculated. By default the distance is calculated between the whole tensors.

Examples

iex> x = Nx.tensor([1.0, 5.0, 3.0, 6.7])
iex> y = Nx.tensor([5.0, 2.5, 3.1, 9.0])
iex> Scholar.Metrics.Similarity.jaccard(x, y)
#Nx.Tensor<
  f32
  0.1428571492433548
>

iex> x = Nx.tensor([1, 2, 3, 5, 7])
iex> y = Nx.tensor([1, 2, 4, 8, 9])
iex> Scholar.Metrics.Similarity.jaccard(x, y)
#Nx.Tensor<
  f32
  0.25
>

iex> x = Nx.tensor([[0, 1, 2], [3, 4, 5]])
iex> y = Nx.tensor([[0, 3, 4], [3, 4, 8]])
iex> Scholar.Metrics.Similarity.jaccard(x, y, axis: 1)
#Nx.Tensor<
  f32[2]
  [0.20000000298023224, 0.5]
>

iex> x = Nx.tensor([1, 2])
iex> y = Nx.tensor([1, 2, 3])
iex> Scholar.Metrics.Similarity.jaccard(x, y)
#Nx.Tensor<
  f32
  0.6666666865348816
>