Add Jaccard Distance

docs/source/api/index.rst

@@ -49,6 +49,7 @@ DISTANCES
     ~dot_product.DotProduct
     ~euclidean.Euclidean
     ~manhattan.Manhattan
+    ~jaccard.Jaccard
 
 EVAL
 ----

quaterion/distances/__init__.py

@@ -4,6 +4,7 @@
 from quaterion.distances.cosine import Cosine
 from quaterion.distances.dot_product import DotProduct
 from quaterion.distances.euclidean import Euclidean
+from quaterion.distances.jaccard import Jaccard
 from quaterion.distances.manhattan import Manhattan
 
 
@@ -14,6 +15,7 @@ class Distance(str, Enum):
     COSINE = "cosine"
     DOT_PRODUCT = "dot_product"
     MANHATTAN = "manhattan"
+    JACCARD = "jaccard"
 
     @staticmethod
     def get_by_name(name: str) -> BaseDistance:
@@ -26,6 +28,7 @@ def get_by_name(name: str) -> BaseDistance:
             "euclidean": Euclidean,
             "manhattan": Manhattan,
             "dot_product": DotProduct,
+            "jaccard": Jaccard,
         }
 
         try:

quaterion/distances/jaccard.py

@@ -0,0 +1,37 @@
+from typing import Optional
+
+import torch
+import torch.nn.functional as F
+from torch import Tensor
+
+from quaterion.distances.base_distance import BaseDistance
+
+
+class Jaccard(BaseDistance):
+    """Compute Weighted Jaccard distances (and its interpretation as similarities).
+
+    Note:
+        The implementation of Weighted Jaccard
+        (https://en.wikipedia.org/wiki/Jaccard_index#Weighted_Jaccard_similarity_and_distance)
+        supports Tensors with positive float values.
+    """
+
+    @staticmethod
+    def distance(x: Tensor, y: Tensor) -> Tensor:
+        return 1 - Jaccard.similarity(x, y)
+
+    @staticmethod
+    def similarity(x: Tensor, y: Tensor) -> Tensor:
+        min_sum = torch.minimum(x, y).sum(dim=-1)
+        max_sum = torch.maximum(x, y).sum(dim=-1)
+        return min_sum / max_sum
+
+    @staticmethod
+    def distance_matrix(x: Tensor, y: Optional[Tensor] = None) -> Tensor:
+        return 1 - Jaccard.similarity_matrix(x.unsqueeze(1), y.unsqueeze(0))
+
+    @staticmethod
+    def similarity_matrix(x: Tensor, y: Optional[Tensor] = None) -> Tensor:
+        if y is None:
+            y = x
+        return Jaccard.similarity(x.unsqueeze(1), y.unsqueeze(0))

tests/test_distances.py

@@ -12,6 +12,13 @@ class TestDistances:
         ]
     )
 
+    x_2 = torch.tensor(
+        [
+            [1.0, 1.5, 2.0, 3.0],
+            [0.5, 2.5, 2.5, 1.0],
+        ]
+    )
+
     x_dim = x.size()[0]
     expected = {
         "cosine": {
@@ -30,6 +37,10 @@ class TestDistances:
             "similarity_matrix": torch.tensor([[16.25, -16.25], [-16.25, 16.25]]),
             "distance_matrix": torch.tensor([[-16.25, 16.25], [16.25, -16.25]]),
         },
+        "jaccard": {
+            "similarity_matrix": torch.tensor([[1.0000, 0.5556], [0.5556, 1.0000]]),
+            "distance_matrix": torch.tensor([[0.0000, 0.4444], [0.4444, 0.0000]]),
+        },
     }
 
     @pytest.mark.parametrize(