Kernel Distances.

prototorch/functions/distances.py

@@ -261,5 +261,34 @@ def tangent_distance(signals, protos, subspaces, squared=False, epsilon=1e-10):
             return diss.permute([1, 0, 2]).squeeze(-1)
 
 
+class KernelDistance:
+    r"""Kernel Distance
+
+    Distance based on a kernel function.
+    """
+    def __init__(self, kernel_fn):
+        self.kernel_fn = kernel_fn
+
+    def __call__(self, x, y):
+        kappa_xx = self.kernel_fn(x, x)
+        kappa_xy = self.kernel_fn(x, y)
+        kappa_yy = self.kernel_fn(y, y)
+
+        return torch.sqrt(kappa_xx - 2 * kappa_xy + kappa_yy)
+
+
+class SquaredKernelDistance(KernelDistance):
+    r"""Squared Kernel Distance
+
+    Kernel distance without final squareroot.
+    """
+    def __call__(self, x, y):
+        kappa_xx = self.kernel_fn(x, x)
+        kappa_xy = self.kernel_fn(x, y)
+        kappa_yy = self.kernel_fn(y, y)
+
+        return kappa_xx - 2 * kappa_xy + kappa_yy
+
+
 # Aliases
 sed = squared_euclidean_distance

prototorch/functions/kernels.py

@@ -0,0 +1,21 @@
+"""
+Experimental Kernels
+"""
+
+import torch
+
+
+class ExplicitKernel:
+    def __init__(self, projection=torch.nn.Identity()):
+        self.projection = projection
+
+    def __call__(self, x, y):
+        return self.projection(x) @ self.projection(y)
+
+
+class RadialBasisFunctionKernel:
+    def __init__(self, sigma) -> None:
+        self.s2 = sigma * sigma
+
+    def __call__(self, x, y):
+        return torch.exp(-torch.sum((x - y)**2) / (2 * self.s2))