Add MinkowskiMetric abstract type

README.md

@@ -165,14 +165,20 @@ At the top of this hierarchy is an abstract class **PreMetric**, which is define
     d(x, x) == 0  for all x
     d(x, y) >= 0  for all x, y
 
-**SemiMetric** is a abstract type that refines **PreMetric**. Formally, a *semi-metric* is a *pre-metric* that is also symmetric, as
+**SemiMetric** is an abstract type that refines **PreMetric**. Formally, a *semi-metric* is a *pre-metric* that is also symmetric, as
 
     d(x, y) == d(y, x)  for all x, y
 
-**Metric** is a abstract type that further refines **SemiMetric**. Formally, a *metric* is a *semi-metric* that also satisfies triangle inequality, as
+**Metric** is an abstract type that further refines **SemiMetric**. Formally, a *metric* is a *semi-metric* that also satisfies triangle inequality, as
 
     d(x, z) <= d(x, y) + d(y, z)  for all x, y, z
 
+**MinkowskiMetric** is an abstract type that encompasses a family of metrics defined by the formula
+
+    d(x, y) = sum(w .* (x - y) .^ p) ^ (1 / p)
+
+where the `p` parameter defines the metric and `w` is a potential weight vector (all 1's by default).
+
 This type system has practical significance. For example, when computing pairwise distances
 between a set of vectors, you may only perform computation for half of the pairs, derive the
 values immediately for the remaining half by leveraging the symmetry of *semi-metrics*. Note

src/metrics.jl

@@ -12,13 +12,21 @@ abstract type UnionSemiMetric <: SemiMetric end
 
 abstract type UnionMetric <: Metric end
 
+# a minkowski metric is a metric that is defined by the formula:
+#
+#   d(x, y) = sum(w .* (x - y) .^ p) ^ (1 / p)
+#
+# where the `p` parameter defines the metric 
+# and `w` is a potential weight vector (all 1's by default).
+abstract type MinkowskiMetric <: UnionMetric end
+
 ###########################################################
 #
 #   Metric types
 #
 ###########################################################
 
-struct Euclidean <: UnionMetric
+struct Euclidean <: MinkowskiMetric
     thresh::Float64
 end
 
@@ -52,7 +60,7 @@ julia> pairwise(Euclidean(1e-12), x, x)
 """
 Euclidean() = Euclidean(0)
 
-struct WeightedEuclidean{W} <: UnionMetric
+struct WeightedEuclidean{W} <: MinkowskiMetric
     weights::W
 end
 
@@ -94,21 +102,21 @@ struct WeightedSqEuclidean{W} <: UnionSemiMetric
     weights::W
 end
 
-struct Chebyshev <: UnionMetric end
+struct Chebyshev <: MinkowskiMetric end
 
-struct Cityblock <: UnionMetric end
-struct WeightedCityblock{W} <: UnionMetric
+struct Cityblock <: MinkowskiMetric end
+struct WeightedCityblock{W} <: MinkowskiMetric
     weights::W
 end
 
 struct TotalVariation <: UnionMetric end
 struct Jaccard <: UnionMetric end
 struct RogersTanimoto <: UnionMetric end
 
-struct Minkowski{T <: Real} <: UnionMetric
+struct Minkowski{T <: Real} <: MinkowskiMetric
     p::T
 end
-struct WeightedMinkowski{W,T <: Real} <: UnionMetric
+struct WeightedMinkowski{W,T <: Real} <: MinkowskiMetric
     weights::W
     p::T
 end