Total variation distance (#118)

* Add total variation distance

* Add TotalVariation to README and benchmarks

Author: devmotion

README.md

@@ -15,6 +15,7 @@ This package also provides optimized functions to compute column-wise and pairwi
 * Euclidean distance
 * Squared Euclidean distance
 * Cityblock distance
+* Total variation distance
 * Jaccard distance
 * Rogers-Tanimoto distance
 * Chebyshev distance
@@ -136,6 +137,7 @@ Each distance corresponds to a distance type. The type name and the correspondin
 |  Euclidean           |  `euclidean(x, y)`         | `sqrt(sum((x - y) .^ 2))` |
 |  SqEuclidean         |  `sqeuclidean(x, y)`       | `sum((x - y).^2)` |
 |  Cityblock           |  `cityblock(x, y)`         | `sum(abs(x - y))` |
+|  TotalVariation      |  `totalvariation(x, y)`    | `sum(abs(x - y)) / 2` |
 |  Chebyshev           |  `chebyshev(x, y)`         | `max(abs(x - y))` |
 |  Minkowski           |  `minkowski(x, y, p)`      | `sum(abs(x - y).^p) ^ (1/p)` |
 |  Hamming             |  `hamming(k, l)`           | `sum(k .!= l)` |

benchmark/benchmarks.jl

@@ -8,6 +8,7 @@ function create_distances(w, Q)
         SqEuclidean(),
         Euclidean(),
         Cityblock(),
+        TotalVariation(),
         Chebyshev(),
         Minkowski(3.0),
         Hamming(),

benchmark/print_table.jl

@@ -11,6 +11,7 @@ order = [
     :SqEuclidean,
     :Euclidean,
     :Cityblock,
+    :TotalVariation,
     :Chebyshev,
     :Minkowski,
     :Hamming,

src/Distances.jl

@@ -23,6 +23,7 @@ export
     Euclidean,
     SqEuclidean,
     Cityblock,
+    TotalVariation,
     Chebyshev,
     Minkowski,
     Jaccard,
@@ -61,6 +62,7 @@ export
     euclidean,
     sqeuclidean,
     cityblock,
+    totalvariation,
     jaccard,
     braycurtis,
     rogerstanimoto,

src/metrics.jl

@@ -14,6 +14,7 @@ struct SqEuclidean <: SemiMetric
 end
 struct Chebyshev <: Metric end
 struct Cityblock <: Metric end
+struct TotalVariation <: Metric end
 struct Jaccard <: Metric end
 struct RogersTanimoto <: Metric end
 
@@ -99,7 +100,7 @@ struct RMSDeviation <: Metric end
 struct NormRMSDeviation <: Metric end
 
 
-const UnionMetrics = Union{Euclidean,SqEuclidean,Chebyshev,Cityblock,Minkowski,Hamming,Jaccard,RogersTanimoto,CosineDist,CorrDist,ChiSqDist,KLDivergence,RenyiDivergence,BrayCurtis,JSDivergence,SpanNormDist,GenKLDivergence}
+const UnionMetrics = Union{Euclidean,SqEuclidean,Chebyshev,Cityblock,TotalVariation,Minkowski,Hamming,Jaccard,RogersTanimoto,CosineDist,CorrDist,ChiSqDist,KLDivergence,RenyiDivergence,BrayCurtis,JSDivergence,SpanNormDist,GenKLDivergence}
 
 """
     Euclidean([thresh])
@@ -219,6 +220,13 @@ euclidean(a::Number, b::Number) = evaluate(Euclidean(), a, b)
 cityblock(a::AbstractArray, b::AbstractArray) = evaluate(Cityblock(), a, b)
 cityblock(a::T, b::T) where {T <: Number} = evaluate(Cityblock(), a, b)
 
+# Total variation
+@inline eval_op(::TotalVariation, ai, bi) = abs(ai - bi)
+@inline eval_reduce(::TotalVariation, s1, s2) = s1 + s2
+eval_end(::TotalVariation, s) = s / 2
+totalvariation(a::AbstractArray, b::AbstractArray) = evaluate(TotalVariation(), a, b)
+totalvariation(a::T, b::T) where {T <: Number} = evaluate(TotalVariation(), a, b)
+
 # Chebyshev
 @inline eval_op(::Chebyshev, ai, bi) = abs(ai - bi)
 @inline eval_reduce(::Chebyshev, s1, s2) = max(s1, s2)

test/test_dists.jl

@@ -47,6 +47,7 @@ end
     test_metricity(SqEuclidean(), x, y, z)
     test_metricity(Euclidean(), x, y, z)
     test_metricity(Cityblock(), x, y, z)
+    test_metricity(TotalVariation(), x, y, z)
     test_metricity(Chebyshev(), x, y, z)
     test_metricity(Minkowski(2.5), x, y, z)
 
@@ -122,6 +123,7 @@ end
 
     @test euclidean(a, b) == 1.0
     @test cityblock(a, b) == 1.0
+    @test totalvariation(a, b) == 0.5
     @test chebyshev(a, b) == 1.0
     @test minkowski(a, b, 2) == 1.0
     @test hamming(a, b) == 1
@@ -140,6 +142,7 @@ end
             @test euclidean(x, y) == sqrt(57.0)
             @test jaccard(x, y) == 13.0 / 28
             @test cityblock(x, y) == 13.0
+            @test totalvariation(x, y) == 6.5
             @test chebyshev(x, y) == 6.0
             @test braycurtis(x, y) == 1.0 - (30.0 / 43.0)
             @test minkowski(x, y, 2) == sqrt(57.0)
@@ -242,6 +245,8 @@ end #testset
         @test isa(euclidean(a, b), T)
         @test cityblock(a, b) == 0.0
         @test isa(cityblock(a, b), T)
+        @test totalvariation(a, b) == 0.0
+        @test isa(totalvariation(a, b), T)
         @test chebyshev(a, b) == 0.0
         @test isa(chebyshev(a, b), T)
         @test braycurtis(a, b) == 0.0
@@ -385,6 +390,7 @@ end
     test_colwise(SqEuclidean(), X, Y, T)
     test_colwise(Euclidean(), X, Y, T)
     test_colwise(Cityblock(), X, Y, T)
+    test_colwise(TotalVariation(), X, Y, T)
     test_colwise(Chebyshev(), X, Y, T)
     test_colwise(Minkowski(2.5), X, Y, T)
     test_colwise(Hamming(), A, B, T)
@@ -459,6 +465,7 @@ end
     test_pairwise(SqEuclidean(), X, Y, T)
     test_pairwise(Euclidean(), X, Y, T)
     test_pairwise(Cityblock(), X, Y, T)
+    test_pairwise(TotalVariation(), X, Y, T)
     test_pairwise(Chebyshev(), X, Y, T)
     test_pairwise(Minkowski(2.5), X, Y, T)
     test_pairwise(Hamming(), A, B, T)