randindex(): fix int overflow

for very large clusterings the agreement/disagreement counts are
very large, so we have to switch to float when multiplying them

fixes #225
enhances #227

Author: alyst

src/randindex.jl

@@ -30,9 +30,10 @@ function randindex(a, b)
     D = c12 + c21
 
     # expected index
-    ERI = (c11+c12)*(c11+c21)+(c21+c22)*(c12+c22)
+    T = typeof(one(A)/one(t))
+    ERI = convert(T, c11+c12)*(c11+c21)+convert(T, c21+c22)*(c12+c22)
     # adjusted Rand - Hubert & Arabie 1985
-    ARI = D == 0 ? 1.0 : (t*A-ERI)/(t*t-ERI) # (9) from Steinley 2004
+    ARI = D == 0 ? 1.0 : (convert(T, t)*A - ERI)/(abs2(convert(T, t)) - ERI) # (9) from Steinley 2004
 
     RI = A/t            # Rand 1971      # Probability of agreement
     MI = D/t            # Mirkin 1970    # p(disagreement)

test/randindex.jl

@@ -36,7 +36,15 @@ a3 = [3, 3, 3, 2, 2, 2, 1, 1, 1, 1]
 
 @test randindex(ones(Int, 3), ones(Int, 3)) == (1, 1, 0, 1)
 
-a, b = rand(1:5, 10_000), rand(1:5, 10_000)
-@test randindex(a, b)[1] < 1.0e-2
+@testset "large independent clusterings (#225)" begin
+    rng = MersenneTwister(123)
+
+    n = 10_000_000
+    k = 5 # number of clusters
+    a = rand(rng, 1:k, n)
+    b = rand(rng, 1:k, n)
+
+    @test collect(randindex(a, b)) ≈ [0.0, ((k-1)^2 + 1)/k^2, 2*(k-1)/k^2, ((k-2)/k)^2] atol=1e-5
+end
 
 end