Create Silhouette coefficient for KMeans clustering.

src/Sil.jl

@@ -0,0 +1,152 @@
+using ClusterAnalysis, DataFrames, Statistics, Tables, BenchmarkTools
+
+## 1. Types declaration
+abstract type Silhouette end
+struct Common <: Silhouette end
+struct Simplified <: Silhouette end
+
+## 2. Functions
+"""
+
+    euclidean(a::AbstractVector, b::AbstractArray)
+
+Calculate the euclidean distance between a data point and bunch of data points.
+
+# Arguments (positional)
+- `a`: First vector.
+- `b`: Second vector.
+
+# Returns
+A Float64 value as the distance.
+
+"""
+function euclidean(a::AbstractVector, b::AbstractArray)
+    √(sum((a' .- b).^2))
+end
+
+"""
+
+    aᵢ(data::AbstractArray{T}, labels::AbstractVector{S}, i::Int64, method::Common) where {T<:Real, S<:Real}
+    aᵢ(data::AbstractArray{T}, labels::AbstractVector{S}, i::Int64, method::Simplified, centers) where {T<:Real, S<:Real}
+
+Calculate the euclidean distance between i'th sample and data points in the same
+cluster.
+
+# Arguments (positional)
+- `data`: data set.
+- `labels`: cluster identity of each sample
+- `i`: The index of the sample.
+
+# Returns
+A Float64 value that represents sum distance between sample i and data points
+in the same cluster.
+"""
+
+function aᵢ(data::AbstractArray{T}, labels::AbstractVector{S}, i::Int64, method::Common) where {T<:Real, S<:Real}
+    labelᵢ = labels[i]
+    same_cluster_members_idx = findall(isequal(labelᵢ), labels)
+    n = length(same_cluster_members_idx)
+
+    sum_dist = euclidean(data[i, :], data[same_cluster_members_idx, :])
+    return sum_dist/(n-1)
+end
+
+function aᵢ(data::AbstractArray{T}, labels::AbstractVector{S}, i::Int64, method::Simplified, centers) where {T<:Real, S<:Real}
+    labelᵢ = labels[i]
+    return euclidean(data[i, :], centers[labelᵢ]')
+end
+
+"""
+    bᵢ(data::AbstractArray{T}, labels::AbstractVector{S}, i::Int64, method::Common, centers) where {T<:Real, S<:Real}
+    bᵢ(data::AbstractArray{T}, labels::AbstractVector{S}, i::Int64, method::Simplified, centers) where {T<:Real, S<:Real}
+
+Calculate the euclidean distance between i'th sample and data points in other clusters.
+
+# Arguments (positional)
+- `data`: data set.
+- `labels`: cluster identity of each sample
+- `i`: The index of the sample.
+- `method`: Common or Simplified version of silhouette.
+- `centers`: Cluster centers.
+
+# Returns
+A Float64 value that represents sum distance between sample i and data points in other clusters.
+"""
+
+function bᵢ(data::AbstractArray{T}, labels::AbstractVector{S}, i::Int64, method::Common, centers) where {T<:Real, S<:Real}
+    labelᵢ = labels[i]
+    dissim_labels = [idx for idx=1:length(centers) if idx!=labelᵢ]
+    mean_dist = similar(dissim_labels, Float64)
+    idx = 0
+    for (idx,j) in enumerate(dissim_labels)
+        related_idx = findall(isequal(j), labels)
+        @inbounds mean_dist[idx] = euclidean(data[i, :], data[related_idx, :])
+    end
+
+    return minimum(mean_dist)
+end
+
+function bᵢ(data::AbstractArray{T}, labels::AbstractVector{S}, i::Int64, method::Simplified, centers) where {T<:Real, S<:Real}
+    labelᵢ = labels[i]
+    clusters_to_iterate = [idx for idx=1:length(centers) if idx!=labelᵢ]
+    center = vcat(transpose.(centers)...)
+    mean_dist = [euclidean(data[i, :], center[clus_idx, :]) for clus_idx in clusters_to_iterate]
+
+    return minimum(mean_dist)
+end
+
+"""
+    sᵢ(aᵢ, bᵢ)
+
+Calculate the silhouette of i'th sample.
+
+# Arguments (positional)
+- `aᵢ`: The sum distance between i'th sample and data points in the same cluster.
+- `bᵢ`: The sum distance between i'th sample and data points in other clusters.
+
+# Returns
+A Float64 value that represents silhouette of i'th sample.
+
+"""
+function sᵢ(aᵢ, bᵢ)
+    return (bᵢ - aᵢ)/max(aᵢ, bᵢ)
+end
+
+"""
+    Silouhette(input_data, model::KmeansResult)
+
+Calculate the silhouette coefficient of the clustering result.
+
+# Arguments (positional)
+- `input_data`: data set.
+- `model`: an `KmeansResult` object.
+
+# Returns
+A Float64 value that represents silhouette coefficient of the clustering result.
+"""
+function Silouhette(input_data, model::KmeansResult)
+    Tables.istable(input_data) ? data=Tables.matrix(input_data) : error()
+    labels = model.cluster
+    centers = model.centroids
+    if big(size(data, 1))^2 > 10^3
+        method = Simplified()
+        sᵢs = [
+            sᵢ(
+                aᵢ(data, labels, i, method, centers),
+                bᵢ(data, labels, i, method, centers)
+            )
+            for i=1:size(data, 1)
+        ]
+    else
+        method = Common()
+        sᵢs = [
+            sᵢ(
+                aᵢ(data, labels, i, method),
+                bᵢ(data, labels, i, method, centers)
+            )
+            for i=1:size(data, 1)
+        ]
+    end
+
+    return mean(sᵢs)
+end