Run k-means clustering on list of cities and plot results as labeled scatterplot in Excel

excel and f# demo

type City = { Name: string; Lat: float; Lng: float }

let cities =
    [ ("San Francisco", "CA", "United States");
      ("New York", "NY", "United States");
      ("Hoboken", "NJ", "United States");
      ("Redmond", "WA", "United States");
      ("Seattle", "WA", "United States");
      ("Boston", "MA", "United States");
      ("Boston", "MA", "United States");
      ("Romeoville", "IL", "United States");
      ("Nashville", "TN", "United States");
      ("Nashville", "TN", "United States");
      ("Detroit", "MI", "United States");
      ("Ann Harbor", "MI", "United States");
      ("Houston", "TX", "United States") ]

let rng = new System.Random()
let fakeService (data: (string * string * string)) =
    let city, state, country = data
    { Name = city; Lat = rng.NextDouble(); Lng = rng.NextDouble() }

// extraction of cities
let positions = cities |> List.map fakeService

// k-means clustering
let pos = positions |> List.map (fun c -> [| c.Lat; c.Lng |])
let factory (ps: (float []) seq) (k: int) = randomCentroids rng pos k
let analysis = kmeans euclidean factory avgCentroid (List.map (fun p -> [| p.Lat; p.Lng |]) positions)

// plot clusters

let plotClusters k = 

    let centers, classifier = analysis k

    let datapoints = 
        positions 
        |> List.map (fun c -> c, [| c.Lat; c.Lng |]) 
        |> List.map (fun (c, p) -> c, List.findIndex (fun c -> c = classifier p) centers)
        |> List.map (fun (c, i) -> (c.Lat, c.Lng, i, c.Name))
    let centroids = centers |> List.map (fun c -> c.[0], c.[1], -1, "CENTROID")

    List.append datapoints centroids |> labeledplot