from typing import Tuple, Iterable, Sequence, List, Dict, DefaultDict
from random import sample
from math import fsum, sqrt
from collections import defaultdict
def partial(func, *args):
"Rewrite functools.partial() in a way that doesn't confuse mypy"
def inner(*moreargs):
return func(*args, *moreargs)
return inner
def mean(data: Iterable[float]) -> float:
'Accurate arithmetic mean'
data = list(data)
return fsum(data) / len(data)
def transpose(matrix: Iterable[Iterable]) -> Iterable[tuple]:
'Swap rows with columns for a 2-D array'
return zip(*matrix)
Point = Tuple[float, ...]
Centroid = Point
def dist(p: Point, q: Point, sqrt=sqrt, fsum=fsum, zip=zip) -> float:
'Multi-dimensional euclidean distance'
return sqrt(fsum((x1 - x2) ** 2.0 for x1, x2 in zip(p, q)))
def assign_data(centroids: Sequence[Centroid], data: Iterable[Point]) -> Dict[Centroid, Sequence[Point]]:
'Assign data the closest centroid'
d : DefaultDict[Point, List[Point]] = defaultdict(list)
for point in data:
centroid: Point = min(centroids, key=partial(dist, point))
d[centroid].append(point)
return dict(d)
def compute_centroids(groups: Iterable[Sequence[Point]]) -> List[Centroid]:
'Compute the centroid of each group'
return [tuple(map(mean, transpose(group))) for group in groups]
def k_means(data: Iterable[Point], k:int=2, iterations:int=10) -> List[Point]:
'Return k-centroids for the data'
data = list(data)
centroids = sample(data, k)
for i in range(iterations):
labeled = assign_data(centroids, data)
centroids = compute_centroids(labeled.values())
return centroids
def quality(labeled: Dict[Centroid, Sequence[Point]]) -> float:
'Mean value of squared distances from data to its assigned centroid'
return mean(dist(c, p) ** 2 for c, pts in labeled.items() for p in pts)
if __name__ == '__main__':
from pprint import pprint
print('Simple example with six 3-D points clustered into two groups')
points = [
(10, 41, 23),
(22, 30, 29),
(11, 42, 5),
(20, 32, 4),
(12, 40, 12),
(21, 36, 23),
]
centroids = k_means(points, k=2)
pprint(assign_data(centroids, points))
print('\nExample with a richer dataset.')
print('See: https://www.datascience.com/blog/introduction-to-k-means-clustering-algorithm-learn-data-science-tutorials')
data = [
(10, 30),
(12, 50),
(14, 70),
(9, 150),
(20, 175),
(8, 200),
(14, 240),
(50, 35),
(40, 50),
(45, 60),
(55, 45),
(60, 130),
(60, 220),
(70, 150),
(60, 190),
(90, 160),
]
print('k quality')
print('- -------')
for k in range(1, 8):
centroids = k_means(data, k, iterations=20)
d = assign_data(centroids, data)
print(f'{k} {quality(d) :8,.1f}')
