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# kmeans.py
# From Classic Computer Science Problems in Python Chapter 6
# Copyright 2018 David Kopec
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from __future__ import annotations
from typing import TypeVar, Generic, List, Sequence
from copy import deepcopy
from functools import partial
from random import uniform
from statistics import mean, pstdev
from dataclasses import dataclass
from data_point import DataPoint
def zscores(original: Sequence[float]) -> List[float]:
avg: float = mean(original)
std: float = pstdev(original)
if std == 0: # return all zeros if there is no variation
return [0] * len(original)
return [(x - avg) / std for x in original]
Point = TypeVar('Point', bound=DataPoint)
class KMeans(Generic[Point]):
@dataclass
class Cluster:
points: List[Point]
centroid: DataPoint
def __init__(self, k: int, points: List[Point]) -> None:
if k < 1: # k-means can't do negative or zero clusters
raise ValueError("k must be >= 1")
self._points: List[Point] = points
self._zscore_normalize()
# initialize empty clusters with random centroids
self._clusters: List[KMeans.Cluster] = []
for _ in range(k):
rand_point: DataPoint = self._random_point()
cluster: KMeans.Cluster = KMeans.Cluster([], rand_point)
self._clusters.append(cluster)
@property
def _centroids(self) -> List[DataPoint]:
return [x.centroid for x in self._clusters]
def _dimension_slice(self, dimension: int) -> List[float]:
return [x.dimensions[dimension] for x in self._points]
def _zscore_normalize(self) -> None:
zscored: List[List[float]] = [[] for _ in range(len(self._points))]
for dimension in range(self._points[0].num_dimensions):
dimension_slice: List[float] = self._dimension_slice(dimension)
for index, zscore in enumerate(zscores(dimension_slice)):
zscored[index].append(zscore)
for i in range(len(self._points)):
self._points[i].dimensions = tuple(zscored[i])
def _random_point(self) -> DataPoint:
rand_dimensions: List[float] = []
for dimension in range(self._points[0].num_dimensions):
values: List[float] = self._dimension_slice(dimension)
rand_value: float = uniform(min(values), max(values))
rand_dimensions.append(rand_value)
return DataPoint(rand_dimensions)
# Find the closest cluster centroid to each point and assign the point to that cluster
def _assign_clusters(self) -> None:
for point in self._points:
closest: DataPoint = min(self._centroids, key=partial(DataPoint.distance, point))
idx: int = self._centroids.index(closest)
cluster: KMeans.Cluster = self._clusters[idx]
cluster.points.append(point)
# Find the center of each cluster and move the centroid to there
def _generate_centroids(self) -> None:
for cluster in self._clusters:
if len(cluster.points) == 0: # keep the same centroid if no points
continue
means: List[float] = []
for dimension in range(cluster.points[0].num_dimensions):
dimension_slice: List[float] = [p.dimensions[dimension] for p in cluster.points]
means.append(mean(dimension_slice))
cluster.centroid = DataPoint(means)
def run(self, max_iterations: int = 100) -> List[KMeans.Cluster]:
for iteration in range(max_iterations):
for cluster in self._clusters: # clear all clusters
cluster.points.clear()
self._assign_clusters() # find cluster each point is closest to
old_centroids: List[DataPoint] = deepcopy(self._centroids) # record
self._generate_centroids() # find new centroids
if old_centroids == self._centroids: # have centroids moved?
print(f"Converged after {iteration} iterations")
return self._clusters
return self._clusters
if __name__ == "__main__":
point1: DataPoint = DataPoint([2.0, 1.0, 1.0])
point2: DataPoint = DataPoint([2.0, 2.0, 5.0])
point3: DataPoint = DataPoint([3.0, 1.5, 2.5])
kmeans_test: KMeans[DataPoint] = KMeans(2, [point1, point2, point3])
test_clusters: List[KMeans.Cluster] = kmeans_test.run()
for index, cluster in enumerate(test_clusters):
print(f"Cluster {index}: {cluster.points}")