K Means Clust
p
"""README, Author - Anurag Kumar(mailto:anuragkumarak95@gmail.com)
Requirements:
- sklearn
- numpy
- matplotlib
Python:
- 3.5
Inputs:
- X , a 2D numpy array of features.
- k , number of clusters to create.
- initial_centroids , initial centroid values generated by utility function(mentioned
in usage).
- maxiter , maximum number of iterations to process.
- heterogeneity , empty list that will be filled with heterogeneity values if passed
to kmeans func.
Usage:
1. define 'k' value, 'X' features array and 'heterogeneity' empty list
2. create initial_centroids,
initial_centroids = get_initial_centroids(
X,
k,
seed=0 # seed value for initial centroid generation,
# None for randomness(default=None)
)
3. find centroids and clusters using kmeans function.
centroids, cluster_assignment = kmeans(
X,
k,
initial_centroids,
maxiter=400,
record_heterogeneity=heterogeneity,
verbose=True # whether to print logs in console or not.(default=False)
)
4. Plot the loss function and heterogeneity values for every iteration saved in
heterogeneity list.
plot_heterogeneity(
heterogeneity,
k
)
5. Transfers Dataframe into excel format it must have feature called
'Clust' with k means clustering numbers in it.
"""
import warnings
import numpy as np
import pandas as pd
from matplotlib import pyplot as plt
from sklearn.metrics import pairwise_distances
warnings.filterwarnings("ignore")
TAG = "K-MEANS-CLUST/ "
def get_initial_centroids(data, k, seed=None):
"""Randomly choose k data points as initial centroids"""
# useful for obtaining consistent results
rng = np.random.default_rng(seed)
n = data.shape[0] # number of data points
# Pick K indices from range [0, N).
rand_indices = rng.integers(0, n, k)
# Keep centroids as dense format, as many entries will be nonzero due to averaging.
# As long as at least one document in a cluster contains a word,
# it will carry a nonzero weight in the TF-IDF vector of the centroid.
centroids = data[rand_indices, :]
return centroids
def centroid_pairwise_dist(x, centroids):
return pairwise_distances(x, centroids, metric="euclidean")
def assign_clusters(data, centroids):
# Compute distances between each data point and the set of centroids:
# Fill in the blank (RHS only)
distances_from_centroids = centroid_pairwise_dist(data, centroids)
# Compute cluster assignments for each data point:
# Fill in the blank (RHS only)
cluster_assignment = np.argmin(distances_from_centroids, axis=1)
return cluster_assignment
def revise_centroids(data, k, cluster_assignment):
new_centroids = []
for i in range(k):
# Select all data points that belong to cluster i. Fill in the blank (RHS only)
member_data_points = data[cluster_assignment == i]
# Compute the mean of the data points. Fill in the blank (RHS only)
centroid = member_data_points.mean(axis=0)
new_centroids.append(centroid)
new_centroids = np.array(new_centroids)
return new_centroids
def compute_heterogeneity(data, k, centroids, cluster_assignment):
heterogeneity = 0.0
for i in range(k):
# Select all data points that belong to cluster i. Fill in the blank (RHS only)
member_data_points = data[cluster_assignment == i, :]
if member_data_points.shape[0] > 0: # check if i-th cluster is non-empty
# Compute distances from centroid to data points (RHS only)
distances = pairwise_distances(
member_data_points, [centroids[i]], metric="euclidean"
)
squared_distances = distances**2
heterogeneity += np.sum(squared_distances)
return heterogeneity
def plot_heterogeneity(heterogeneity, k):
plt.figure(figsize=(7, 4))
plt.plot(heterogeneity, linewidth=4)
plt.xlabel("# Iterations")
plt.ylabel("Heterogeneity")
plt.title(f"Heterogeneity of clustering over time, K={k:d}")
plt.rcParams.update({"font.size": 16})
plt.show()
def kmeans(
data, k, initial_centroids, maxiter=500, record_heterogeneity=None, verbose=False
):
"""Runs k-means on given data and initial set of centroids.
maxiter: maximum number of iterations to run.(default=500)
record_heterogeneity: (optional) a list, to store the history of heterogeneity
as function of iterations
if None, do not store the history.
verbose: if True, print how many data points changed their cluster labels in
each iteration"""
centroids = initial_centroids[:]
prev_cluster_assignment = None
for itr in range(maxiter):
if verbose:
print(itr, end="")
# 1. Make cluster assignments using nearest centroids
cluster_assignment = assign_clusters(data, centroids)
# 2. Compute a new centroid for each of the k clusters, averaging all data
# points assigned to that cluster.
centroids = revise_centroids(data, k, cluster_assignment)
# Check for convergence: if none of the assignments changed, stop
if (
prev_cluster_assignment is not None
and (prev_cluster_assignment == cluster_assignment).all()
):
break
# Print number of new assignments
if prev_cluster_assignment is not None:
num_changed = np.sum(prev_cluster_assignment != cluster_assignment)
if verbose:
print(
f" {num_changed:5d} elements changed their cluster assignment."
)
# Record heterogeneity convergence metric
if record_heterogeneity is not None:
# YOUR CODE HERE
score = compute_heterogeneity(data, k, centroids, cluster_assignment)
record_heterogeneity.append(score)
prev_cluster_assignment = cluster_assignment[:]
return centroids, cluster_assignment
# Mock test below
if False: # change to true to run this test case.
from sklearn import datasets as ds
dataset = ds.load_iris()
k = 3
heterogeneity = []
initial_centroids = get_initial_centroids(dataset["data"], k, seed=0)
centroids, cluster_assignment = kmeans(
dataset["data"],
k,
initial_centroids,
maxiter=400,
record_heterogeneity=heterogeneity,
verbose=True,
)
plot_heterogeneity(heterogeneity, k)
def report_generator(
predicted: pd.DataFrame, clustering_variables: np.ndarray, fill_missing_report=None
) -> pd.DataFrame:
"""
Generate a clustering report given these two arguments:
predicted - dataframe with predicted cluster column
fill_missing_report - dictionary of rules on how we are going to fill in missing
values for final generated report (not included in modelling);
>>> predicted = pd.DataFrame()
>>> predicted['numbers'] = [1, 2, 3]
>>> predicted['col1'] = [0.5, 2.5, 4.5]
>>> predicted['col2'] = [100, 200, 300]
>>> predicted['col3'] = [10, 20, 30]
>>> predicted['Cluster'] = [1, 1, 2]
>>> report_generator(predicted, ['col1', 'col2'], 0)
Features Type Mark 1 2
0 # of Customers ClusterSize False 2.000000 1.000000
1 % of Customers ClusterProportion False 0.666667 0.333333
2 col1 mean_with_zeros True 1.500000 4.500000
3 col2 mean_with_zeros True 150.000000 300.000000
4 numbers mean_with_zeros False 1.500000 3.000000
.. ... ... ... ... ...
99 dummy 5% False 1.000000 1.000000
100 dummy 95% False 1.000000 1.000000
101 dummy stdev False 0.000000 NaN
102 dummy mode False 1.000000 1.000000
103 dummy median False 1.000000 1.000000
<BLANKLINE>
[104 rows x 5 columns]
"""
# Fill missing values with given rules
if fill_missing_report:
predicted = predicted.fillna(value=fill_missing_report)
predicted["dummy"] = 1
numeric_cols = predicted.select_dtypes(np.number).columns
report = (
predicted.groupby(["Cluster"])[ # construct report dataframe
numeric_cols
] # group by cluster number
.agg(
[
("sum", "sum"),
("mean_with_zeros", lambda x: np.mean(np.nan_to_num(x))),
("mean_without_zeros", lambda x: x.replace(0, np.nan).mean()),
(
"mean_25-75",
lambda x: np.mean(
np.nan_to_num(
sorted(x)[
round(len(x) * 25 / 100) : round(len(x) * 75 / 100)
]
)
),
),
("mean_with_na", "mean"),
("min", lambda x: x.min()),
("5%", lambda x: x.quantile(0.05)),
("25%", lambda x: x.quantile(0.25)),
("50%", lambda x: x.quantile(0.50)),
("75%", lambda x: x.quantile(0.75)),
("95%", lambda x: x.quantile(0.95)),
("max", lambda x: x.max()),
("count", lambda x: x.count()),
("stdev", lambda x: x.std()),
("mode", lambda x: x.mode()[0]),
("median", lambda x: x.median()),
("# > 0", lambda x: (x > 0).sum()),
]
)
.T.reset_index()
.rename(index=str, columns={"level_0": "Features", "level_1": "Type"})
) # rename columns
# calculate the size of cluster(count of clientID's)
# avoid SettingWithCopyWarning
clustersize = report[
(report["Features"] == "dummy") & (report["Type"] == "count")
].copy()
# rename created predicted cluster to match report column names
clustersize.Type = "ClusterSize"
clustersize.Features = "# of Customers"
# calculating the proportion of cluster
clusterproportion = pd.DataFrame(
clustersize.iloc[:, 2:].to_numpy() / clustersize.iloc[:, 2:].to_numpy().sum()
)
# rename created predicted cluster to match report column names
clusterproportion["Type"] = "% of Customers"
clusterproportion["Features"] = "ClusterProportion"
cols = clusterproportion.columns.tolist()
cols = cols[-2:] + cols[:-2]
clusterproportion = clusterproportion[cols] # rearrange columns to match report
clusterproportion.columns = report.columns
# generating dataframe with count of nan values
a = pd.DataFrame(
abs(
report[report["Type"] == "count"].iloc[:, 2:].to_numpy()
- clustersize.iloc[:, 2:].to_numpy()
)
)
a["Features"] = 0
a["Type"] = "# of nan"
# filling values in order to match report
a.Features = report[report["Type"] == "count"].Features.tolist()
cols = a.columns.tolist()
cols = cols[-2:] + cols[:-2]
a = a[cols] # rearrange columns to match report
a.columns = report.columns # rename columns to match report
# drop count values except for cluster size
report = report.drop(report[report.Type == "count"].index)
# concat report with cluster size and nan values
report = pd.concat([report, a, clustersize, clusterproportion], axis=0)
report["Mark"] = report["Features"].isin(clustering_variables)
cols = report.columns.tolist()
cols = cols[0:2] + cols[-1:] + cols[2:-1]
report = report[cols]
sorter1 = {
"ClusterSize": 9,
"ClusterProportion": 8,
"mean_with_zeros": 7,
"mean_with_na": 6,
"max": 5,
"50%": 4,
"min": 3,
"25%": 2,
"75%": 1,
"# of nan": 0,
"# > 0": -1,
"sum_with_na": -2,
}
report = (
report.assign(
Sorter1=lambda x: x.Type.map(sorter1),
Sorter2=lambda x: list(reversed(range(len(x)))),
)
.sort_values(["Sorter1", "Mark", "Sorter2"], ascending=False)
.drop(["Sorter1", "Sorter2"], axis=1)
)
report.columns.name = ""
report = report.reset_index()
report = report.drop(columns=["index"])
return report
if __name__ == "__main__":
import doctest
doctest.testmod()
