Cluster a list of geographic points by distance and constraints

Question

I have a delivery app, and I want to group orders (each order has a lat and lng coordinates) by location proximity (linear distance) and constraints like max orders and max total products (each order has an amount of products) inside a group.

For proximity grouping I used DBSCAN

coordinates = [[lat,lng],[lat,lng]],[lat,lng]],[lat,lng]],[lat,lng]]]
distance_matrix = squareform(pdist(coordinates, (lambda u,v: haversine(u,v))))

#eps=0.1 => 100m radius, 50m linear
db = DBSCAN(eps=0.1, min_samples=2, metric='precomputed')
results = db.fit(distance_matrix)

How can I add constraints in this functionality?

Is there anyway of doing this by using something else than DBSCAN or HDBSCAN ?

@GilseungAhn max orders inside a group and max products inside a group — Alex, Apr 07 '20 at 04:17
Well.. In this case, you need to develop a mathematical model for the clustering with constraints and solve it. In addition, is there an objective such as the number of clusters to be minimized? — Gilseung Ahn, Apr 07 '20 at 04:21
@GilseungAhn Ideally will be to respect all the constraints and have minimum clusters. — Alex, Apr 07 '20 at 04:28

score 1 · Answer 1 · answered Apr 08 '20 at 02:15

This is an interesting question. I suppose it can be done a bunch of different ways. Here is one solution for you to condsider.

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from sklearn.cluster import KMeans
import seaborn as sns; sns.set()
import csv


df = pd.read_csv('C:\\your_path\\properties_2017.csv')
# df.head(10)
df = df.head(10000)

df.shape


df.dropna(axis=0,how='any',subset=['latitude','longitude'],inplace=True)

# Variable with the Longitude and Latitude
X=df.loc[:,['parcelid','latitude','longitude']]
X.head(10)

K_clusters = range(1,10)
kmeans = [KMeans(n_clusters=i) 

for i in K_clusters]
Y_axis = df[['latitude']]
X_axis = df[['longitude']]
score = [kmeans[i].fit(Y_axis).score(Y_axis)

for i in range(len(kmeans))] # Visualize
plt.plot(K_clusters, score)
plt.xlabel('Number of Clusters')
plt.ylabel('Score')
plt.title('Elbow Curve')
plt.show()

kmeans = KMeans(n_clusters = 10, init ='k-means++')
kmeans.fit(X[X.columns[1:3]]) # Compute k-means clustering.X['cluster_label'] = kmeans.fit_predict(X[X.columns[1:3]])centers = kmeans.cluster_centers_ # Coordinates of cluster centers.labels = kmeans.predict(X[X.columns[1:3]]) # Labels of each pointX.head(10)

X['cluster_label'] = kmeans.fit_predict(X[X.columns[1:3]])
centers = kmeans.cluster_centers_ # Coordinates of cluster centers.
labels = kmeans.predict(X[X.columns[1:3]]) # Labels of each pointX.head(10)

X.head(5)

X = X[['parcelid','cluster_label']]
X.head(5)


clustered_data = df.merge(X, left_on='parcelid', right_on='parcelid')
clustered_data.head(5)

centers = kmeans.cluster_centers_
print(centers)


X=df.loc[:,['parcelid','latitude','longitude']]
X.plot.scatter(x = 'latitude', y = 'longitude', c=labels, s=50, cmap='viridis')
plt.scatter(centers[:, 0], centers[:, 1], c='red', s=200, alpha=0.5)

data = X labels = kmeans.labels_

plt.subplots_adjust(bottom = 0.1)
plt.scatter(data.iloc[:, 1], data.iloc[:, 2], c=kmeans.labels_, cmap='rainbow') 

for label, x, y in zip(labels, data.iloc[:, 1], data.iloc[:, 2]):
    plt.annotate(
        label,
        xy=(x, y), xytext=(-20, 20),
        textcoords='offset points', ha='right', va='bottom',
        bbox=dict(boxstyle='round,pad=0.5', fc='red', alpha=0.5),
        arrowprops=dict(arrowstyle = '->', connectionstyle='arc3,rad=0'))

plt.show()

# labels pointing to each data point (this is a big jumbled together; you should probably select fewer data points to analyze).

Reference:

https://levelup.gitconnected.com/clustering-gps-co-ordinates-forming-regions-4f50caa7e4a1

Data source:

https://www.kaggle.com/c/zillow-prize-1/data

score 0 · Answer 2 · answered Apr 07 '20 at 05:24

Unfortunately, I think the model you want should be developed from the scratch.

Your question can be modeled as following optimization model.

Objective function: minimize the number of clusters, K Constraint (1) The size of every cluster is equal or smaller than S (parameter) (2) The number of orders in every cluster is equal or smaller than O (parameter) (3) For a sample x and its cluster Ck, dist(x, Ck) be the minimum among dist(x, C1), dist(x, C2), ..., dist(x, CK).

Solving this problem would require a lot of efforts...

Cluster a list of geographic points by distance and constraints

2 Answers2