DISTANCE
cityblock
Compute the City Block (Manhattan) distance.
Example of usage
Compare two named customer profiles and assert the computed score.
Domains of usage
Customer segmentation · Behavioural analytics · Similarity search
Usage / limitations
+Use when: Compare customer profiles using the cityblock metric; choose it when its assumptions fit your features.
−Limitations: Feature scales and representations influence the result; compare only appropriately prepared profiles.
Mathematical formula
d(x,y) = Σᵢ |xᵢ − yᵢ|This metric returns a distance or similarity computed from aligned feature vectors. Interpret its scale according to the metric definition.
Sample dataShow
"{'variable': 'customer_signals', 'domain': 'Retail customer engagement analytics', 'feature_names': ['weekday_orders', 'weekend_orders', 'return_visits'], 'customer_A': {'weekday_orders': 12.0, 'weekend_orders': 5.0, 'return_visits': 3.0}, 'customer_B': {'weekday_orders': 9.0, 'weekend_orders': 8.0, 'return_visits': 4.0}}"Code example (Python)
import numpy as np
customer_signals = {'variable': 'customer_signals', 'domain': 'Retail customer engagement analytics', 'feature_names': ['weekday_orders', 'weekend_orders', 'return_visits'], 'customer_A': {'weekday_orders': 12.0, 'weekend_orders': 5.0, 'return_visits': 3.0}, 'customer_B': {'weekday_orders': 9.0, 'weekend_orders': 8.0, 'return_visits': 4.0}}
feature_names = customer_signals["feature_names"]
# DataLens.ai example
# Domain: Retail customer engagement analytics
# Compare two labelled customer profiles using cityblock.
import numpy as np
# Read the feature values in a consistent order.
left = np.array([customer_signals["customer_A"][name] for name in feature_names], dtype=float)
right = np.array([customer_signals["customer_B"][name] for name in feature_names], dtype=float)
# Calculate the requested distance or similarity.
from scipy.spatial.distance import cityblock
result = cityblock(left, right)
# Regression check against the expected result for this dataset.
observed = float(np.asarray(result).ravel()[0])
assert np.isclose(observed, 7.0, rtol=1e-8, atol=1e-9), (observed, 7.0)
print("Expected output verified")
# DataLens.ai example
# Domain: Retail customer engagement analytics
# Compare two labelled customer profiles using cityblock.
import numpy as np
# Read the feature values in a consistent order.
left = np.array([customer_signals["customer_A"][name] for name in feature_names], dtype=float)
right = np.array([customer_signals["customer_B"][name] for name in feature_names], dtype=float)
# Calculate the requested distance or similarity.
from scipy.spatial.distance import cityblock
result = cityblock(left, right)
# Regression check against the expected result for this dataset.
observed = float(np.asarray(result).ravel()[0])
assert np.isclose(observed, 7.0, rtol=1e-8, atol=1e-9), (observed, 7.0)
print("Expected output verified")