Distance metrics (euclidean, cosine, manhattan) in SciPy - Mini Project: Build & Apply

Distance metrics (euclidean, cosine, manhattan)

📖 Scenario: You work as a data analyst for a company that wants to compare customer preferences. You have two customers' ratings for different products. You want to measure how similar or different these customers are using three common distance metrics: Euclidean, Cosine, and Manhattan distances.

🎯 Goal: Build a small program that calculates the Euclidean, Cosine, and Manhattan distances between two given customer rating vectors using scipy. This will help you understand how these distance metrics work and how to use them in Python.

📋 What You'll Learn

Create two lists called customer1 and customer2 with exact rating values.

Create a variable called metrics that holds the names of the distance metrics as strings.

Use scipy.spatial.distance functions to calculate Euclidean, Cosine, and Manhattan distances between customer1 and customer2.

Print the results clearly labeled.

💡 Why This Matters

🌍 Real World

Distance metrics help compare customers, products, or documents by measuring how similar or different they are. This is useful in recommendation systems, clustering, and search engines.

💼 Career

Data scientists and analysts use distance metrics to analyze patterns, group data, and build machine learning models that rely on similarity measures.

1

Create customer rating lists

Create two lists called customer1 and customer2 with these exact values: customer1 = [4, 3, 5, 1, 2] and customer2 = [5, 1, 4, 2, 3].

SciPy

# Create the two customer rating lists
# Your code here

Hint

Use square brackets to create lists and separate numbers with commas.

2

Create a list of metric names

Create a list called metrics that contains these exact strings: 'euclidean', 'cosine', and 'cityblock'.

SciPy

customer1 = [4, 3, 5, 1, 2]
customer2 = [5, 1, 4, 2, 3]

# Create the list of metric names
# Your code here

Hint

Use a list with the exact strings inside single quotes.

3

Calculate distances using scipy

Import scipy.spatial.distance as dist. Then create a dictionary called results where keys are metric names from metrics and values are the distances calculated by calling dist.(customer1, customer2) for each metric in metrics.

SciPy

customer1 = [4, 3, 5, 1, 2]
customer2 = [5, 1, 4, 2, 3]
metrics = ['euclidean', 'cosine', 'cityblock']

# Import scipy.spatial.distance as dist
# Create results dictionary with distances
# Your code here

Hint

Use getattr(dist, metric) to call the function by name inside a dictionary comprehension.

4

Print the distance results

Use a for loop with variables metric and value to iterate over results.items(). Inside the loop, print the metric name and its distance value in this exact format: "Euclidean distance: 2.828" (rounded to 3 decimal places). Use metric.capitalize() to capitalize the metric name and print the value rounded with round(value, 3).

SciPy

import scipy.spatial.distance as dist

customer1 = [4, 3, 5, 1, 2]
customer2 = [5, 1, 4, 2, 3]
metrics = ['euclidean', 'cosine', 'cityblock']

results = {metric: getattr(dist, metric)(customer1, customer2) for metric in metrics}

# Print each distance with metric name capitalized and value rounded to 3 decimals
# Your code here

Hint

Use a for loop and f-string to format the output exactly as shown.

Practice

1. Which distance metric measures the straight-line distance between two points in space?

easy

A. Jaccard distance

B. Cosine distance

C. Manhattan distance

D. Euclidean distance

Solution

1. Step 1: Understand distance types

   Euclidean distance is the direct straight-line distance between two points.

2. Step 2: Compare with other distances

   Cosine measures angle difference, Manhattan sums absolute differences, Jaccard measures set similarity.

3. Final Answer:

   Euclidean distance -> Option D

4. Quick Check:

   Straight-line distance = Euclidean distance [OK]

Hint: Straight line means Euclidean distance [OK]

Common Mistakes:

• Confusing cosine with Euclidean
• Thinking Manhattan is straight-line
• Mixing Jaccard with numeric distances

2. Which of the following is the correct way to import the Euclidean distance function from scipy?

easy

A. from scipy.spatial.distance import euclidean

B. import scipy.distance.euclidean

C. from scipy.distance import euclidean

D. import euclidean from scipy.spatial

Solution

1. Step 1: Recall scipy import syntax

   The correct import path for distance functions is scipy.spatial.distance.

2. Step 2: Check each option

   from scipy.spatial.distance import euclidean uses correct syntax: from scipy.spatial.distance import euclidean. Others are invalid or incorrect syntax.

3. Final Answer:

   from scipy.spatial.distance import euclidean -> Option A

4. Quick Check:

   Correct import path = from scipy.spatial.distance import euclidean [OK]

Hint: Use 'from scipy.spatial.distance import' for distance functions [OK]

Common Mistakes:

• Using wrong module path
• Incorrect import syntax
• Trying to import from scipy.distance

3. What is the output of this code?

from scipy.spatial.distance import cosine
v1 = [1, 0, 1]
v2 = [0, 1, 0]
result = cosine(v1, v2)
print(round(result, 2))

medium

A. 1.0

B. 0.5

C. 0.0

D. 0.71

Solution

1. Step 1: Calculate cosine similarity basics

   Vectors v1 and v2 are orthogonal (no overlap), so cosine similarity is 0.

2. Step 2: Calculate cosine distance

   Cosine distance = 1 - cosine similarity = 1 - 0 = 1.0.

3. Final Answer:

   1.0 -> Option A

4. Quick Check:

   Orthogonal vectors cosine distance = 1.0 [OK]

Hint: Cosine distance = 1 - cosine similarity [OK]

Common Mistakes:

• Confusing cosine similarity with distance
• Rounding errors
• Assuming zero distance for orthogonal vectors

4. Find the error in this code snippet calculating Manhattan distance:

from scipy.spatial.distance import manhattan
a = [1, 2, 3]
b = [4, 5]
print(manhattan(a, b))

medium

A. Function name should be cityblock, not manhattan

B. Import statement is incorrect

C. Lists a and b must be the same length

D. Manhattan distance requires numpy arrays, not lists

Solution

1. Step 1: Check input vector lengths

   Vectors a and b have different lengths (3 and 2), which is invalid for distance calculation.

2. Step 2: Validate function and import

   Import and function name are correct; scipy.spatial.distance.manhattan is valid and accepts lists.

3. Final Answer:

   Lists a and b must be the same length -> Option C

4. Quick Check:

   Equal length vectors needed for distance [OK]

Hint: Vectors must be same length for distance functions [OK]

Common Mistakes:

• Assuming different length lists work
• Confusing function name with cityblock
• Thinking lists are invalid inputs

5. You have two points: p1 = [3, 4, 5] and p2 = [1, 1, 1]. Which distance metric will give the largest value?
Options:
A) Euclidean
B) Cosine
C) Manhattan
D) All equal

hard

A. Euclidean

B. Manhattan

C. Cosine

D. All equal

Solution

1. Step 1: Calculate Euclidean distance

   Euclidean = sqrt((3-1)^2 + (4-1)^2 + (5-1)^2) = sqrt(4 + 9 + 16) = sqrt(29) ≈ 5.39.

2. Step 2: Calculate Manhattan distance

   Manhattan = |3-1| + |4-1| + |5-1| = 2 + 3 + 4 = 9.

3. Step 3: Calculate Cosine distance

   Cosine similarity = (3*1 + 4*1 + 5*1) / (sqrt(3^2+4^2+5^2)*sqrt(1^2+1^2+1^2)) = 12 / (7.07*1.73) ≈ 0.98; Cosine distance = 1 - 0.98 = 0.02.

4. Final Answer:

   Manhattan -> Option B

5. Quick Check:

   Manhattan distance > Euclidean > Cosine distance [OK]

Hint: Manhattan sums absolute differences, usually largest [OK]

Common Mistakes:

• Assuming Euclidean is always largest
• Confusing cosine distance scale
• Ignoring absolute values in Manhattan