Euclidean distance vs Manhattan distance
Issue #87 | Jan 20th, 2025
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Welcome to the new edition of Business Analytics Review!
In today’s edition, we are going to discuss two common ways used in machine learning to measure the distance between points in a multi-dimensional space; Euclidean distance and Manhattan distance. These are commonly used to measure similarity or dissimilarity between data points.
Euclidean distance is defined as the straight-line distance between two points in Euclidean space. It represents the length of the shortest path connecting the two points, making it intuitive for measuring physical distances in two or three-dimensional spaces.
Manhattan distance, also known as taxicab or city block distance, measures the total absolute differences along each dimension. It reflects the path one would take to navigate a grid-like path (like city streets), only moving along axes. It is particularly useful in high-dimensional spaces where features may be independent or when dealing with categorical data.
Applications
Euclidean Distance: Commonly used in clustering algorithms and when data points are expected to be distributed normally
Algorithms:
K-means clustering: Determines the centroid of clusters using Euclidean distance
K-Nearest Neighbors (KNN): Measures proximity of data points to classify them
Principal Component Analysis (PCA): Relies on Euclidean distance to maximize variance
When to Use:
Features are continuous and normally distributed
The relationships between features are linear
High precision in distance measurement is important
Manhattan Distance: Often used in scenarios involving high-dimensional spaces or when features are not correlated. It can also be more suitable when dealing with sparse data
Algorithms:
KNN: Can be used as an alternative distance metric, especially in sparse data
Clustering (e.g., K-medians): Performs better when dealing with sparse or grid-like data
Linear programming or optimization problems: Useful in scenarios with axis-aligned constraints
When to Use:
Features are sparse or follow a grid-like structure (e.g., text data, images, or geographic data)
The dataset has many irrelevant dimensions or is high-dimensional
There are outliers, as it is less sensitive to extreme values
Recommended Reads on Distance Metrics
Different Types of Distance Metrics used in Machine Learning
Distance metrics are crucial for various machine learning algorithms, influencing their performance and effectiveness in tasks such as classification and clustering
Understanding Distance Metrics Used in Machine Learning
Choosing the right metric can significantly affect model performance in both supervised and unsupervised learning contexts
When would one use Manhattan distance as opposed to Euclidean distance?
While both distances have their uses, Manhattan distance is often preferred in scenarios involving high dimensionality, non-comparable features, and grid-like structures
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Tool of the Day: SciPy Library in Python
SciPy is a powerful Python library that provides extensive functionalities for calculating distances, particularly through its scipy.spatial.distance module. This module includes various methods to compute distances between points in n-dimensional space, making it a versatile tool for data analysis and machine learning tasks. Learn more
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