Euclidean distance

Q: How deeply does Machine Learning for Tabular Data: XGBoost, Deep Learning, and AI cover Euclidean distance?

Defines direct-path distance, relates it to the L2 norm, and stops short of a dense mathematical derivation.

As explained in Machine Learning for Tabular Data: XGBoost, Deep Learning, and AI

Euclidean distance is the straight-line distance between two points in Euclidean space.

Euclidean distance measures the straight-line distance between two points in Euclidean space. It assumes a direct path and can suit physical-distance features. section 7.1.3

When engineering geographical features, compare distance measures with the movement the feature should represent:

Choose Euclidean distance when direct physical separation matters. section 7.1.3
Choose Manhattan distance when city streets, road networks, and horizontal or vertical travel better reflect accessibility. section 7.1.3
Recognize Euclidean distance as closely related to the L2 norm; Manhattan distance similarly corresponds to the L1 norm. section 7.1.3

Tokyo accommodation features

For Airbnb listings near Tokyo’s Imperial Palace, convert coordinate differences into meters before inspecting distances. A nearest-listing result can then support a location feature, while city accessibility may favor Manhattan distance instead. section 7.1.3

Listing 7.5 Computing a distance metric from the city center

imperial_palace_lat = 35.6841822633
imperial_palace_lon = 139.751471994
 
def degrees_to_meters(distance_degrees, latitude):
    conversion_factor = 111000                              #1
    distance_meters = (distance_degrees * conversion_factor 
                       * np.cos(np.radians(latitude)))      #2
    return distance_meters 
 
distance_degrees = (
    np.abs(
        summary_listings['latitude'] 
        imperial_palace_lat) + 
    np.abs(
        summary_listings['longitude'] 
        imperial_palace_lon)
)                                                           #3
 
summary_listings['imperial_palace_distance'] = (
    degrees_to_meters(distance_degrees,
    summary_listings['latitude']
)

Inspect the coordinate-to-meters workflow used to create a distance feature from latitude and longitude. section 7.1.3

How Machine Learning for Tabular Data: XGBoost, Deep Learning, and AI covers it

Cover of Machine Learning for Tabular Data: XGBoost, Deep Learning, and AI

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Also explained in

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Advanced Algorithms and Data StructuresEuclidean distance is the straight-line distance between points in Euclidean space, computed from the square root of the sum of squared coordinate differences.
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Data Without LabelsEuclidean distance is the straight-line distance between points in a coordinate space, computed as the square root of the summed squared coordinate differences.
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Natural Language Processing in Action, Second EditionEuclidean distance is the straight-line distance between two points or vectors computed from the square root of the sum of squared coordinate differences.
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Statistics Slam DunkEuclidean distance is the straight-line distance between points computed as the square root of the sum of squared coordinate differences.
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Optimization Algorithms: AI techniques for design, planning, and control problemsEuclidean distance is the straight-line distance between points calculated from the square root of the sum of squared coordinate differences.
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MongoDB 8.0 in Action, Third EditionEuclidean distance is the straight-line distance between two points or vectors in Euclidean space.

Compare how 8 books explain Euclidean distance →

Related concepts

K-means clusteringused by · K-means clustering partitions data into a specified number of groups by assigning observations to representative centers and iteratively updating those centers to reduce within-group distances.
Manhattan distancecontrasts with · Manhattan distance is the sum of the absolute differences between corresponding coordinates of two points or vectors.
minkowski distanceequivalent to · Minkowski distance is a parameterized metric between points based on a positive-order norm, including Manhattan and Euclidean distance as special cases.
distancekind of · Distance is a measure of separation between points or entities in a defined space or context.
l2 normequivalent to · The L2 norm is the nonnegative Euclidean magnitude of a vector, equal to the square root of the sum of its components’ squares, and to absolute value for a scalar.
cosine distancealternative to · Cosine distance is a measure of dissimilarity between nonzero vectors based on their angular separation, commonly defined as one minus cosine similarity.

This explainer was generated by Manning's knowledge graph from the text of Machine Learning for Tabular Data: XGBoost, Deep Learning, and AI. The section links point to the parts of the book it draws on.