How deeply does Statistics Slam Dunk cover Euclidean distance?

Explains the coordinate formula, works two NBA examples, and applies R distance-matrix computation.

Euclidean distance

Euclidean distance is the straight-line distance between points computed as the square root of the sum of squared coordinate differences.

Euclidean distance measures the straight-line separation between two points. For coordinates (x1, y1) and (x2, y2), square each coordinate difference, add the results, and take the square root. section 3.9

NBA draft example

Using pick number and average win shares, the distance between picks 1 and 3 is sqrt((1 - 3)^2 + (69.6 - 66.9)^2) = 3.36. Comparing picks 2 and 3 gives 15.43, indicating greater dissimilarity. section 3.9

euclidean_distance <- sqrt((1 - 3)^2 + (69.6 - 66.9)^2)
euclidean_distance
## [1] 3.36006

Run the calculation directly in R with the square-root formula, then use dist(..., method = "euclidean") to create a distance matrix for all observations. section 3.9

How Statistics Slam Dunk covers it

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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 Statistics Slam Dunk. The section links point to the parts of the book it draws on.