Data Foundations: Objects, Attributes, and Proximity Measures

In Introduction to Data Mining (2nd Edition) — Tan, Steinbach, Karpatne, and Kumar, a data set is represented as objects described by attributes. Numeric objects can be viewed as points in an attribute space, and pairwise distances can be organized in a distance matrix.

Proximity measures

Proximity describes how near or far two objects are. Smaller distance generally indicates greater similarity; larger distance indicates dissimilarity. The Minkowski metric uses parameter r and includes common special cases.

• Euclidean distance: square corresponding differences, add them, and take the square root; it is straight-line distance.
• Manhattan distance: add absolute differences; it is also called city-block or taxicab distance.
• Hamming distance: for binary vectors, count positions whose bits differ.
• Supremum distance: use the largest single-attribute difference.

Why the choice matters

Clustering, nearest-neighbor search, and related mining methods depend on proximity. The chosen measure changes what counts as similar, so match it to the attribute type and the analytical goal.

Key takeaway: objects and attributes provide the representation; distance measures provide a quantitative way to compare objects.