Minimum Distance Probability (MDP)

TL;DR

Classifies items into groups by computing a “minimum distance” between an item and each group.
Assigns the item to the group whose distance to the item is smallest.
Uses item features (attributes) to compute those distances.

Definition

Minimum distance probability (MDP) is a method of discriminant analysis, a technique for classifying items into different groups or categories based on their characteristics. In MDP, the group most likely to be correct for a given item is the one with the smallest distance from that item.

Explanation

MDP operates by defining a set of features (characteristics) for each item. For each candidate group, a distance between the item and the group is computed using those features. The “minimum distance” is the smallest of those distances across all groups. The item is then classified into the group that yields this minimum distance. Distance calculation may involve comparing feature values (for example, differences in color, size, shape) and combining those differences to produce an overall distance value for each group.

Examples

Fruit classification

Given a dataset of fruits to classify into two groups (apples and oranges), define features such as color, size, and shape. For a given fruit, calculate its distance to each group by finding differences in the fruit’s color, size, and shape relative to a representative apple and a representative orange, and summing those differences. Classify the fruit as an apple if its minimum distance is to the apples group, or as an orange if its minimum distance is to the oranges group.

People classification

Given a dataset of people to classify into two groups (men and women), use features such as height, weight, and shoe size. For each person, calculate the distance to each group using these features, then classify the person into the group with the smaller distance.

Discriminant analysis
Feature (characteristic used for comparison)