The cardinality of a Set refers to the number of elements it contains.
In math notation, we represent the cardinality of a set as . For example, the set has a cardinality of 3, expressed as .
In machine learning, the "cardinality of a feature" denotes the number of unique elements or categories within that feature. High-cardinality features may require feature engineering or be excluded entirely (for example,
Use of the vertical bar
Initially it seemed confusing to me that mathematical notation employs the vertical bar symbol for different purposes.
- The absolute value of a number is expressed as .
The Matrix Determinate of a matrix is expressed as :
However, these notations share a common theme of representing size or magnitude:
- In set theory, cardinality describes the size of a set by the number of elements it contains.
- For numbers, the absolute value captures the distance from zero on the number line.
- In linear algebra, the Matrix Determinate determinant describes how much a Matrix Transformation scales space.