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Everything about Binary relation
Relationship between elements of two sets
In mathematics, a binary relation associates some elements of one set called the domain with some elements of another set called the codomain. Precisely, a binary relation over sets X and Y is a set of ordered pairs (x,y), where x is an element of X and y is an element of Y. It encodes the common concept of relation: an element is related to an element if and only if the pair belongs to the set of ordered pairs that defines the binary relation. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Binary relationA 5-minute orientation
- Skim a recent paper: The Matthews correlation coefficient (MCC) should replace the ROC AUC as the standard metric for assessing binary classificationInfluential work since 2022
- Pick up a classic book: Zero is not the only storyThe most-reprinted book on the subject
- Read the landmark paper: The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluationCited 5,773 times
- Go sideways: Homogeneous relationA closely related topic
- Go sideways: Relation (mathematics)A closely related topic
📖 Definitions
Noun A subset of the Cartesian product A×A (the set of ordered pairs (a, b) of elements of A, alternatively written as A2).
Noun A subset of the Cartesian product A×B.
🏆 Landmark papers (most cited)
The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation
A Massive Pulsar in a Compact Relativistic Binary
Relation between percolation and particle coordination in binary powder mixtures
Biomedical Relation Extraction: From Binary to Complex
Compact binary relation representations with rich functionality
The mass-radius relation in binary systems
Dual core-nilpotent decomposition and dual binary relation
Sparse Binary Relation Representations for Genome Graph Annotation
🆕 Influential since 2022
The Matthews correlation coefficient (MCC) should replace the ROC AUC as the standard metric for assessing binary classification
Transgender and non-binary people’s perception of their healthcare in relation to endometriosis
A Mass–Magnitude Relation for Low-mass Stars Based on Dynamical Measurements of Thousands of Binary Star Systems
Perov Fixed-Point Results on F-Contraction Mappings Equipped with Binary Relation
Solidification shrinkage and shrinkage-induced melt convection and their relation with solute segregation in binary alloys
📚 Books worth reading
Zero is not the only storyPremendra Priyadarshi · 2007
Common groundGary Y. Okihiro · 2001
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Homogeneous relation In mathematics, a homogeneous relation (also called endorelation) on a set X is a binary relation between X and itself, i.e. it is a subset of the Cartesian…
- Relation (mathematics) In mathematics, a relation denotes some kind of relationship between two objects in a set, which may or may not hold. As an example, "is less than" is…
- Closure (mathematics) In mathematics, a subset of a larger set is closed under a given operation on the larger set if performing that operation on members of the subset always…
- Reflexive relation In mathematics, a binary relation R on a set X is reflexive if it relates every element of X to itself. An example of a reflexive relation is the relation…
- Partially ordered set In mathematics, especially order theory, a partial order on a set is an arrangement such that, for certain pairs of elements, one precedes the other. The…
- Composition of relations In the mathematics of binary relations, the composition of relations is the forming of a new binary relation R;S from two given binary relations R and…
- Transitive relation In mathematics, a binary relation R on a set X is transitive if, for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates…
- Glossary of order theory Look up Appendix:Glossary of order theory in Wiktionary, the free dictionary. This is a glossary of some terms used in various branches of mathematics…