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Label propagation is a semi-supervised algorithm in machine learning that assigns labels to previously unlabeled data points. At the start of the algorithm, a (generally small) subset of the data points have labels (or classifications). These labels are propagated to the unlabeled points throughout the course of the algorithm. [1]
In the mathematical discipline of graph theory, a graph labeling is the assignment of labels, traditionally represented by integers, to edges and/or vertices of a graph. [ 1 ] Formally, given a graph G = ( V , E ) , a vertex labeling is a function of V to a set of labels; a graph with such a function defined is called a vertex-labeled graph .
Connected-component labeling (CCL), connected-component analysis (CCA), blob extraction, region labeling, blob discovery, or region extraction is an algorithmic application of graph theory, where subsets of connected components are uniquely labeled based on a given heuristic. Connected-component labeling is not to be confused with segmentation.
A graceful labeling. Vertex labels are in black, edge labels in red.. In graph theory, a graceful labeling of a graph with m edges is a labeling of its vertices with some subset of the integers from 0 to m inclusive, such that no two vertices share a label, and each edge is uniquely identified by the absolute difference between its endpoints, such that this magnitude lies between 1 and m ...
Label each minimum with a distinct label. Initialize a set S with the labeled nodes. Extract from S a node x of minimal altitude F, that is to say F(x) = min{F(y)|y ∈ S}. Attribute the label of x to each non-labeled node y adjacent to x, and insert y in S. Repeat Step 2 until S is empty.
The algorithm maintains the condition that 𝓁 is a valid labeling during its execution. This can be proven true by examining the effects of the push and relabel operations on the label function 𝓁. The relabel operation increases the label value by the associated minimum plus one which will always satisfy the 𝓁(u) ≤ 𝓁(v) + 1 constraint.
Pattern recognition is the task of assigning a class to an observation based on patterns extracted from data. While similar, pattern recognition (PR) is not to be confused with pattern machines (PM) which may possess (PR) capabilities but their primary function is to distinguish and create emergent patterns.
Function labels consist of an identifier, followed by a colon. Each such label points to a statement in a function and its identifier must be unique within that function. Other functions may use the same name for a label. Label identifiers occupy their own namespace – one can have variables and functions with the same name as a label.