Singleappearing

Singleappearing refers to the property of an element that occurs exactly once within a defined domain, such as a string, list, dataset, or time series. The concept is used in data analysis and text processing to identify rare or unique items that do not repeat within the considered scope. A singleappearing item is defined by its frequency count being equal to one.

Definition and scope: The scope can be a sequence of characters, a column in a dataset, a window of a time series, or a multiset. An element is singleappearing if its observed frequency in that scope is one. This is distinct from broader notions of uniqueness in databases or mathematics, and from singleton items that may refer to isolated cases in a structure rather than to counts within a local context.

Examples: In the string "abracadabra," the letters 'c' and 'd' each appear exactly once, making them singleappearing within that string. In a data column, the value 7 might be singleappearing if it occurs only a single time in the entire column.

Detection and methods: Simple counting—scanning the domain and tallying frequencies—can identify singleappearing items. In streaming or large-scale data, hash maps or online counting algorithms can track frequencies incrementally. Approximate methods (for example, some probabilistic data structures) may estimate counts but cannot always confirm a true singleton without a second pass or exact counting.

Applications and variants: Uses include data cleaning to flag rare values, anomaly detection, and natural language processing to extract unique tokens. Variants include identifying single appearances within sliding windows or time intervals, and handling multi-byte or normalized encodings to ensure accurate counting.

See also: frequency analysis, distinct values, unique elements, anomaly detection.