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A nested set collection or nested set family is a collection of sets that consists of chains of subsets forming a hierarchical structure, like Russian dolls. It is used as reference concept in scientific hierarchy definitions, and many technical approaches, like the tree in computational data structures or nested set model of relational databases.
In numerical mathematics, hierarchical matrices (H-matrices) [1] [2] [3] are used as data-sparse approximations of non-sparse matrices. While a sparse matrix of dimension can be represented efficiently in () units of storage by storing only its non-zero entries, a non-sparse matrix would require () units of storage, and using this type of matrices for large problems would therefore be ...
The nested set model is a technique for representing nested set collections (also known as trees or hierarchies) in relational databases.. It is based on Nested Intervals, that "are immune to hierarchy reorganization problem, and allow answering ancestor path hierarchical queries algorithmically — without accessing the stored hierarchy relation".
The high rank matrix completion in general is NP-Hard. However, with certain assumptions, some incomplete high rank matrix or even full rank matrix can be completed. Eriksson, Balzano and Nowak [10] have considered the problem of completing a matrix with the assumption that the columns of the matrix belong to a union of multiple low-rank subspaces.
Hierarchical Data Format (HDF) is a set of file formats (HDF4, HDF5) designed to store and organize large amounts of data.Originally developed at the U.S. National Center for Supercomputing Applications, it is supported by The HDF Group, a non-profit corporation whose mission is to ensure continued development of HDF5 technologies and the continued accessibility of data stored in HDF.
In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children (depending on the type of tree), but must be connected to exactly one parent, [ 1 ] [ 2 ] except for the root node, which has no parent (i.e., the ...
The term hierarchy is used to stress a hierarchical relation among the elements. Sometimes, a set comes equipped with a natural hierarchical structure. For example, the set of natural numbers N is equipped with a natural pre-order structure, where n ≤ n ′ {\displaystyle n\leq n'} whenever we can find some other number m {\displaystyle m} so ...
NumPy (pronounced / ˈ n ʌ m p aɪ / NUM-py) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. [3]