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A simple unweighted network of size is called sparse if the number of links in it is much smaller than the maximum possible number of links : [1] = (). In any given (real) network, the number of nodes N and links M are just two numbers, therefore the meaning of the much smaller sign (above) is purely colloquial and informal, and so are statements like "many real networks are sparse."
Compressed sensing (also known as compressive sensing, compressive sampling, or sparse sampling) is a signal processing technique for efficiently acquiring and reconstructing a signal, by finding solutions to underdetermined linear systems.
Sparse approximation ideas and algorithms have been extensively used in signal processing, image processing, machine learning, medical imaging, array processing, data mining, and more. In most of these applications, the unknown signal of interest is modeled as a sparse combination of a few atoms from a given dictionary, and this is used as the ...
SPARSE contains TALLY, the class of unary languages, since these have at most one string of any one length. Although not all languages in P/poly are sparse, there is a polynomial-time Turing reduction from any language in P/poly to a sparse language. [1] Fortune showed in 1979 that if any sparse language is co-NP-complete, then P = NP. [2]
For a graph family, the existence of k and l such that the graphs in the family are all (k,l)-sparse is equivalent to the graphs in the family having bounded degeneracy or having bounded arboricity. More precisely, it follows from a result of Nash-Williams (1964) that the graphs of arboricity at most a are exactly the (a,a)-sparse graphs. [5]
Sparse may refer to: Sparse, a software static analysis tool; Sparse language, a type of formal language in computational complexity theory; Sparse matrix, in numerical analysis, a matrix populated primarily with zeros; Sparse file, a computer file mostly empty; Sparse network, a network with many fewer connections than possible
A sparse index in databases is a file with pairs of keys and pointers for every block in the data file. Every key in this file is associated with a particular pointer to the block in the sorted data file. In clustered indices with duplicate keys, the sparse index points to the lowest search key in each block.
Sparse dictionary learning (also known as sparse coding or SDL) is a representation learning method which aims to find a sparse representation of the input data in the form of a linear combination of basic elements as well as those basic elements themselves.