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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."
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 ...
In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. [1] There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse but a common criterion is that the number of non-zero elements is roughly equal to the number of ...
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 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]
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
Fig. 1: A sketch of a small network displaying community structure, with three groups of nodes with dense internal connections and sparser connections between groups.. In the study of networks, such as computer and information networks, social networks and biological networks, a number of different characteristics have been found to occur commonly, including the small-world property, heavy ...
There is an exponential increase in volume associated with adding extra dimensions to a mathematical space.For example, 10 2 = 100 evenly spaced sample points suffice to sample a unit interval (try to visualize a "1-dimensional" cube) with no more than 10 −2 = 0.01 distance between points; an equivalent sampling of a 10-dimensional unit hypercube with a lattice that has a spacing of 10 −2 ...