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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."
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 ...
The opposite, a graph with only a few edges, is a sparse graph. The distinction of what constitutes a dense or sparse graph is ill-defined, and is often represented by 'roughly equal to' statements. Due to this, the way that density is defined often depends on the context of the problem.
However, if there is a unique sparse solution to the underdetermined system, then the compressed sensing framework allows the recovery of that solution. Solution / reconstruction method Example of the retrieval of an unknown signal (gray line) from few measurements (black dots) using the knowledge that the signal is sparse in the Hermite ...
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.
A frontal solver is an approach to solving sparse linear systems which is used extensively in finite element analysis. [1] Algorithms of this kind are variants of Gauss elimination that automatically avoids a large number of operations involving zero terms due to the fact that the matrix is only sparse. [2]
Sparse principal component analysis (SPCA or sparse PCA) is a technique used in statistical analysis and, in particular, in the analysis of multivariate data sets. It extends the classic method of principal component analysis (PCA) for the reduction of dimensionality of data by introducing sparsity structures to the input variables.
Protocol Independent Multicast - Sparse-Mode (PIM-SM) is a protocol for efficiently routing Internet Protocol (IP) packets to multicast groups that may span wide-area and inter-domain internets.