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We propose a sparsity function as follows (14).
In this paper we present a continuous yet non-differentiable sparsity function which constitutes a tight lower bound on the cardinality function.
The novelty of this approach is that we cast the problem of minimizing the new sparsity function as a problem with a bilinear objective function.
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where the ℓ 1 norm is replaced by the ℓ p norm as sparsity promoting function and r is a slack variable that represents the corrupting sparse vector.
To exploit spatial sparsity, we use a basis function to tailor the sparse representation of the rainfall intensity.
By minimizing the sum of this performance measure and a sparsity-promoting penalty function, the alternating direction method of multipliers identifies sparsity structures that strike a balance between the performance measure and the number of edges in the graph.
We present a numerical comparison to other sparsity encouraging penalty functions for several applications.
The sparse-autoencoder is a variant of autoencoder (AE) with added sparsity in its cost function [5].
Figure 3 shows the contour set for two levels of sparsity ( and ) as a function of the number of projections and of the quantization distortion of the measurements.
For the second configuration, the average values of the four metrics as a function of sparsity s are depicted in Fig. 3 for the BIHT, RFPI, LP, GAMP, and Algorithm 3 with fixed m=1000 and n=1000.
Our maximization problem becomes (2) where the objective function contains sparsity penalizations of the loading vectors (i = 1, 2, 3) and q.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com