منابع مشابه
Seeded PageRank Solution Paths
We study the behaviour of network diffusions based on the PageRank random walk from a set of seed nodes. These diffusions are known to reveal small, localized clusters (or communities), and also large macro-scale clusters by varying a parameter that has a dual-interpretation as an accuracy bound and as a regularization level. We propose a new method that quickly approximates the result of the d...
متن کاملPersonalized PageRank Solution Paths
Personalized PageRank vectors used for many community detection and graph diffusion problems have a subtle dependence on a parameter epsilon that controls their accuracy. This parameter governs the sparsity of the solution and can be interpreted as a regularization parameter. We study algorithms to estimate the solution path as a function of the sparsity and propose two methods for this task. T...
متن کاملImage denoising via solution paths
Many image denoising methods can be characterized as minimizing “loss + penalty,” where the “loss” measures the fidelity of the denoised image to the data, and the “penalty” measures the smoothness of the denoising function. In this paper, we propose two models that use the L1-norm of the pixel updates as the penalty. The L1-norm penalty has the advantage of changing only the noisy pixels, whil...
متن کاملPiecewise Linear Regularized Solution Paths
We consider the generic regularized optimization problem β̂(λ) = arg minβ L(y,Xβ) + λJ (β). Efron, Hastie, Johnstone and Tibshirani [Ann. Statist. 32 (2004) 407–499] have shown that for the LASSO—that is, if L is squared error loss and J (β)= ‖β‖1 is the 1 norm of β—the optimal coefficient path is piecewise linear, that is, ∂β̂(λ)/∂λ is piecewise constant. We derive a general characterization of ...
متن کاملFollowing Curved Regularized Optimization Solution Paths
Regularization plays a central role in the analysis of modern data, where non-regularized fitting is likely to lead to over-fitted models, useless for both prediction and interpretation. We consider the design of incremental algorithms which follow paths of regularized solutions, as the regularization varies. These approaches often result in methods which are both efficient and highly flexible....
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ژورنال
عنوان ژورنال: European Journal of Applied Mathematics
سال: 2016
ISSN: 0956-7925,1469-4425
DOI: 10.1017/s0956792516000280