A Nearly-Linear Time Framework for Graph-Structured Sparsity
نویسندگان
چکیده
We introduce a framework for sparsity structures defined via graphs. Our approach is flexible and generalizes several previously studied sparsity models. Moreover, we provide efficient projection algorithms for our sparsity model that run in nearly-linear time. In the context of sparse recovery, our framework achieves an informationtheoretically optimal sample complexity for a wide range of parameters. We complement our theoretical analysis with experiments showing that our algorithms also improve on prior work in practice.
منابع مشابه
Nearly Linear-Time Model-Based Compressive Sensing
Compressive sensing is a method for recording a k-sparse signal x ∈ R with (possibly noisy) linear measurements of the form y = Ax, where A ∈ Rm×n describes the measurement process. Seminal results in compressive sensing show that it is possible to recover the signal x from m = O(k log n k ) measurements and that this is tight. The model-based compressive sensing framework overcomes this lower ...
متن کاملA Nearly-Linear Time Framework for Graph-Structured Sparsity
We start with a more detailed description of our experimental setup. All three images used in Section 6 (Figure 2) are grayscale images of dimension 100 × 100 pixels with sparsity around 4% to 6%. The background-subtracted image was also used for the experimental evaluation in (Huang et al., 2011). The angiogram image is a slightly sparsified version of the image on the Wikipedia page about ang...
متن کاملTechnical Report: A Generalized Matching Pursuit Approach for Graph-Structured Sparsity
Sparsity-constrained optimization is an important and challenging problem that has wide applicability in data mining, machine learning, and statistics. In this paper, we focus on sparsity-constrained optimization in cases where the cost function is a general nonlinear function and, in particular, the sparsity constraint is defined by a graph-structured sparsity model. Existing methods explore t...
متن کاملA Generalized Matching Pursuit Approach for Graph-Structured Sparsity
Sparsity-constrained optimization is an important and challenging problem that has wide applicability in data mining, machine learning, and statistics. In this paper, we focus on sparsity-constrained optimization in cases where the cost function is a general nonlinear function and, in particular, the sparsity constraint is defined by a graph-structured sparsity model. Existing methods explore t...
متن کاملA Fast Algorithm for Separated Sparsity via Perturbed Lagrangians
Sparsity-based methods are widely used in machine learning, statistics, and signal processing. Thereis now a rich class of structured sparsity approaches that expand the modeling power of the sparsityparadigm and incorporate constraints such as group sparsity, graph sparsity, or hierarchical sparsity. Whilethese sparsity models offer improved sample complexity and better interpr...
متن کامل