Abstract
We present a novel condition, which we term the net- work nullspace property, which ensures accurate recovery of graph signals representing massive network-structured datasets from few signal values. The network nullspace property couples the cluster structure of the underlying network-structure with the geometry of the sampling set. Our results can be used to design efficient sampling strategies based on the network topology.
Highlights
A recent line of work proposed efficient convex optimization methods for recovering graph signals which represent label information of network structured datasets
We introduce a novel recovery condition, termed the network nullspace property (NNSP), which guarantees convex optimization to accurately recovery of clustered (“piece-wise constant”) graph signals from knowledge of its values on a small subset of sampled nodes
Our analysis reveals that if cluster boundaries are wellconnected to the sampled nodes, accurate recovery of clustered graph signals is possible by solving a convex optimization problem
Summary
A recent line of work proposed efficient convex optimization methods for recovering graph signals which represent label information of network structured datasets (cf. [1, 2]). These methods rest on the hypothesis that the true underlying graph signal is nearly constant over well-connected subsets of nodes (clusters). We introduce a novel recovery condition, termed the network nullspace property (NNSP), which guarantees convex optimization to accurately recovery of clustered (“piece-wise constant”) graph signals from knowledge of its values on a small subset of sampled nodes. The NCC is a stronger condition in the sense that once the NCC is satisfied, the NNSP is guaranteed to hold
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