The densest k-clique problem is solved via semidefinite programming for weighted graphs.
problem Clustering dense weighted graphs into disjoint subgraphs maximizing density.
method Solving a semidefinite relaxation to recover clusters with high probability.
result Clusters can be recovered from the solution of a semidefinite relaxation with high probability.
New convex method solves densest subgraph problem with high probability.
problem Finding the densest subgraph in a graph.
method Convex relaxation of low-rank plus sparse decomposition of adjacency matrices.
result Optimal solution of convex relaxation recovers densest subgraph with high probability.
Faster algorithm for generalized mean densest subgraph problem.
problem Finding subgraphs with highest average p-th-power degree. method GENPEEL++ algorithm, which yields (2(p+1))1/p-approximation for p∈[1,+∞) with time complexity O(m(logn)). result GENPEEL++ algorithm provides faster and more efficient solution for generalized mean densest subgraph problem.
Detecting edge correlation between two graphs sharpens a threshold based on densest subgraph.
problem Detecting edge correlation between two Erdős-Rényi graphs.
method Formulated as a hypothesis testing problem, connecting to densest subgraph detection.
result Sharp information-theoretic threshold established for edge correlation detection.
This paper considers the sparse eigenvalue problem, which is to extract dominant (largest) sparse eigenvectors with at most k non-zero components. We propose a simple yet effective solution called truncated power method that can approximately solve the underlying nonconvex optimization problem. A strong sparse recove…
A method to give users control over automated decisions by enumerating decision subspaces.
problem Users lack control over automated decision-making processes.
method Formalizes the problem as an evasion attack and uses subspace enumeration.
result Implemented for decision forests, showing how to map the problem to k-clique enumeration. Exact partitioning of high-order planted models achieved through convex optimization.
problem Efficiently partitioning hypergraphs generated by high-order planted models.
method Solving a computationally efficient convex optimization problem with a tensor nuclear norm constraint.
result Exact recovery of true underlying cluster structures with high probability.
Paper shows dictionary learning is hard but proposes efficient schemes.
problem Sparse representation dictionary learning problem
method Polynomial time reduction of densest cut problem, successive convex approximation strategies
result Proposed scheme converges to stationary points under mild assumptions
This paper studies the problem of detecting the presence of a small dense community planted in a large Erdős-Rényi random graph G(N,q), where the edge probability within the community exceeds q by a constant factor. Assuming the hardness of the planted clique detection problem, we show that the computatio…
Study information limits for community detection in sub-hypergraphs.
problem Identify limits for exact community detection in sub-hypergraphs.
method Use Fano's inequality to define model parameters and identify success and failure regions.
result Identify regions where algorithms succeed or fail in exact recovery.
Sparse linear regression is hard to solve efficiently, even with k-sparse solutions.
problem Sparse linear regression problem with k-sparse solutions.
method Fine-grained complexity and hardness assumptions.
result No better-than-brute-force algorithms exist for sparse linear regression.
New GAN model deblends galaxy images with high accuracy and speed.
problem Deblending blended galaxy images in dense regions of the universe.
method Branched generative adversarial network (GAN) to produce images of deblended galaxies.
result High peak signal-to-noise ratio and structural similarity scores compared to ground truth images.
A biclustering algorithm finds dense disjoint subgraphs in weighted bipartite graphs.
problem Finding dense disjoint bicliques in a weighted bipartite graph.
method Semidefinite programming-based branch-and-cut algorithm with upper and lower bounds.
result The algorithm can solve much larger instances than general-purpose solvers.
Algorithm predicts item rankings from pairwise preferences with fewer samples than known methods.
problem Optimal recovery of true rankings from randomly chosen pairwise preferences.
method Embedding graph structure into orthonormal representations, using SVM for ranking prediction.
result Statistical consistency on Kendall's tau and Spearman's footrule with sample complexity of $O(n^2 χ(ar{G}))^{ rac{2}{3}}$ pairs.
We consider two closely related problems: planted clustering and submatrix localization. The planted clustering problem assumes that a random graph is generated based on some underlying clusters of the nodes; the task is to recover these clusters given the graph. The submatrix localization problem concerns locating hid…
We consider the classic problem of establishing a statistical ranking of a set of n items given a set of inconsistent and incomplete pairwise comparisons between such items. Instantiations of this problem occur in numerous applications in data analysis (e.g., ranking teams in sports data), computer vision, and machine …
After having investigated the regular prisms and prism tilings in the $\SLR$ space in the previous work \cite{Sz13-1} of the second author, we consider the problem of geodesic ball packings related to those tilings and their symmetry groups pq21. $\SLR$ is one of the eight Thurston geometries that can be de…