A new kernel for ranked data tackles computational challenges.
problem Complex geometric structure and partial rankings make existing algorithms infeasible for real-world applications.
method Derives a graph cut kernel that combines submodular optimization and kernel-based methods.
result The graph cut kernel efficiently handles large-scale ranked data.
It has been recently shown that a large class of balanced graph cuts allows for an exact relaxation into a nonlinear eigenproblem. We review briefly some of these results and propose a family of algorithms to compute nonlinear eigenvectors which encompasses previous work as special cases. We provide a detailed analysis…
This paper provides theoretical guarantees for spectral clustering using graph cuts.
problem Lack of performance guarantees for spectral clustering.
method Convex relaxation of graph cuts, spectral proximity condition, algebraic connectivity, inter-cluster connectivity.
result Deterministic bounds for successful spectral clustering are derived.
New algorithm for multiway spectral clustering on Grassmann manifolds.
problem Efficiently computing multiple eigenvectors of a nonlinear graph Laplacian.
method Direct multiway spectral clustering in p-norm, reformulated as minimization on Grassmann manifold. result Monotonic decrease of balanced graph cuts leads to optimal solutions.
Algorithms based on spectral graph cut objectives such as normalized cuts, ratio cuts and ratio association have become popular in recent years because they are widely applicable and simple to implement via standard eigenvector computations. Despite strong performance for a number of clustering tasks, spectral graph cu…
The maximum a posteriori (MAP) configuration of binary variable models with submodular graph-structured energy functions can be found efficiently and exactly by graph cuts. Max-product belief propagation (MP) has been shown to be suboptimal on this class of energy functions by a canonical counterexample where MP conver…
Proposes a new method for hyperspectral image dimensionality reduction.
problem Highly correlated noisy hyperspectral images.
method Trace Lasso-L1 Graph Cut method using L1-norm for robustness and sparsity.
result Optimal projection matrix maximizing between-class dispersion to within-class dispersion.
Graph cuts find global optima for Potts models in slight perturbations.
problem Finding optimal solutions in Potts models with graph cuts.
method α-expansion algorithm for MAP inference, with certification for perturbations.
result All local minima are global minima in slight perturbations, and solutions are close to original.
This paper establishes the consistency of a family of graph-cut-based algorithms for clustering of data clouds. We consider point clouds obtained as samples of a ground-truth measure. We investigate approaches to clustering based on minimizing objective functionals defined on proximity graphs of the given sample. Our f…
The paper optimizes spatial experimental designs to improve causal effect estimation.
problem Optimizing spatial experimental designs to enhance causal effect estimation accuracy.
method Proposes a surrogate function for MSE and uses graph cut algorithms to learn optimal designs.
result The method accommodates spatial interference and covariance, is computationally efficient, and validated by theoretical and numerical experiments.
Improved model capacity for graph cut algorithms by relaxing submodularity constraints.
problem Improving graph cut algorithms for complex image processing tasks.
method Enforce probably approximately submodular pairwise potentials instead of guaranteed submodular ones.
result Substantial improvement in model capacity with reduced inference error.
Novel semi-supervised method for online structure learning in noisy data streams.
problem Discovering complex relations in noisy data streams with limited labelled data.
method Combines graph-cut minimization and first-order logic for online, single-pass label completion.
result Improves accuracy of structure learning system by completing missing labels.
New Karger-like algorithms solve graph cuts, useful for image segmentation.
problem Finding minimum cuts in graphs and graph-based semi-supervised learning.
method Extensions of Karger's contraction algorithm for s-t-mincut and normalized cut problems. result Simple new algorithm based on Karger's original, yields linear runtime and interpretable potential.
Study shows convergence rates for Cheeger cuts on data clouds.
problem Optimizing graph cuts for clustering data sampled from a manifold.
method Analyzes statistical properties of Cheeger cuts on proximity graphs built from data.
result Obtains high probability convergence rates for Cheeger constant and cuts.
Paper proposes a new method to minimize submodular functions with fewer calls to simpler oracles.
problem Minimizing the sum of submodular set functions with limited information.
method Introduces a modified convex problem requiring constrained total variation oracles that can be solved with fewer calls to minimization oracles.
result Shows significant reduction in the number of calls to minimization oracles.
Efficiently learns perturb-and-map models using weighted log-likelihood.
problem Structured output prediction with weighted Hamming losses.
method Generalizes perturb-and-MAP framework, uses dynamic graph cuts for MAP inference, and double stochastic gradient descent for efficient learning.
result Shows efficiency in learning log-supermodular models with weak supervision.
We give polynomial-time algorithms for the exact computation of lowest-energy (ground) states, worst margin violators, log partition functions, and marginal edge probabilities in certain binary undirected graphical models. Our approach provides an interesting alternative to the well-known graph cut paradigm in that it …
Poisson learning improves graph-based semi-supervised learning at very low label rates.
problem Degeneracy of Laplacian semi-supervised learning at low label rates.
method Replaces label assignment with source and sink placement, solving Poisson equation.
result Provably more stable and informative predictions than Laplacian learning.
Graph theory improves portfolio optimization for diversified investments.
problem Standard portfolio optimization ignores data structure, leading to suboptimal results.
method Introduces portfolio cut paradigm to incorporate graph theory into portfolio optimization.
result Graph-theoretic portfolio partitioning allows for robust and tractable asset allocation schemes.
PPC learns binary codes from data similarities and dissimilarities.
problem Creating efficient binary codes from data similarities and dissimilarities.
method PPC learns binary codes by modeling attractive and repulsive forces in a signed graph.
result PPC achieves superior results in nearest-neighbor searches compared to spectral methods.
The paper proposes a method to learn discriminative multilevel dictionaries for supervised image classification.
problem Improving sparse representation for supervised image classification.
method Learning structured multilevel dictionaries with discriminative constraints for each class, using reconstruction errors of image patches.
result Competitive results compared to state-of-the-art methods on texture image classification.
Improves scalability of Bayesian optimization for combinatorial spaces.
problem Optimizing expensive functions over large combinatorial spaces.
method Parametrized Submodular Relaxation (PSR) to solve AFO problems for BOCS.
result Significant improvements in scalability and accuracy for BOCS model.
We propose a new method to model multi-way similarities into hypergraphs for clustering.
problem Clustering real-valued data using hypergraphs with multi-way similarities.
method Formulate multi-way similarities using kernel functions, establish connections to hypergraph cut, and develop a fast spectral clustering algorithm.
result Our method outperforms existing graph and heuristic modeling methods in clustering performance.
Novel framework provides statistical significance for image segmentation results.
problem Evaluating the reliability of individual image segmentation results.
method Selective inference to account for segmentation bias in p-value computation.
result Valid p-values for segmentation results, accounting for bias.
Survey on community detection methods and their theoretical properties.
problem Consistent estimation of community labels in networks.
method Various community detection methods and their theoretical properties.
result Review of community detection methods and their theoretical properties.
In this paper we relate the partition function to the max-statistics of random variables. In particular, we provide a novel framework for approximating and bounding the partition function using MAP inference on randomly perturbed models. As a result, we can use efficient MAP solvers such as graph-cuts to evaluate the c…
SoulMate links short texts through multi-aspect embeddings.
problem Linking authors of noisy, ambiguous short texts.
method Neural network-based temporal-textual framework generating author subgraphs.
result Higher performance in linking short-text authors compared to competitors.
Transformer-based method discovers objects from images without labels.
problem Discovering objects in images without labeled data.
method Graph-based approach using self-supervised transformer features and normalized graph-cut.
result Significantly boosts performance in unsupervised object discovery.
Spectral clustering is a popular and versatile clustering method based on a relaxation of the normalised graph cut objective. Despite its popularity, however, there is no single agreed upon method for tuning the important scaling parameter, nor for determining automatically the number of clusters to extract. Popular he…
In this paper, we study statistical classification accuracy of two different Markov field environments for pixelwise image segmentation, considering the labels of the image as hidden states and solving the estimation of such labels as a solution of the MAP equation. The emission distribution is assumed the same in all …
This paper studies the large sample asymptotics of data analysis procedures based on the optimization of functionals defined on k-NN graphs on point clouds. The paper is framed in the context of minimization of balanced cut functionals, but our techniques, ideas and results can be adapted to other functionals of rele…
Inference in general Markov random fields (MRFs) is NP-hard, though identifying the maximum a posteriori (MAP) configuration of pairwise MRFs with submodular cost functions is efficiently solvable using graph cuts. Marginal inference, however, even for this restricted class, is in #P. We prove new formulations of deriv…
Unified framework for differentiable graph partitioning with probabilistic cuts.
problem Lack of general guarantees and principled gradients in prior probabilistic relaxations of graph cuts.
method Unified probabilistic framework covering a wide class of cuts, including Normalized Cut, with tight analytic upper bounds.
result Rigorous, numerically stable foundation for scalable, differentiable graph partitioning.
An autonomous variational inference algorithm for arbitrary graphical models requires the ability to optimize variational approximations over the space of model parameters as well as over the choice of tractable families used for the variational approximation. In this paper, we present a novel combination of graph part…
We propose and analyze a constrained level-set method for semi-automatic image segmentation. Our level-set model with constraints on the level-set function enables us to specify which parts of the image lie inside respectively outside the segmented objects. Such a-priori information can be expressed in terms of upper a…
We consider active, semi-supervised learning in an offline transductive setting. We show that a previously proposed error bound for active learning on undirected weighted graphs can be generalized by replacing graph cut with an arbitrary symmetric submodular function. Arbitrary non-symmetric submodular functions can be…
Proposes TDNs for learning complex video structures.
problem Complex temporal dependencies in sequential data, especially videos.
method Temporal Dependency Networks (TDNs) using graph representations and graph convolutions.
result Efficiently learns complex semantic structures of video data.
Empirical error estimates improve graph sparsification reliability.
problem Uncertainty in sparsification error limits downstream computations reliability.
method Data-driven approach to compute empirical error estimates.
result Empirical error estimates provide theoretical guarantees and are computationally feasible.
Proposes GIC for graph convolution, improving graph classification.
problem Graphs lack local convolution kernels like images.
method GIC framework using edge-induced and vertex-induced Gaussian mixtures.
result GIC achieves state-of-the-art results on graph classification.
New method for probabilistic modeling of integer submodular functions.
problem Lack of probabilistic modeling for integer submodular functions.
method Proposed Generalized Multilinear Extension and block-coordinate ascent algorithm.
result Demonstrated effectiveness and viability on real-world datasets.
New Frank-Wolfe algorithm solves nonsmooth convex problems quickly.
problem Nonsmooth convex optimization problems in machine learning.
method Deterministic Frank-Wolfe algorithm with coreset guarantees.
result Approximate solutions to various machine learning problems in sublinear time.
Proposes a new graph trend filtering model for inhomogeneous graph signals.
problem Estimating piecewise smooth signals over a graph with varying smoothness levels.
method Introduces a l2,0 norm penalized Graph Trend Filtering (GTF) model and two solution methods: spectral decomposition and simulated annealing.
result The GTF model performs better than existing approaches in denoising, support recovery, and semi-supervised classification.
CB-GLNs learn video data's complex dependencies via graph representation.
problem Capturing complex dependency structures in sequential data like videos.
method Represent video data as a graph, find compositional dependencies via graph-cut and message passing.
result CB-GLNs efficiently learn video data's semantic compositional structure.
As an increasing number of genome-wide association studies reveal the limitations of attempting to explain phenotypic heritability by single genetic loci, there is growing interest for associating complex phenotypes with sets of genetic loci. While several methods for multi-locus mapping have been proposed, it is often…
The paper explains how data augmentation improves semi-supervised learning efficiency.
problem Improving accuracy from a small fraction of labeled data.
method Data augmentation induces a similarity graph, which is graph-Laplacian-regularized for downstream learning.
result A fast transductive rate of O(1/nL) is achieved, reducing the number of labels needed. TokenCut detects and segments objects in images and videos without supervision.
problem Detecting and segmenting salient objects in images and videos without labeled data.
method Graph-based approach using self-supervised transformer features and Normalized Cut algorithm.
result Achieves state-of-the-art results on various detection and segmentation tasks.
The paper introduces submodular information measures for machine learning applications.
problem Generalizing information-theoretic measures to non-random variables.
method Developing combinatorial information measures based on submodular functions.
result Submodular mutual information is submodular in one argument for certain submodular functions.
Submodular functions can be exactly minimized in polynomial time, and the special case that graph cuts solve with max flow \cite{KZ:PAMI04} has had significant impact in computer vision \cite{BVZ:PAMI01,Kwatra:SIGGRAPH03,Rother:GrabCut04}. In this paper we address the important class of sum-of-submodular (SoS) function…