This research introduces dynamic portfolio cuts using a spectral approach for graph-theoretic diversification.
problem Traditional methods for estimating asset-return covariance assume statistical time-invariance, failing to capture the nonstationary nature of asset price movements.
method Introduces graph spectral estimators that account for nonstationarity, partitioning the market graph into time-evolving clusters for dynamic portfolio cuts.
result Demonstrates the advantages of the proposed framework over traditional methods through numerical case studies using real-world price data.
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.
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.
Study optimal adjustment sets for causal policies with hidden variables.
problem Estimating dynamic treatment regimes with hidden variables.
method Developed criteria for graphs without hidden variables to compare estimators, extended to dynamic policies and hidden variables.
result Existence and computation of optimal minimal and globally optimal adjustment sets.
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…
We showed in another paper [arXiv:1103.1759] that every connected graph can be realized as the cut locus of some point on some riemannian surface S. Here, criteria for the orientability of S are given, and are applied to classify the distinct, orientable, cut locus structures on graphs with four generating cycles.
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.
Proves a generalized Whitehead cut vertex lemma for tree groups.
problem Extending Whitehead's cut vertex lemma to tree group conjugacy classes.
method Proves a version of Whitehead's lemma for tree groups.
result Establishes a cut vertex in star graphs for tree group conjugacy classes.
Spectral clustering is sensitive to how graphs are constructed from data particularly when proximal and imbalanced clusters are present. We show that Ratio-Cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced data since they tend to emphasize cut sizes over cut values. We propose a graph partit…
Proves bounds on spanning two-forests and random cut sizes.
problem Counting spanning two-forests and estimating random cut sizes.
method Uses pairwise effective resistances and potential theory.
result Establishes bounds on the number of spanning two-forests and average cut size.
Spectral clustering (SC) and graph-based semi-supervised learning (SSL) algorithms are sensitive to how graphs are constructed from data. In particular if the data has proximal and unbalanced clusters these algorithms can lead to poor performance on well-known graphs such as k-NN, full-RBF, ε-graphs. This is becaus…
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.
A novel hypergraph partitioning method using tensor eigenvalue decomposition captures super-dyadic interactions.
problem Capturing super-dyadic interactions in k-uniform hypergraphs.
method Tensor-based representation and tensor eigenvalue decomposition for capturing interactions.
result Improved min-cut solution on 2-uniform hypergraphs (graphs) compared to standard spectral partitioning.
Paper connects probability density cuts to graph theory eigenfunctions.
problem Developing sparse cuts for probability densities.
method Defines sparse cuts and principal eigenfunctions for probability densities, proving Cheeger and Buser inequalities.
result No such inequalities hold for prior definitions, proving new inequalities for probability densities.
Spectral clustering methods which are frequently used in clustering and community detection applications are sensitive to the specific graph constructions particularly when imbalanced clusters are present. We show that ratio cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced cluster sizes sin…
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.
Develops a new weighted Laplacian method for graph problems.
problem Graph partitioning and balanced minimum cut problems.
method Weighted Laplacian method based on graph theory and PDEs.
result Established equivalence relations among graph problems.
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.
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…
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.
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…
The monitoring of large dynamic networks is a major chal- lenge for a wide range of application. The complexity stems from properties of the underlying graphs, in which slight local changes can lead to sizable variations of global prop- erties, e.g., under certain conditions, a single link cut that may be overlooked du…
Min-cut clustering, based on minimizing one of two heuristic cost-functions proposed by Shi and Malik, has spawned tremendous research, both analytic and algorithmic, in the graph partitioning and image segmentation communities over the last decade. It is however unclear if these heuristics can be derived from a more g…
We proved in another paper that every connected graph can be realized as the cut locus of some point on some riemannian surface. Here we give upper bounds on the number of such realizations.
Spectral Clustering as a relaxation of the normalized/ratio cut has become one of the standard graph-based clustering methods. Existing methods for the computation of multiple clusters, corresponding to a balanced k-cut of the graph, are either based on greedy techniques or heuristics which have weak connection to th…
We prove that every connected graph can be realized as the cut locus of some point on some Riemannian surface S which, in some cases, has constant curvature. We study the stability of such realizations, and their generic behavior.
PGNs dynamically infer and use graph structures to improve model generalization.
problem Static graph structures inferred by machine learning practitioners are often suboptimal for tasks.
method PGNs augment graphs with dynamically inferred pointers for improved model generalization.
result PGNs outperform unrestricted GNNs and Deep Sets on dynamic graph connectivity tasks.
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.
Spectral clustering has become one of the most widely used clustering techniques when the structure of the individual clusters is non-convex or highly anisotropic. Yet, despite its immense popularity, there exists fairly little theory about performance guarantees for spectral clustering. This issue is partly due to the…
TGN outperforms static GNNs in detecting financial fraud.
problem Anomaly detection in dynamic financial networks.
method Temporal Graph Networks (TGN) for capturing edge dynamics.
result TGN significantly outperforms static GNNs in AUC metrics.
Graph construction is a crucial step in spectral clustering (SC) and graph-based semi-supervised learning (SSL). Spectral methods applied on standard graphs such as full-RBF, ε-graphs and k-NN graphs can lead to poor performance in the presence of proximal and unbalanced data. This is because spectral methods based…
New invariant defined for Weinstein domains, related to Kirby-Thompson's invariant.
problem Defining a symplectic invariant for Weinstein domains.
method Contact cut graph, Lefschetz fibrations, multisections with divides.
result Definition of Weinstein L-invariant and its relation to Kirby-Thompson's invariant. This paper presents a method to summarize directed graphs while preserving edge information.
problem Summarizing directed graphs while maintaining edge directionality.
method A model based on minimizing reconstruction error with non-negative constraints, related to Max-Cut criterion, using multiplicative update algorithms.
result The proposed method identifies compressed nodes and directed compressed relations, providing a more accurate representation of directed graphs.
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…
We investigate Legendrian graphs in (R3,ξstd). We extend the classical invariants, Thurston-Bennequin number and rotation number to Legendrian graphs. We prove that a graph can be Legendrian realized with all its cycles Legendrian unknots with tb=−1 and rot=0 if and only if it does not contain K4 as a mi…
Paper provides a performance guarantee for spectral clustering.
problem Finding the global solution to the minimum ratio cut problem.
method Two-step spectral clustering method with a rounding step, analyzed using two-to-infinity norm perturbation bounds.
result Spectral clustering is guaranteed to output the global solution under certain conditions.
The paper studies grid homology for spatial graphs and proves a Künneth formula for connected sums.
problem Understanding grid homology for spatial graphs with various types of edges.
method Developed grid homology for spatial graphs with cut edges and applied it to prove a Künneth formula for connected sums.
result A Künneth formula for knot Floer homology of connected sums is proven using grid homology.
We provide an example in each rank of an ageometric fully irreducible outer automorphism whose ideal Whitehead graph has a cut vertex. Consequently, we show that there exist examples in each rank of Handel-Mosher axis bundles that are not just a single axis, as well as of "nongeneric" behavior in the sense of the "trai…
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.
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.
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.
Can one reduce the size of a graph without significantly altering its basic properties? The graph reduction problem is hereby approached from the perspective of restricted spectral approximation, a modification of the spectral similarity measure used for graph sparsification. This choice is motivated by the observation…
Tangles improve clustering in various datasets.
problem Clustering diverse datasets efficiently and accurately.
method Tangles aggregate cuts to identify dense structures, leading to soft cluster characterization.
result Tangle framework generates hierarchical soft dendrograms for cluster exploration.
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.
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.
The graph Laplacian plays key roles in information processing of relational data, and has analogies with the Laplacian in differential geometry. In this paper, we generalize the analogy between graph Laplacian and differential geometry to the hypergraph setting, and propose a novel hypergraph p-Laplacian. Unlike the …
The homology of Kontsevich's commutative graph complex parameterizes finite type invariants of odd dimensional manifolds. This {\it graph homology} is also the twisted homology of Outer Space modulo its boundary, so gives a nice point of contact between geometric group theory and quantum topology. In this paper we give…
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…