IA Scholar Query: Min-Max Correlation Clustering via MultiCut.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgThu, 15 Sep 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Fair Correlation Clustering in General Graphs
https://scholar.archive.org/work/ozbukldhwncpbcaezchzmn4kt4
We consider the family of Correlation Clustering optimization problems under fairness constraints. In Correlation Clustering we are given a graph whose every edge is labeled either with a + or a -, and the goal is to find a clustering that agrees the most with the labels: + edges within clusters and - edges across clusters. The notion of fairness implies that there is no over, or under, representation of vertices in the clustering: every vertex has a color and the distribution of colors within each cluster is required to be the same as the distribution of colors in the input graph. Previously, approximation algorithms were known only for fair disagreement minimization in complete unweighted graphs. We prove the following: (1) there is no finite approximation for fair disagreement minimization in general graphs unless P = NP (this hardness holds also for bicriteria algorithms); and (2) fair agreement maximization in general graphs admits a bicriteria approximation of ≈ 0.591 (an improved ≈ 0.609 true approximation is given for the special case of two uniformly distributed colors). Our algorithm is based on proving that the sticky Brownian motion rounding of [Abbasi Zadeh-Bansal-Guruganesh-Nikolov-Schwartz-Singh SODA'20] copes well with uncut edges.Roy Schwartz, Roded Zats, Amit Chakrabarti, Chaitanya Swamywork_ozbukldhwncpbcaezchzmn4kt4Thu, 15 Sep 2022 00:00:00 GMTParameterized algorithmics for time-evolving structures: temporalizing and multistaging
https://scholar.archive.org/work/uyaoernzvvb7rmwysi2x6b5yzi
The thesis studies temporal graph problems and multistage problems. Since these problems typically are computationally hard, the focus is on developing fast exact (FPT-)algorithms. Temporal graph problems. A temporal graph is a graph whose edge set changes over time. Here, an edge at a specific time step is called time-edge. One of our main contributions is the introduction of a set of parameters tailored for temporal graph problems. We focus mainly on four problems on temporal graphs. Minimizing Reachability by Delaying. Given a temporal graph, a set of source vertices, and three integers k, r, and δ, the problem Minimizing Temporal Reachability by Delaying asks whether we can delay at most k time-edges by δ time steps (i.e., moving the edges δ time steps into the future) such that the sources can reach at most r vertices via temporal paths (i.e., paths using edges appearing in non-decreasing time-order). Our main contribution here is an algorithm running in O(r!k|G|) time, where |G| is the size of the temporal graph. This stands in contrast to the W[1]-hardness when parameterized by r for the problem of deleting instead of delaying time-edges. Restless Temporal Paths. A restless temporal path is a temporal path that can stay only a bounded amount of time at one vertex. Our main contribution here is a randomized algorithm to find a length-at-most-k restless temporal path from vertex s to vertex z in 4^ℓ |G|^O(1) time, where ℓ is the difference between k and the length of the shortest temporal path from s to z. Moreover, we show that finding these restless temporal paths is fixed-parameter tractable when parameterized by the timed feedback vertex number (that is, a temporal version of the classical feedback vertex number introduced in this thesis). This stands in contrast to the W[1]-hardness when parameterized by the feedback vertex number of the underlying graph. Temporal Separation. A temporal separator is a vertex set that intersects the vertices of all temporal paths between two distinguished vertices. We co [...]Philipp Zschoche, Technische Universität Berlin, Rolf Niedermeierwork_uyaoernzvvb7rmwysi2x6b5yziThu, 15 Sep 2022 00:00:00 GMTLifted edges as connectivity priors for multicut and disjoint paths
https://scholar.archive.org/work/edizj43isvflhhihrsapdwjlhu
This work studies graph decompositions and their representation by 0/1 labeling of edges. We study two problems. The first is multicut (MC) which represents decompositions of undirected graphs (clustering of nodes into connected components). The second is disjoint paths (DP) in directed acyclic graphs where the clusters correspond to nodedisjoint paths. Unlike an alternative representation by node labeling, the number of clusters is not part of the input but is fully determined by the costs of edges. I would like to thank all my co-authors for a pleasant and constructive cooperation. Besides my supervisor Paul Swoboda, I would like to name especially Roberto Henschel, Timo Kaiser, Bjoern Andres, and Jan-Hendrik Lange for their major contribution to the shared publications that are part of this thesis. The publications could not be realized without their part of the work. I would like to thank Bjoern Andres for his supervision and help during the work on our common paper. I would like to mention also Michal Rolinek who helped us with our latest publication. I would like to thank Jiles Vreeken, Marcel Schulz and Markus List who cooperated with me on a research project that is not part of this thesis. I am very grateful to Bernt Schiele, the director of our department, who provided me with good working conditions, fully supported me in combining my working duties with family, and found a solution in the difficult stage of my PhD study by finding a new supervisor. Also, other people at MPI and Saarland University helped me to organize my work and family life and helped me with administrative issues.Andrea Hornakova, Universität Des Saarlandeswork_edizj43isvflhhihrsapdwjlhuMon, 29 Aug 2022 00:00:00 GMTTransformer-based assignment decision network for multiple object tracking
https://scholar.archive.org/work/5el7ft67nbex7hztp56g2b2yau
Data association is a crucial component for any multiple object tracking (MOT) method that follows the tracking-by-detection paradigm. To generate complete trajectories such methods employ a data association process to establish assignments between detections and existing targets during each timestep. Recent data association approaches try to solve a multi-dimensional linear assignment task or a network flow minimization problem or either tackle it via multiple hypotheses tracking. However, during inference an optimization step that computes optimal assignments is required for every sequence frame adding significant computational complexity in any given solution. To this end, in the context of this work we introduce Transformer-based Assignment Decision Network (TADN) that tackles data association without the need of any explicit optimization during inference. In particular, TADN can directly infer assignment pairs between detections and active targets in a single forward pass of the network. We have integrated TADN in a rather simple MOT framework, we designed a novel training strategy for efficient end-to-end training and demonstrate the high potential of our approach for online visual tracking-by-detection MOT on two popular benchmarks, i.e. MOT17 and UA-DETRAC. Our proposed approach outperforms the state-of-the-art in most evaluation metrics despite its simple nature as a tracker which lacks significant auxiliary components such as occlusion handling or re-identification. The implementation of our method is publicly available at https://github.com/psaltaath/tadn-mot.Athena Psalta, Vasileios Tsironis, Konstantinos Karantzaloswork_5el7ft67nbex7hztp56g2b2yauSat, 06 Aug 2022 00:00:00 GMTCorrelation Clustering with Sherali-Adams
https://scholar.archive.org/work/ut57yvckxrgpfd423jlvlyw5ae
Given a complete graph G = (V, E) where each edge is labeled + or -, the Correlation Clustering problem asks to partition V into clusters to minimize the number of +edges between different clusters plus the number of -edges within the same cluster. Correlation Clustering has been used to model a large number of clustering problems in practice, making it one of the most widely studied clustering formulations. The approximability of Correlation Clustering has been actively investigated [BBC04, CGW05, ACN08], culminating in a 2.06-approximation algorithm [CMSY15], based on rounding the standard LP relaxation. Since the integrality gap for this formulation is 2, it has remained a major open question to determine if the approximation factor of 2 can be reached, or even breached. In this paper, we answer this question affirmatively by showing that there exists a (1.994 + ϵ)-approximation algorithm based on O(1/ϵ^2) rounds of the Sherali-Adams hierarchy. In order to round a solution to the Sherali-Adams relaxation, we adapt the correlated rounding originally developed for CSPs [BRS11, GS11, RT12]. With this tool, we reach an approximation ratio of 2+ϵ for Correlation Clustering. To breach this ratio, we go beyond the traditional triangle-based analysis by employing a global charging scheme that amortizes the total cost of the rounding across different triangles.Vincent Cohen-Addad, Euiwoong Lee, Alantha Newmanwork_ut57yvckxrgpfd423jlvlyw5aeFri, 22 Jul 2022 00:00:00 GMTHierarchical Clustering in Graph Streams: Single-Pass Algorithms and Space Lower Bounds
https://scholar.archive.org/work/2io2t2zfbfbhpmzwyelbtwsyqe
The Hierarchical Clustering (HC) problem consists of building a hierarchy of clusters to represent a given dataset. Motivated by the modern large-scale applications, we study the problem in the model, in which the memory is heavily limited and only a single or very few passes over the input are allowed. Specifically, we investigate whether a good hierarchical clustering can be obtained, or at least whether we can approximately estimate the value of the optimal hierarchy. To measure the quality of a hierarchy, we use the HC minimization objective introduced by Dasgupta. Assuming that the input is an n-vertex weighted graph whose edges arrive in a stream, we derive the following results on space-vs-accuracy tradeoffs: * With O(n·polylog n) space, we develop a single-pass algorithm, whose approximation ratio matches the currently best offline algorithm. * When the space is more limited, namely, n^1-o(1), we prove that no algorithm can even estimate the value of optimum HC tree to within an o(logn/loglogn) factor, even when allowed polylog n passes over the input. * In the most stringent setting of polylog n space, we rule out algorithms that can even distinguish between "highly"-vs-"poorly" clusterable graphs, namely, graphs that have an n^1/2-o(1) factor gap between their HC objective value. * Finally, we prove that any single-pass streaming algorithm that computes an optimal HC tree requires to store almost the entire input even if allowed exponential time. Our algorithmic results establish a general structural result that proves that cut sparsifiers of input graph can preserve cost of "balanced" HC trees to within a constant factor. Our lower bound results include a new streaming lower bound for a novel problem "One-vs-Many-Expanders", which can be of independent interest.Sepehr Assadi, Vaggos Chatziafratis, Jakub Łącki, Vahab Mirrokni, Chen Wangwork_2io2t2zfbfbhpmzwyelbtwsyqeWed, 15 Jun 2022 00:00:00 GMTGASP, a generalized framework for agglomerative clustering of signed graphs and its application to Instance Segmentation
https://scholar.archive.org/work/b2jqp6ijqbfl3hwecsf5tqtbna
We propose a theoretical framework that generalizes simple and fast algorithms for hierarchical agglomerative clustering to weighted graphs with both attractive and repulsive interactions between the nodes. This framework defines GASP, a Generalized Algorithm for Signed graph Partitioning, and allows us to explore many combinations of different linkage criteria and cannot-link constraints. We prove the equivalence of existing clustering methods to some of those combinations and introduce new algorithms for combinations that have not been studied before. We study both theoretical and empirical properties of these combinations and prove that some of these define an ultrametric on the graph. We conduct a systematic comparison of various instantiations of GASP on a large variety of both synthetic and existing signed clustering problems, in terms of accuracy but also efficiency and robustness to noise. Lastly, we show that some of the algorithms included in our framework, when combined with the predictions from a CNN model, result in a simple bottom-up instance segmentation pipeline. Going all the way from pixels to final segments with a simple procedure, we achieve state-of-the-art accuracy on the CREMI 2016 EM segmentation benchmark without requiring domain-specific superpixels.Alberto Bailoni, Constantin Pape, Nathan Hütsch, Steffen Wolf, Thorsten Beier, Anna Kreshuk, Fred A. Hamprechtwork_b2jqp6ijqbfl3hwecsf5tqtbnaFri, 03 Jun 2022 00:00:00 GMTLearning to solve Minimum Cost Multicuts efficiently using Edge-Weighted Graph Convolutional Neural Networks
https://scholar.archive.org/work/76cxr6t6wbcwrkineqvtpmxddy
The minimum cost multicut problem is the NP-hard/APX-hard combinatorial optimization problem of partitioning a real-valued edge-weighted graph such as to minimize the total cost of the partition. While graph convolutional neural networks (GNN) have proven to be promising in the context of combinatorial optimization, most of them are only tailored to or tested on positive-valued edge weights, i.e. they do not comply to the nature of the multicut problem. We therefore adapt various GNN architectures including Graph Convolutional Networks, Signed Graph Convolutional Networks and Graph Isomorphic Networks to facilitate the efficient encoding of real-valued edge costs. Moreover, we employ a reformulation of the multicut ILP constraints to a polynomial program as loss function that allows to learn feasible multicut solutions in a scalable way. Thus, we provide the first approach towards end-to-end trainable multicuts. Our findings support that GNN approaches can produce good solutions in practice while providing lower computation times and largely improved scalability compared to LP solvers and optimized heuristics, especially when considering large instances.Steffen Jung, Margret Keuperwork_76cxr6t6wbcwrkineqvtpmxddyMon, 04 Apr 2022 00:00:00 GMTSTURE: Spatial-Temporal Mutual Representation Learning for Robust Data Association in Online Multi-Object Tracking
https://scholar.archive.org/work/rikcrqpryrbrdkjszezbd6b2w4
Online multi-object tracking (MOT) is a longstanding task for computer vision and intelligent vehicle platform. At present, the main paradigm is tracking-by-detection, and the main difficulty of this paradigm is how to associate current candidate detections with historical tracklets. However, in the MOT scenarios, each historical tracklet is composed of an object sequence, while each candidate detection is just a flat image, which lacks temporal features of the object sequence. The feature difference between current candidate detections and historical tracklets makes the object association much harder. Therefore, we propose a Spatial-Temporal Mutual Representation Learning (STURE) approach which learns spatial-temporal representations between current candidate detections and historical sequences in a mutual representation space. For historical trackelets, the detection learning network is forced to match the representations of sequence learning network in a mutual representation space. The proposed approach is capable of extracting more distinguishing detection and sequence representations by using various designed losses in object association. As a result, spatial-temporal feature is learned mutually to reinforce the current detection features, and the feature difference can be relieved. To prove the robustness of the STURE, it is applied to the public MOT challenge benchmarks and performs well compared with various state-of-the-art online MOT trackers based on identity-preserving metrics.Haidong Wang, Zhiyong Li, Yaping Li, Ke Nai, Ming Wenwork_rikcrqpryrbrdkjszezbd6b2w4Mon, 28 Mar 2022 00:00:00 GMTRAMA: A Rapid Multicut Algorithm on GPU
https://scholar.archive.org/work/iwkl4tz4djeg5ib7y7n5ine4aa
We propose a highly parallel primal-dual algorithm for the multicut (a.k.a. correlation clustering) problem, a classical graph clustering problem widely used in machine learning and computer vision. Our algorithm consists of three steps executed recursively: (1) Finding conflicted cycles that correspond to violated inequalities of the underlying multicut relaxation, (2) Performing message passing between the edges and cycles to optimize the Lagrange relaxation coming from the found violated cycles producing reduced costs and (3) Contracting edges with high reduced costs through matrix-matrix multiplications. Our algorithm produces primal solutions and lower bounds that estimate the distance to optimum. We implement our algorithm on GPUs and show resulting one to two orders-of-magnitudes improvements in execution speed without sacrificing solution quality compared to traditional sequential algorithms that run on CPUs. We can solve very large scale benchmark problems with up to 𝒪(10^8) variables in a few seconds with small primal-dual gaps. Our code is available at https://github.com/pawelswoboda/RAMA.Ahmed Abbas, Paul Swobodawork_iwkl4tz4djeg5ib7y7n5ine4aaFri, 11 Mar 2022 00:00:00 GMTNear-Optimal Correlation Clustering with Privacy
https://scholar.archive.org/work/akkff4swwvfb3gnqnix67v5ida
Correlation clustering is a central problem in unsupervised learning, with applications spanning community detection, duplicate detection, automated labelling and many more. In the correlation clustering problem one receives as input a set of nodes and for each node a list of co-clustering preferences, and the goal is to output a clustering that minimizes the disagreement with the specified nodes' preferences. In this paper, we introduce a simple and computationally efficient algorithm for the correlation clustering problem with provable privacy guarantees. Our approximation guarantees are stronger than those shown in prior work and are optimal up to logarithmic factors.Vincent Cohen-Addad, Chenglin Fan, Silvio Lattanzi, Slobodan Mitrović, Ashkan Norouzi-Fard, Nikos Parotsidis, Jakub Tarnawskiwork_akkff4swwvfb3gnqnix67v5idaWed, 02 Mar 2022 00:00:00 GMTStructured Prediction Problem Archive
https://scholar.archive.org/work/mrt6hdeiqffwjk4fyj7pj45fsy
Structured prediction problems are one of the fundamental tools in machine learning. In order to facilitate algorithm development for their numerical solution, we collect in one place a large number of datasets in easy to read formats for a diverse set of problem classes. We provide archival links to datasets, description of the considered problems and problem formats, and a short summary of problem characteristics including size, number of instances etc. For reference we also give a non-exhaustive selection of algorithms proposed in the literature for their solution. We hope that this central repository will make benchmarking and comparison to established works easier. We welcome submission of interesting new datasets and algorithms for inclusion in our archive.Paul Swoboda, Andrea Hornakova, Paul Roetzer, Bogdan Savchynskyy, Ahmed Abbaswork_mrt6hdeiqffwjk4fyj7pj45fsyFri, 25 Feb 2022 00:00:00 GMTA Polyhedral Study of Lifted Multicuts
https://scholar.archive.org/work/o2vu5e53dzbchl46uprcmi6sge
Fundamental to many applications in data analysis are the decompositions of a graph, i.e. partitions of the node set into component-inducing subsets. One way of encoding decompositions is by multicuts, the subsets of those edges that straddle distinct components. Recently, a lifting of multicuts from a graph G = (V, E) to an augmented graph Ĝ = (V, E ∪ F) has been proposed in the field of image analysis, with the goal of obtaining a more expressive characterization of graph decompositions in which it is made explicit also for pairs F ⊆V2∖ E of non-neighboring nodes whether these are in the same or distinct components. In this work, we study in detail the polytope in ℝ^E ∪ F whose vertices are precisely the characteristic vectors of multicuts of Ĝ lifted from G, connecting it, in particular, to the rich body of prior work on the clique partitioning and multilinear polytope.Bjoern Andres, Silvia Di Gregorio, Jannik Irmai, Jan-Hendrik Langework_o2vu5e53dzbchl46uprcmi6sgeWed, 16 Feb 2022 00:00:00 GMTHigher-Order Multicuts for Geometric Model Fitting and Motion Segmentation
https://scholar.archive.org/work/rwomnprw35bsxph4cjxfv74ahe
Minimum cost lifted multicut problem is a generalization of the multicut problem and is a means to optimizing a decomposition of a graph w.r.t. both positive and negative edge costs. Its main advantage is that multicut-based formulations do not require the number of components given a priori; instead, it is deduced from the solution. However, the standard multicut cost function is limited to pairwise relationships between nodes, while several important applications either require or can benefit from a higher-order cost function, i.e. hyper-edges. In this paper, we propose a pseudo-boolean formulation for a multiple model fitting problem. It is based on a formulation of any-order minimum cost lifted multicuts, which allows to partition an undirected graph with pairwise connectivity such as to minimize costs defined over any set of hyper-edges. As the proposed formulation is NP-hard and the branch-and-bound algorithm is too slow in practice, we propose an efficient local search algorithm for inference into resulting problems. We demonstrate versatility and effectiveness of our approach in several applications: geometric multiple model fitting, homography and motion estimation, motion segmentation.Evgeny Levinkov, Amirhossein Kardoost, Bjoern Andres, Margret Keuperwork_rwomnprw35bsxph4cjxfv74aheMon, 07 Feb 2022 00:00:00 GMTPractical Almost-Linear-Time Approximation Algorithms for Hybrid and Overlapping Graph Clustering
https://scholar.archive.org/work/muxog5ovxbfbxpls5btwc6oz2q
In many graph-clustering applications, overwhelming empirical evidence suggests that communities and clusters are naturally overlapping, calling for novel overlapping graph-partitioning algorithms (OGP). In this work, we introduce a framework based on two novel clustering objectives, which naturally extend the wellstudied notion of conductance to overlapping clusters and to clusters with hybrid vertex-and edge-boundary structure. Our main algorithmic contributions are nearly-linear-time algorithms O(log n)-approximation algorithms for both these objectives. To this end, we show that the cut-matching framework of Khandekar et al. ( 2014 ) can be extended to overlapping partitions and give novel cut-improvement primitives that perform a small number of s-t maximum flow computations over the instance graph to detect sparse overlapping partitions near an input partition. Crucially, we implement our approximation algorithm to produce both overlapping and hybrid partitions for large graphs, easily scaling to tens of millions of edges, and test our implementation on real-world datasets against other competitive baselines.Lorenzo Orecchia, Konstantinos Ameranis, Charalampos E. Tsourakakis, Kunal Talwarwork_muxog5ovxbfbxpls5btwc6oz2qRibbon drawing in VR : brushes and applications
https://scholar.archive.org/work/d54axnadrngm5ouwhscinez2ie
Virtual reality drawing applications let users draw 3D shapes using brushes that form ribbon-shaped, or ruled-surface, strokes. Each ribbon is uniquely defined by its user-specified ruling length, path, and the ruling directions at each point along this path. A collection of these virtual ribbons with proper normal orientations can communicate complex surfaces; thus, artists frequently describe their envisioned 3D surfaces by drawing dense brush strokes that cover the surface of the intended shapes. In this thesis, we analyze these ribbon brushes, and propose ways to expand the scope of their applications and improve their usability. Currently, the practical use of these drawings is limited since most geometry processing algorithms and downstream applications such as 3D printing require manifold meshes. Furthermore, existing brushes use the trajectory of a handheld controller in 3D space as the ribbon path, and compute the ruling directions using a fixed mapping from a specific controller coordinate-frame axis. This fixed mapping requires users to rotate the controller and thus their wrists to change ribbon normal or ruling directions, which requires substantial physical effort to draw even medium complexity ribbons. As people have limited ability to rotate their wrists continuously, the range of ribbon geometries they can comfortably draw with these brushes is limited. We solve these problems by first developing SurfaceBrush, a surfacing method that converts such VR drawings into user-intended manifold free-form 3D surfaces. We then present AdaptiBrush, a ribbon brush system that dramatically extends the space of ribbon geometries users can comfortably draw while enabling them to accurately predict the ribbon shape that a given hand motion produces. Our work expands the range of applications of VR drawing and makes VR drawing a viable alternative to 3D modeling for inexperienced users.Enrique Alberto Rosales Ruizwork_d54axnadrngm5ouwhscinez2ieModelli matematici e algoritmi risolutivi per la pianificazione dell'espansione della generazione e della trasmissione con elevate quote di generazione rinnovabile
https://scholar.archive.org/work/c4szjdlddbdohixl27vjexsjwq
Giovanni MICHELIwork_c4szjdlddbdohixl27vjexsjwqFri, 08 Oct 2021 00:00:00 GMTFitting Distances by Tree Metrics Minimizing the Total Error within a Constant Factor
https://scholar.archive.org/work/w24obzp6qbcyxdvu5rrhw6svhu
We consider the numerical taxonomy problem of fitting a positive distance function D:S 2→ℝ_>0 by a tree metric. We want a tree T with positive edge weights and including S among the vertices so that their distances in T match those in D. A nice application is in evolutionary biology where the tree T aims to approximate the branching process leading to the observed distances in D [Cavalli-Sforza and Edwards 1967]. We consider the total error, that is the sum of distance errors over all pairs of points. We present a deterministic polynomial time algorithm minimizing the total error within a constant factor. We can do this both for general trees, and for the special case of ultrametrics with a root having the same distance to all vertices in S. The problems are APX-hard, so a constant factor is the best we can hope for in polynomial time. The best previous approximation factor was O((log n)(loglog n)) by Ailon and Charikar [2005] who wrote "Determining whether an O(1) approximation can be obtained is a fascinating question".Vincent Cohen-Addad, Debarati Das, Evangelos Kipouridis, Nikos Parotsidis, Mikkel Thorupwork_w24obzp6qbcyxdvu5rrhw6svhuWed, 06 Oct 2021 00:00:00 GMT