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Large-Margin Metric Learning for Partitioning Problems [article]

Rémi Lajugie
2013 arXiv   pre-print
In this paper, we consider unsupervised partitioning problems, such as clustering, image segmentation, video segmentation and other change-point detection problems.  ...  Our main goal is to learn a Mahalanobis metric for these unsupervised problems, leading to feature weighting and/or selection.  ...  versus the Euclidean distance, and other metric learning algorithms such as RCA or [32] .  ... 
arXiv:1303.1280v1 fatcat:wxhpxl6jenhtfnue7po6mvrnau

Clustering with Semidefinite Programming and Fixed Point Iteration [article]

Pedro Felzenszwalb, Caroline Klivans, Alice Paul
2022 arXiv   pre-print
We introduce a novel method for clustering using a semidefinite programming (SDP) relaxation of the Max k-Cut problem.  ...  Each step of this iterative procedure solves a relaxation of the closest vertex problem and leads to a new clustering problem where the underlying clusters are more clearly defined.  ...  SDP Relaxation for Max k-Cut The Goemans and Williamson (1995) approximation algorithm for Max Cut (clustering into two clusters) is based on an SDP relaxation and a randomized rounding method.  ... 
arXiv:2012.09202v2 fatcat:rxxywzwwyzf3hidbkcshkynjs4

Tight Continuous Relaxation of the Balanced k-Cut Problem [article]

Syama Sundar Rangapuram, Pramod Kaushik Mudrakarta, Matthias Hein
2015 arXiv   pre-print
Extensive comparisons show that our method outperforms all existing approaches for ratio cut and other balanced k-cut criteria.  ...  For the optimization of our tight continuous relaxation we propose a new algorithm for the difficult sum-of-ratios minimization problem which achieves monotonic descent.  ...  Conclusion We presented a framework for directly minimizing the balanced k-cut problem based on a new continuous relaxation.  ... 
arXiv:1505.06478v1 fatcat:pjlx6gpzxne6rh7anrysig6rby

Estimation of Distribution Algorithm for the Max-Cut Problem [chapter]

Samuel de Sousa, Yll Haxhimusa, Walter G. Kropatsch
2013 Lecture Notes in Computer Science  
We have applied the Max-Cut problem for image segmentation and defined the edges' weights as a modified function of the L2 norm between the RGB values of nodes.  ...  In this paper, we investigate the Max-Cut problem and propose a probabilistic heuristic to address its classic and weighted version.  ...  Acknowledgments Samuel de Sousa acknowledges financial support by the Austrian Agency for International Cooperation in Education & Research (OeAD) within the OeAD Sonderstipendien program, financed by  ... 
doi:10.1007/978-3-642-38221-5_26 fatcat:5ua4k43o7jdavimf5s5t4bmfne

Towards Optimal Discriminating Order for Multiclass Classification

Dong Liu, Shuicheng Yan, Yadong Mu, Xian-Sheng Hua, Shih-Fu Chang, Hong-Jiang Zhang
2011 2011 IEEE 11th International Conference on Data Mining  
the margin between these two partitioned class subsets.  ...  Experiment results indicate that SDT clearly beats the state-of-the-art multiclass classification algorithms.  ...  ACKNOWLEDGEMENT We would like to acknowledge to support of "NExT Research Center" funded by MDA, Singapore, under the research grant: WBS:R-252-300-001-490.  ... 
doi:10.1109/icdm.2011.147 dblp:conf/icdm/LiuYMHCZ11 fatcat:tgts5yk5ynbgxjg6bmpob7775y

Learning kernels for variants of normalized cuts: Convex relaxations and applications

Lopamudra Mukherjee, Vikas Singh, Jiming Peng, Chris Hinrichs
2010 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition  
We propose a new algorithm for learning kernels for variants of the Normalized Cuts (NCuts) objective -i.e., given a set of training examples with known partitions, how should a basis set of similarity  ...  A salient feature of our model is that the eventual problem size is only a function of the number of input kernels and not the training set size.  ...  Weights learnt by the algorithm are also good solutions to kernel learning problems for max-margin classification, typically addressed using MKL methods.  ... 
doi:10.1109/cvpr.2010.5540076 pmid:21445225 pmcid:PMC3063999 dblp:conf/cvpr/MukherjeeSPH10 fatcat:4tqd4nwzjnagle4rbqmsdtczmu

Ensemble Clustering for Biological Datasets [chapter]

Harun Pirim, Sadi Evren
2012 Bioinformatics  
Acknowledgement Authors thank Dilip Gautam for his contribution to this chapter.  ...  Author details Harun Pirim King Fahd University of Petroleum and Mineralş Sadi EvrenŞeker Istanbul University, Turkey References  ...  However, there is no best clustering approach for the problem on hand and clustering algorithms are biased towards certain criteria.  ... 
doi:10.5772/49956 fatcat:hvm276nmebgsvdczm6euk47k6m

Unsupervised Discretization by Two-dimensional MDL-based Histogram [article]

Lincen Yang, Mitra Baratchi, Matthijs van Leeuwen
2020 arXiv   pre-print
To address this problem, we propose an expressive model class that allows for far more flexible partitions of two-dimensional data.  ...  As the flexibility of our model class comes at the cost of a vast search space, we introduce a heuristic algorithm, named PALM, which partitions each dimension alternately and then merges neighbouring  ...  Revisiting MDL histograms for one-dimensional data We first show that searching for the best cut lines on one certain dimension of given two-dimensional data is equivalent to searching for the best cut  ... 
arXiv:2006.01893v2 fatcat:zi66e6wxtfb4fciyhcn5ajfggu

Hierarchical Clustering Using the Arithmetic-Harmonic Cut: Complexity and Experiments

Romeo Rizzi, Pritha Mahata, Luke Mathieson, Pablo Moscato, Vladimir Brusic
2010 PLoS ONE  
To this end, we implement a memetic algorithm for the problem and demonstrate the effectiveness of the arithmetic-harmonic cut on a number of datasets including a cancer type dataset and a corona virus  ...  We show that the problem of finding such a cut is NP-hard and APX -hard but is fixed-parameter tractable, which indicates that although the problem is unlikely to have a polynomial time algorithm (even  ...  Author Contributions Conceived and designed the experiments: RR, P. Mahata, LM, P. Moscato. Performed the experiments: RR, P. Mahata, LM. Analyzed the data: P. Mahata, P. Moscato.  ... 
doi:10.1371/journal.pone.0014067 pmid:21151943 pmcid:PMC2997101 fatcat:y2qqfrzekrhj3nefge4uf7cd4a

Constrained 1-Spectral Clustering [article]

Syama Sundar Rangapuram, Matthias Hein
2015 arXiv   pre-print
Motivated by the recently proposed 1-spectral clustering for the unconstrained problem, our method is based on a tight relaxation of the constrained normalized cut into a continuous optimization problem  ...  Opposite to all other methods which have been suggested for constrained spectral clustering, we can always guarantee to satisfy all constraints.  ...  Spectral clustering is a graph-based clustering algorithm originally derived as a relaxation of the NPhard normalized cut problem.  ... 
arXiv:1505.06485v1 fatcat:7drc5fuj5retjjtxhkejdfsbhu

Quantum-Assisted Graph Clustering and Quadratic Unconstrained D-ary Optimisation [article]

Sayantan Pramanik, M Girish Chandra
2021 arXiv   pre-print
By carefully examining the two cluster Max-Cut problem within the framework of quantum Ising model, an extension has been worked out for max 3-cut with the identification of an appropriate Hamiltonian.  ...  As an additional novelty, a qudit circuit to solve max-d cut through Quantum Approximate Optimization algorithm is systematically constructed.  ...  ACKNOWLEDGMENT The authors sincerely thank Mr. Mahesh Rangarajan, Dr. Arpan Pal and Dr. Balamuralidhar P of TCS R&I for their support and encouragement.  ... 
arXiv:2004.02608v2 fatcat:srf5pfgarrfqjaipsmixcysqy4

Visualization tools for parameter selection in cluster analysis [article]

Alexander Rolle, Luis Scoccola
2019 arXiv   pre-print
This gives geometric structure to such sets of clustering, and can be used to visualize the set of results one obtains by running a clustering algorithm with a range of parameters.  ...  We propose an algorithm, HPREF (Hierarchical Partitioning by Repeated Features), that produces a hierarchical partition of a set of clusterings of a fixed dataset, such as sets of clusterings produced  ...  Acknowledgments We would like to thank Dan Christensen, Camila de Souza, and Rick Jardine for their helpful comments and suggestions.  ... 
arXiv:1902.01436v3 fatcat:sxzudsujjjgftaochl4a4lrtru

An O*(2^n ) Algorithm for Graph Coloring and Other Partitioning Problems via Inclusion--Exclusion

Mikko Koivisto
2006 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)  
This problem subsumes various classical graph partitioning problems, such as graph coloring, domatic partitioning, and MAX k-CUT, as well as machine learning problems like decision graph learning and model-based  ...  On the other hand, the presented algorithms are suitable  ...  Acknowledgements I am grateful to Heikki Mannila for valuable conversations on this work.  ... 
doi:10.1109/focs.2006.11 dblp:conf/focs/Koivisto06 fatcat:rjb5ch4azbew5brgekdihsg224

Regularized Tree Partitioning and Its Application to Unsupervised Image Segmentation

Jingdong Wang, Huaizu Jiang, Yangqing Jia, Xian-Sheng Hua, Changshui Zhang, Long Quan
2014 IEEE Transactions on Image Processing  
We give the properties that result in an efficient algorithm for NTP and ATP.  ...  We study normalized cut (NCut) and average cut (ACut) criteria over a tree, forming two approaches: normalized tree partitioning (NTP) and average tree partitioning (ATP).  ...  Besides, there are supervised clustering and segmentation approaches, such as graph-cuts [6] , label propagation [41] , and semi-supervised learning algorithms [51] .  ... 
doi:10.1109/tip.2014.2307479 pmid:24808356 fatcat:d56yolqv6jdzvmpnv7ryrnndka

HyperSF: Spectral Hypergraph Coarsening via Flow-based Local Clustering [article]

Ali Aghdaei, Zhiqiang Zhao, Zhuo Feng
2021 arXiv   pre-print
Our approach leverages a recent strongly-local max-flow-based clustering algorithm for detecting the sets of hypergraph vertices that minimize ratio cut.  ...  To further improve the algorithm efficiency, we propose a divide-and-conquer scheme by leveraging spectral clustering of the bipartite graphs corresponding to the original hypergraphs.  ...  ACKNOWLEDGMENT This work is supported in part by the National Science Foundation under Grants CCF-2041519 (CAREER), CCF-2021309 (SHF), and CCF-2011412 (SHF).  ... 
arXiv:2108.07901v3 fatcat:nd74hogturfubmlkubln543jai
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