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### Optimal separable partitioning in the plane

Michal Benelli, Refael Hassin
<span title="">1995</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lx7dev2le5anbg6oarljwh7lie" style="color: black;">Discrete Applied Mathematics</a> </i> &nbsp;
Sets of points are called separable if their convex hulls are disjoint. We suggest a technique for optimally partitioning of a set N into two separable subsets, N" N2.  ...  We assume that a monotone measure, p, is defined over the subsets of N, and the objective is to minimize maWN,),AN,)). *Corresponding author. 0166-218X/95/\$09.50 0 1995-Elsevier Science B.V.  ...  (In [5] it is proved that under this measure an optimal solution can be separated by a circle.) (3) The Steiner-Weber problem (see [lo] ) is to find a point P in the plane minimizing the sum of Euclidean  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0166-218x(95)80002-l">doi:10.1016/0166-218x(95)80002-l</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/avc2onrgmrcz5k33eodn7ahwnm">fatcat:avc2onrgmrcz5k33eodn7ahwnm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171003022941/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/c29/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS8wMTY2MjE4eDk1ODAwMDJs.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/14/54/145402f1fdccdb0ee8f462c9a0d7542f2b6f50b4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0166-218x(95)80002-l"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

### On the number of separable partitions

Frank K. Hwang, Uriel G. Rothblum
<span title="2009-11-03">2009</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tsm6lnbvf5ahzjp7czojbjig5i" style="color: black;">Journal of combinatorial optimization</a> </i> &nbsp;
Consider partitions of a given set A of n distinct points in general position in R d into parts where each pair of parts can be separated by a hyperplane that contains a given set of points E.  ...  Applications of the result to partition problems are presented.  ...  In particular, there is a broad class of optimization problems over partitions which are guaranteed to have optimal solutions that are separable.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10878-009-9263-4">doi:10.1007/s10878-009-9263-4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cr6iw5im4beo5kqsgww3atjoxy">fatcat:cr6iw5im4beo5kqsgww3atjoxy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190303164103/http://pdfs.semanticscholar.org/ccc7/e029458d3a750ec1d8456bbd3f15ec028982.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/cc/c7/ccc7e029458d3a750ec1d8456bbd3f15ec028982.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10878-009-9263-4"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

### Edge Partitions of Optimal 2-plane and 3-plane Graphs [article]

Michael Bekos, Emilio Di Giacomo, Walter Didimo, Giuseppe Liotta, Fabrizio Montecchiani, Chrysanthi Raftopoulou
<span title="2018-06-21">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
the optimal 2-plane graph is such that its crossing-free edges form a graph with no separating triangles.  ...  (iv) We exhibit an infinite family of simple optimal 2-plane graphs such that in any edge partition composed of a 1-plane graph and a plane graph, the plane graph has maximum vertex degree at least 6 and  ...  Research started at the 2017 GNV Workshop, held in Heiligkreuztal (Germany).  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1802.10300v2">arXiv:1802.10300v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/saomatadovfudkg4lk6ti7rrim">fatcat:saomatadovfudkg4lk6ti7rrim</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200924084642/https://arxiv.org/pdf/1802.10300v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/1c/40/1c40376402b131682823b3d054f71e68db936efd.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1802.10300v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

### Generating sacrificial multi-piece molds using accessibility driven spatial partitioning

J. Huang, S.K. Gupta, K. Stoppel
<span title="">2003</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wquzxyrherhzfhmbojag5cxcra" style="color: black;">Computer-Aided Design</a> </i> &nbsp;
The algorithm presented in this paper analyzes the accessibility of the gross mold shape and partitions it using accessibility information.  ...  Using the algorithm presented in this paper, mold design steps can be significantly automated for making geometrically complex parts and facilitating the creation of physical part from the CAD model in  ...  Opinions expressed in this paper are those of authors and do not necessarily reflect opinion of the sponsors.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0010-4485(03)00008-3">doi:10.1016/s0010-4485(03)00008-3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sh5s2uvdwbgczl5wburnbsjvuy">fatcat:sh5s2uvdwbgczl5wburnbsjvuy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170810070659/http://terpconnect.umd.edu/~skgupta/Publication/CAD03_Huang_draft.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e5/d9/e5d96605cbaf58174e5d18f7e8be29fbb814d333.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0010-4485(03)00008-3"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

### Measuring Human Performance on Clustering Problems: Some Potential Objective Criteria and Experimental Research Opportunities

Michael Brusco
<span title="2007-06-13">2007</span> <i title="Purdue University (bepress)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/353babry3vd4ppawplpj2ybhpi" style="color: black;">Journal of Problem Solving</a> </i> &nbsp;
The purpose of this paper is to outline a program of study for the measurement of human performance on discrete optimization problems related to clustering of points in the two-dimensional plane.  ...  To facilitate future experimental testing of human subjects on clustering problems, optimal partitions were obtained for 233 two-dimensional clustering problems ranging in size from 10 to 70 points.  ...  In this discrete optimization task, subjects are presented with N points in the two-dimensional plane.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.7771/1932-6246.1001">doi:10.7771/1932-6246.1001</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4oa4vejwfvdppm4kybvnlmxsa4">fatcat:4oa4vejwfvdppm4kybvnlmxsa4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180723093853/https://docs.lib.purdue.edu/cgi/viewcontent.cgi?referer=&amp;httpsredir=1&amp;article=1001&amp;context=jps" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/86/ac/86ac0f3086f6b85ad67ca2cf9c6c9d5fa1d86e0f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.7771/1932-6246.1001"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

### Rectilinear parsing of architecture in urban environment

Peng Zhao, Tian Fang, Jianxiong Xiao, Honghui Zhang, Qinping Zhao, Long Quan
<span title="">2010</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ilwxppn4d5hizekyd3ndvy2mii" style="color: black;">2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition</a> </i> &nbsp;
The partition problem is formulated as a dynamic programming optimization for a sequence of natural vertical separating lines. Each façade is regularized by a floor line and a roof line.  ...  In our approach, we first parse the environment into buildings, the ground, and the sky using a joint 2D-3D segmentation method. Then, we partition buildings into individual façades.  ...  We thank Google for the image data and a research gift. We also thank Lei Yang for the proofreading and Hao Hu for useful discussions.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/cvpr.2010.5540192">doi:10.1109/cvpr.2010.5540192</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/cvpr/ZhaoFXZZQ10.html">dblp:conf/cvpr/ZhaoFXZZQ10</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4bpjxnwmbvb45cd6v3imgw54ri">fatcat:4bpjxnwmbvb45cd6v3imgw54ri</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922235136/http://vision.cs.princeton.edu/projects/2010/CVPR_line/paper.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a8/38/a8381491b97e287827410326695f5be8e217d637.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/cvpr.2010.5540192"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

### Global optimization of nonconvex problems with multilinear intermediates

Xiaowei Bao, Aida Khajavirad, Nikolaos V. Sahinidis, Mohit Tawarmalani
<span title="2014-05-10">2014</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4upcxg4hoza3djydsaam4mbmz4" style="color: black;">Mathematical Programming Computation</a> </i> &nbsp;
When used as cutting planes, these facets can significantly enhance the quality of conventional relaxations in general-purpose global solvers.  ...  However, in general, the size of this LP grows exponentially with the number of variables in the multilinear function.  ...  Moreover, in all three test sets, the Multilinear cutting plane statistics for fourth-order polynomial optimization problems.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s12532-014-0073-z">doi:10.1007/s12532-014-0073-z</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xni6phwtgjdszhjdbf72ox7fge">fatcat:xni6phwtgjdszhjdbf72ox7fge</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20151215034926/http://mpc.zib.de:80/index.php/MPC/article/viewFile/154/76" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ec/9a/ec9aa6454392b032f5ac37e92a8aed5ee44ac19b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s12532-014-0073-z"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

### Graph Based Hybrid Clustering With Unbounded Regions

Hong Zhang
<span title="">2017</span> <i title="Symbiosis Group"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fp43b6sgujafbiblmolbcxqnmm" style="color: black;">Journal of Computer Science Applications and Information Technology</a> </i> &nbsp;
A clustering algorithm using Markov Chain Monte Carlo method is developed for finding optimal adjustments to the partition automatically.  ...  Our method uses a graph to model the initial manual partition of the dataset. Based on the graph model, an algorithm is developed for automatic detection of the regions defined by the partition.  ...  The adjusted partition is much closer to the optimal separation of the 2 components.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.15226/2474-9257/2/2/00113">doi:10.15226/2474-9257/2/2/00113</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cpgbdq4mcza7bctyxh7frw63nq">fatcat:cpgbdq4mcza7bctyxh7frw63nq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180720123731/https://symbiosisonlinepublishing.com/computer-science-technology/computerscience-information-technology13.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/50/d0/50d093dfcca5f3f00374381ad9af733fbae5dd4c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.15226/2474-9257/2/2/00113"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

### Minimizing Impurity Partition Under Constraints [article]

Thuan Nguyen, Thinh Nguyen
<span title="2019-12-31">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Moreover, we show that the optimal partition produces a hard partition that is equivalent to the cuts by hyperplanes in the probability space of the posterior probability that finally yields a polynomial  ...  In this paper, we formulate and solve a variant of the partition problem called the minimum impurity partition under constraint (MIPUC).  ...  Hyperplane separation Similar to the work in [6] , we show that the optimal partitions correspond to the regions separated by hyper-plane cuts in the probability space of the posterior distribution.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1912.13141v1">arXiv:1912.13141v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vqvowcx37bg7pmz2j5o2ptkeva">fatcat:vqvowcx37bg7pmz2j5o2ptkeva</a> </span>
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### UNSUPERVISED LEARNING FROM COMPLEX DATA: THE MATRIX INCISION TREE ALGORITHM

Ju Han Kim, Lucila Ohno-Machado, Isaac S. Kohane
<span title="">2000</span> <i title="WORLD SCIENTIFIC"> Biocomputing 2001 </i> &nbsp;
The matrix incision tree algorithm reveals the hierarchical structural organization of observed data by determining the successive hyperplanes that 'optimally' separate the data hyperspace.  ...  This paper describes a novel method to organize a complex high-dimensional space into successive lower-dimensional spaces based on the geometric properties of the data structure in the absence of a priori  ...  Acknowledgments LOM was funded under grant R29 LM06538-01 from the National Library of Medicine, NIH.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1142/9789814447362_0004">doi:10.1142/9789814447362_0004</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lmyf65ngkbfiveqv3jhhmpr4fq">fatcat:lmyf65ngkbfiveqv3jhhmpr4fq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20040917164224/http://linkage.rockefeller.edu:80/wli/moved.8.04/microarray/kim01.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/df/59/df59df595dfe5400da0b822dec9d90d790917bc7.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1142/9789814447362_0004"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> worldscientific.com </button> </a>

### Location-area partition in a cellular radio network

D-W Tcha, T-J Choi, Y-S Myung
<span title="">1997</span> <i title="Informa UK Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fq4jrflj6zesjk7f4nb4otuwwy" style="color: black;">Journal of the Operational Research Society</a> </i> &nbsp;
In the cutting plane algorithm, we add all the violated 2- partition inequaltities found by the above separation heur- istic to the current LP, and solve the resulting LP to get a new optimal LP solution  ...  If x* is integral, stop with an optimal solution of the CPP. Otherwise, call the separation heuristic (described below).  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1057/palgrave.jors.2600448">doi:10.1057/palgrave.jors.2600448</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vejmav3ebjbjlgkf57jwvtxapy">fatcat:vejmav3ebjbjlgkf57jwvtxapy</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/details/sim_journal-of-the-operational-research-society_1997-11_48_11/page/1076" title="read fulltext microfilm" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Archive [Microfilm] <div class="menu fulltext-thumbnail"> <img src="https://archive.org/serve/sim_journal-of-the-operational-research-society_1997-11_48_11/__ia_thumb.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1057/palgrave.jors.2600448"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

### Location-area partition in a cellular radio network

D-W Tcha, T-J Choi, Y-S Myung
<span title="">1997</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fq4jrflj6zesjk7f4nb4otuwwy" style="color: black;">Journal of the Operational Research Society</a> </i> &nbsp;
In the cutting plane algorithm, we add all the violated 2- partition inequaltities found by the above separation heur- istic to the current LP, and solve the resulting LP to get a new optimal LP solution  ...  If x* is integral, stop with an optimal solution of the CPP. Otherwise, call the separation heuristic (described below).  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1038/sj.jors.2600448">doi:10.1038/sj.jors.2600448</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kituibgkzbddzkagk37tkl7h7q">fatcat:kituibgkzbddzkagk37tkl7h7q</a> </span>
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### Towards Optimal Discriminating Order for Multiclass Classification

Dong Liu, Shuicheng Yan, Yadong Mu, Xian-Sheng Hua, Shih-Fu Chang, Hong-Jiang Zhang
<span title="">2011</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/gckg3mzs4fhxhbrvmbsa54bccm" style="color: black;">2011 IEEE 11th International Conference on Data Mining</a> </i> &nbsp;
In this paper, we investigate how to design an optimized discriminating order for boosting multiclass classification.  ...  the margin between these two partitioned class subsets.  ...  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.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/icdm.2011.147">doi:10.1109/icdm.2011.147</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/icdm/LiuYMHCZ11.html">dblp:conf/icdm/LiuYMHCZ11</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tgts5yk5ynbgxjg6bmpob7775y">fatcat:tgts5yk5ynbgxjg6bmpob7775y</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170706074134/http://www.ee.columbia.edu/%7Edongliu/Papers/Order_ICDM11.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/94/04/94047043e3f4484f8ab6592bc8ab51a58d3ec5a8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/icdm.2011.147"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

### Communication-Channel Optimized Partition [article]

Thuan Nguyen, Thinh Nguyen
<span title="2020-01-06">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Second, we show that the optimal partition should produce a hard partition that is equivalent to the cuts by hyper-planes in the probability space of the posterior probability p(X|Y).  ...  One wants to design the optimal quantizer/classifier Q^* such that the cost function F(X; T) between the input X and the final output T is minimized while the probability of the partitioned output Z satisfies  ...  Hyper-plane separation Similar to the work in [5] , in this paper, we show that the optimal partition is equivalent to the cuts by hyper-planes in the space of the posterior probability.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2001.01708v1">arXiv:2001.01708v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7hkw7sipnjhyxgrtmby4za2ivi">fatcat:7hkw7sipnjhyxgrtmby4za2ivi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200321005643/https://arxiv.org/pdf/2001.01708v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2001.01708v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

### A cutting-plane approach to the edge-weighted maximal clique problem

G. Dijkhuizen, U. Faigle
<span title="">1993</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2fqqu5s6wbgk5gcucpt3wqm3gy" style="color: black;">European Journal of Operational Research</a> </i> &nbsp;
the true optimal objective function value.  ...  We investigate the computational performance of a cutting-plane algorithm for the problem of determining a maximal subclique in an edge-weighted complete graph.  ...  In fact, many of the basic inequalities used in cutting-plane algorithms for the partition problem (e.g., the so-called triangle inequalities and partition inequalities in Section 2) are valid and facet  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0377-2217(93)90097-7">doi:10.1016/0377-2217(93)90097-7</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sjzqevyb4vcyhcidxgvlrirpeu">fatcat:sjzqevyb4vcyhcidxgvlrirpeu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180719005524/https://ris.utwente.nl/ws/files/6505310/Faigle93cutting.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/93/12/9312112759f93377dccd061dd65fd041900043cc.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0377-2217(93)90097-7"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>
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