Learning Laplacian Matrix in Smooth Graph Signal Representations

The construction of a meaningful graph plays a crucial role in the success of many graph-based representations and algorithms for handling structured data, especially in the emerging field of graph signal processing. However, a meaningful graph is not always readily available from the data, nor easy...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	IEEE transactions on signal processing Jg. 64; H. 23; S. 6160 - 6173
Hauptverfasser:	Xiaowen Dong, Thanou, Dorina, Frossard, Pascal, Vandergheynst, Pierre
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	IEEE 01.12.2016
Schlagworte:	Analytical models factor analysis Gaussian prior graph signal processing Kernel Laplace equations Laplacian matrix learning representation theory Signal processing Signal processing algorithms Signal representation Topology
ISSN:	1053-587X, 1941-0476
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Abstract	The construction of a meaningful graph plays a crucial role in the success of many graph-based representations and algorithms for handling structured data, especially in the emerging field of graph signal processing. However, a meaningful graph is not always readily available from the data, nor easy to define depending on the application domain. In particular, it is often desirable in graph signal processing applications that a graph is chosen such that the data admit certain regularity or smoothness on the graph. In this paper, we address the problem of learning graph Laplacians, which is equivalent to learning graph topologies, such that the input data form graph signals with smooth variations on the resulting topology. To this end, we adopt a factor analysis model for the graph signals and impose a Gaussian probabilistic prior on the latent variables that control these signals. We show that the Gaussian prior leads to an efficient representation that favors the smoothness property of the graph signals. We then propose an algorithm for learning graphs that enforces such property and is based on minimizing the variations of the signals on the learned graph. Experiments on both synthetic and real world data demonstrate that the proposed graph learning framework can efficiently infer meaningful graph topologies from signal observations under the smoothness prior.
AbstractList	The construction of a meaningful graph plays a crucial role in the success of many graph-based representations and algorithms for handling structured data, especially in the emerging field of graph signal processing. However, a meaningful graph is not always readily available from the data, nor easy to define depending on the application domain. In particular, it is often desirable in graph signal processing applications that a graph is chosen such that the data admit certain regularity or smoothness on the graph. In this paper, we address the problem of learning graph Laplacians, which is equivalent to learning graph topologies, such that the input data form graph signals with smooth variations on the resulting topology. To this end, we adopt a factor analysis model for the graph signals and impose a Gaussian probabilistic prior on the latent variables that control these signals. We show that the Gaussian prior leads to an efficient representation that favors the smoothness property of the graph signals. We then propose an algorithm for learning graphs that enforces such property and is based on minimizing the variations of the signals on the learned graph. Experiments on both synthetic and real world data demonstrate that the proposed graph learning framework can efficiently infer meaningful graph topologies from signal observations under the smoothness prior.
Author	Thanou, Dorina Xiaowen Dong Vandergheynst, Pierre Frossard, Pascal
Author_xml	– sequence: 1 surname: Xiaowen Dong fullname: Xiaowen Dong email: xdong@mit.edu organization: MIT Media Lab., Cambridge, MA, USA – sequence: 2 givenname: Dorina surname: Thanou fullname: Thanou, Dorina email: dorina.thanou@epfl.ch organization: Signal Process. Labs., Ecole Polytech. Fed. de Lausanne, Lausanne, Switzerland – sequence: 3 givenname: Pascal surname: Frossard fullname: Frossard, Pascal email: pascal.frossard@epfl.ch organization: Signal Process. Labs., Ecole Polytech. Fed. de Lausanne, Lausanne, Switzerland – sequence: 4 givenname: Pierre surname: Vandergheynst fullname: Vandergheynst, Pierre email: pierre.vandergheynst@epfl.ch organization: Signal Process. Labs., Ecole Polytech. Fed. de Lausanne, Lausanne, Switzerland
BookMark	eNp9kE1Lw0AQhhepYFu9C172D6TO7FeSm1K0ChHFVvAWtptNu5Juwm4O-u-b0uLBg6cZhnleXp4JGfnWW0KuEWaIkN-ulm8zBqhmTAHLID8jY8wFJiBSNRp2kDyRWfp5QSYxfgGgELkak7vC6uCd39BCd402Tnv6ovvgvqnzdLlr235LF0F3W7p0G68b-m67YKP1ve5d6-MlOa91E-3VaU7Jx-PDav6UFK-L5_l9kRieYp8Yo7iouarBWIGMpYhZKtZcGECO-RorXtV1Jvlwr6yUmawMt6o2a6ZVxSSfEnXMNaGNMdi6NO5YoQ_aNSVCefBQDh7Kg4fy5GEA4Q_YBbfT4ec_5OaIOGvt73sqJZM58D30XWpp
CODEN	ITPRED
CitedBy_id	crossref_primary_10_1109_LSP_2019_2936665 crossref_primary_10_1016_j_specom_2020_12_010 crossref_primary_10_1109_TSP_2022_3184455 crossref_primary_10_1109_ACCESS_2021_3120994 crossref_primary_10_1016_j_dsp_2020_102782 crossref_primary_10_1016_j_sigpro_2020_107931 crossref_primary_10_1109_TIFS_2023_3302508 crossref_primary_10_1007_s00041_025_10177_4 crossref_primary_10_1007_s10115_025_02406_5 crossref_primary_10_1109_MSP_2023_3262906 crossref_primary_10_1109_TNNLS_2022_3190420 crossref_primary_10_1016_j_sigpro_2018_02_017 crossref_primary_10_1109_LCOMM_2022_3149814 crossref_primary_10_1016_j_dsp_2021_103360 crossref_primary_10_1109_JIOT_2021_3067717 crossref_primary_10_1016_j_sigpro_2022_108574 crossref_primary_10_1109_JPROC_2018_2820126 crossref_primary_10_1109_LSP_2019_2896435 crossref_primary_10_1109_JSEN_2022_3156152 crossref_primary_10_1109_TSIPN_2022_3202035 crossref_primary_10_1109_TSP_2024_3392348 crossref_primary_10_3390_math12121820 crossref_primary_10_1109_LSP_2025_3553064 crossref_primary_10_1109_TSP_2020_2993780 crossref_primary_10_1109_JSTSP_2017_2726975 crossref_primary_10_1016_j_sigpro_2024_109663 crossref_primary_10_1109_TSP_2024_3361712 crossref_primary_10_1109_TSP_2019_2903025 crossref_primary_10_1016_j_neuroimage_2021_118289 crossref_primary_10_1016_j_crhy_2019_08_003 crossref_primary_10_1016_j_jneumeth_2020_108649 crossref_primary_10_1109_TSIPN_2016_2613687 crossref_primary_10_1109_LSP_2021_3093872 crossref_primary_10_1109_TSIPN_2025_3572698 crossref_primary_10_1016_j_ifacol_2020_12_2684 crossref_primary_10_1016_j_jnca_2022_103434 crossref_primary_10_1007_s11042_022_13904_x crossref_primary_10_1109_ACCESS_2019_2934490 crossref_primary_10_1109_JBHI_2023_3267789 crossref_primary_10_1109_TII_2018_2868364 crossref_primary_10_1109_TSP_2023_3340009 crossref_primary_10_1016_j_neucom_2023_02_007 crossref_primary_10_1109_TIT_2024_3413534 crossref_primary_10_1109_TSP_2025_3588173 crossref_primary_10_1109_TSP_2021_3057258 crossref_primary_10_1109_TSP_2023_3303639 crossref_primary_10_1016_j_jnca_2025_104116 crossref_primary_10_1007_s11634_023_00565_3 crossref_primary_10_1016_j_neucom_2020_12_015 crossref_primary_10_3390_app14104094 crossref_primary_10_1109_TSP_2022_3167525 crossref_primary_10_1007_s41109_021_00438_8 crossref_primary_10_1109_LSP_2021_3123459 crossref_primary_10_1109_TSIPN_2023_3345142 crossref_primary_10_1007_s12530_020_09348_z crossref_primary_10_1109_TSP_2022_3205474 crossref_primary_10_1109_TCSII_2021_3109339 crossref_primary_10_1109_TNSE_2022_3169220 crossref_primary_10_1016_j_sigpro_2022_108708 crossref_primary_10_1109_TSIPN_2020_2984499 crossref_primary_10_1109_LSP_2025_3568370 crossref_primary_10_1016_j_dsp_2021_103270 crossref_primary_10_1109_MSP_2018_2887284 crossref_primary_10_1080_10556788_2023_2269594 crossref_primary_10_1007_s11571_020_09662_x crossref_primary_10_1109_JIOT_2022_3196154 crossref_primary_10_1016_j_sigpro_2021_108149 crossref_primary_10_1109_TSP_2024_3514091 crossref_primary_10_1109_TIP_2020_3042088 crossref_primary_10_1016_j_sigpro_2025_109995 crossref_primary_10_1109_TSP_2025_3553915 crossref_primary_10_1109_TSP_2022_3149134 crossref_primary_10_1016_j_jneuroling_2020_100936 crossref_primary_10_1109_MSP_2020_3014590 crossref_primary_10_1109_TPWRD_2021_3135075 crossref_primary_10_1109_MCS_2021_3092810 crossref_primary_10_1109_TKDE_2023_3264971 crossref_primary_10_1109_TKDE_2023_3264970 crossref_primary_10_1109_TSIPN_2021_3107628 crossref_primary_10_3390_e21010022 crossref_primary_10_1109_TSP_2022_3160277 crossref_primary_10_1016_j_dsp_2024_104914 crossref_primary_10_1016_j_neuroimage_2022_119037 crossref_primary_10_3390_electronics11213462 crossref_primary_10_1109_TSP_2019_2899822 crossref_primary_10_1109_LSP_2017_2712141 crossref_primary_10_1109_TSP_2023_3347646 crossref_primary_10_1109_TSIPN_2021_3100302 crossref_primary_10_3390_a13090228 crossref_primary_10_1109_TSIPN_2017_2742940 crossref_primary_10_1002_hbm_25410 crossref_primary_10_1109_TSIPN_2022_3169632 crossref_primary_10_1109_LSP_2020_3023587 crossref_primary_10_1016_j_eswa_2020_113587 crossref_primary_10_1109_TSP_2020_3009645 crossref_primary_10_1109_TSP_2022_3159393 crossref_primary_10_1016_j_iot_2024_101284 crossref_primary_10_1016_j_bspc_2023_105537 crossref_primary_10_1109_LSP_2022_3165468 crossref_primary_10_1109_TSIPN_2020_2983139 crossref_primary_10_1109_TSP_2019_2896229 crossref_primary_10_1109_TSP_2023_3263675 crossref_primary_10_1109_TSIPN_2025_3540701 crossref_primary_10_1109_TPAMI_2022_3225572 crossref_primary_10_1109_TSIPN_2025_3527888 crossref_primary_10_1109_TSP_2023_3238272 crossref_primary_10_1016_j_jneuroling_2025_101285 crossref_primary_10_3390_s20216001 crossref_primary_10_1109_TSP_2024_3436524 crossref_primary_10_1109_TSIPN_2022_3183498 crossref_primary_10_1109_TSP_2019_2925602 crossref_primary_10_1109_TSP_2019_2904922 crossref_primary_10_1186_s13634_024_01201_8 crossref_primary_10_1109_TSP_2024_3446453 crossref_primary_10_1016_j_imu_2021_100662 crossref_primary_10_1109_TSP_2018_2870386 crossref_primary_10_1109_ACCESS_2022_3167055 crossref_primary_10_1007_s10898_024_01401_4 crossref_primary_10_1016_j_jfranklin_2025_107793 crossref_primary_10_1109_LSP_2023_3298280 crossref_primary_10_1109_TSIPN_2025_3599780 crossref_primary_10_1016_j_sigpro_2019_107381 crossref_primary_10_1016_j_chaos_2023_113977 crossref_primary_10_1016_j_neuri_2022_100091 crossref_primary_10_1109_TSIPN_2017_2731164 crossref_primary_10_1016_j_dsp_2021_103192 crossref_primary_10_1016_j_jfranklin_2023_04_030 crossref_primary_10_1109_ACCESS_2020_2983590 crossref_primary_10_1016_j_sigpro_2021_108101 crossref_primary_10_1109_TIP_2022_3145242 crossref_primary_10_1016_j_bspc_2023_104952 crossref_primary_10_1016_j_sigpro_2022_108744 crossref_primary_10_3390_bioengineering11070671 crossref_primary_10_1016_j_dsp_2024_104565 crossref_primary_10_3390_info9060143 crossref_primary_10_1080_00401706_2023_2197471 crossref_primary_10_1016_j_neucom_2020_12_061 crossref_primary_10_1109_TSP_2021_3060619 crossref_primary_10_1109_TSP_2024_3419182 crossref_primary_10_1109_TPAMI_2020_3013433 crossref_primary_10_1109_TSP_2023_3267990 crossref_primary_10_1109_TSIPN_2024_3352236 crossref_primary_10_1109_TSIPN_2025_3589719 crossref_primary_10_1109_TSIPN_2017_2731051 crossref_primary_10_1016_j_jmva_2023_105209 crossref_primary_10_1109_TBME_2020_3022335 crossref_primary_10_1109_TSIPN_2022_3170652 crossref_primary_10_1109_TAI_2021_3076021 crossref_primary_10_1186_s12859_023_05250_y crossref_primary_10_1007_s43926_021_00011_w crossref_primary_10_1109_TIP_2016_2627807 crossref_primary_10_1109_TPWRD_2023_3266302 crossref_primary_10_1080_01431161_2020_1782507 crossref_primary_10_1109_TSP_2017_2752689 crossref_primary_10_1109_TSP_2023_3300632 crossref_primary_10_1109_LSP_2025_3531218 crossref_primary_10_1109_TCSII_2020_3045217 crossref_primary_10_1109_RBME_2021_3122522 crossref_primary_10_1109_JSEN_2023_3337519 crossref_primary_10_1016_j_knosys_2022_110159 crossref_primary_10_1109_TSP_2025_3526287 crossref_primary_10_1016_j_bspc_2024_106954 crossref_primary_10_1016_j_sigpro_2024_109732 crossref_primary_10_1109_TSP_2019_2952055 crossref_primary_10_3390_ijgi11010018 crossref_primary_10_1186_s13634_025_01211_0 crossref_primary_10_1109_TCAD_2022_3198513 crossref_primary_10_1016_j_dsp_2020_102728 crossref_primary_10_1155_2019_3208569 crossref_primary_10_1109_OJSP_2025_3588447 crossref_primary_10_1109_TSP_2022_3167145 crossref_primary_10_1109_TSIPN_2018_2872157 crossref_primary_10_1109_JIOT_2024_3416525 crossref_primary_10_1186_s13634_024_01128_0 crossref_primary_10_3390_e21080759 crossref_primary_10_1109_TSP_2022_3229950 crossref_primary_10_1016_j_sigpro_2021_108256 crossref_primary_10_1109_TSIPN_2022_3206578 crossref_primary_10_1016_j_sigpro_2023_109308 crossref_primary_10_1016_j_cmpb_2024_108479 crossref_primary_10_1109_ACCESS_2020_3018151 crossref_primary_10_1109_LSP_2017_2763154 crossref_primary_10_1109_TSP_2020_3016494 crossref_primary_10_1109_TSP_2024_3354572 crossref_primary_10_1109_JPROC_2018_2799702 crossref_primary_10_3390_app13127130 crossref_primary_10_1109_LSP_2020_3005053 crossref_primary_10_1109_TAC_2021_3056362 crossref_primary_10_1109_JSEN_2021_3106656 crossref_primary_10_1016_j_compeleceng_2025_110200 crossref_primary_10_1016_j_neucom_2024_128210 crossref_primary_10_1109_LSP_2024_3501273 crossref_primary_10_1109_TSIPN_2020_3046217 crossref_primary_10_1109_TSP_2024_3349788 crossref_primary_10_1016_j_dsp_2022_103792 crossref_primary_10_1109_TSIPN_2020_2964249 crossref_primary_10_1016_j_sigpro_2024_109519 crossref_primary_10_1109_ACCESS_2021_3119569 crossref_primary_10_1109_TSIPN_2020_3015341 crossref_primary_10_1016_j_sigpro_2023_109230 crossref_primary_10_1109_TSP_2020_3039880 crossref_primary_10_1016_j_neunet_2023_05_016 crossref_primary_10_1016_j_jat_2021_105620 crossref_primary_10_1109_TSIPN_2023_3295770 crossref_primary_10_3390_jlpea13020039 crossref_primary_10_1109_TSP_2024_3439554 crossref_primary_10_1109_TCNS_2024_3371548 crossref_primary_10_1016_j_cmpb_2024_108290 crossref_primary_10_1016_j_yofte_2022_103006 crossref_primary_10_1109_TIP_2019_2932853 crossref_primary_10_1145_3339823 crossref_primary_10_1109_ACCESS_2019_2916567 crossref_primary_10_1109_TSIPN_2020_2975393 crossref_primary_10_1109_TSIPN_2023_3240893 crossref_primary_10_1016_j_sigpro_2023_108950 crossref_primary_10_1093_comnet_cnz031 crossref_primary_10_1109_TSP_2024_3381071 crossref_primary_10_1109_TIM_2024_3373062 crossref_primary_10_1109_TSIPN_2021_3059995 crossref_primary_10_1137_19M1285469 crossref_primary_10_1016_j_sigpro_2023_109120 crossref_primary_10_1109_TSP_2019_2929471 crossref_primary_10_1109_TAI_2025_3545800 crossref_primary_10_1109_TSP_2019_2961296 crossref_primary_10_1109_TSIPN_2024_3485532 crossref_primary_10_1109_TSIPN_2020_2988572 crossref_primary_10_1109_TSIPN_2017_2749976 crossref_primary_10_1016_j_sigpro_2023_108927 crossref_primary_10_1007_s11760_023_02492_4 crossref_primary_10_1109_TSIPN_2022_3161079 crossref_primary_10_1109_TIP_2019_2906554 crossref_primary_10_1109_TSP_2020_3042940 crossref_primary_10_1088_1741_2552_ad2496 crossref_primary_10_1109_JPROC_2018_2804318 crossref_primary_10_1109_TSIPN_2019_2936361 crossref_primary_10_1016_j_asr_2021_01_058 crossref_primary_10_1109_TSIPN_2025_3594003 crossref_primary_10_1109_TSP_2021_3115947 crossref_primary_10_1109_ACCESS_2021_3126675 crossref_primary_10_1109_LSP_2019_2922952 crossref_primary_10_7554_eLife_61927 crossref_primary_10_1109_MSP_2018_2890143 crossref_primary_10_3390_math9020168 crossref_primary_10_1109_TSIPN_2020_3038475 crossref_primary_10_1016_j_jag_2022_103150 crossref_primary_10_1109_TSP_2020_2982325 crossref_primary_10_1109_TSIPN_2020_2995515 crossref_primary_10_1109_TSP_2023_3348202 crossref_primary_10_1109_JSEN_2021_3124818 crossref_primary_10_1016_j_sigpro_2021_108335 crossref_primary_10_1016_j_dsp_2022_103762 crossref_primary_10_1109_TSIPN_2019_2936358 crossref_primary_10_1049_ell2_12459 crossref_primary_10_1007_s00041_021_09850_1 crossref_primary_10_1007_s10915_025_02922_0 crossref_primary_10_1109_TSIPN_2023_3279513 crossref_primary_10_1103_PhysRevResearch_5_033129 crossref_primary_10_1109_TSP_2017_2733489 crossref_primary_10_1109_TSP_2021_3093765 crossref_primary_10_1016_j_patrec_2018_06_006 crossref_primary_10_1186_s13636_023_00272_z
Cites_doi	10.1093/biostatistics/kxm045 10.1002/9780470316894 10.1109/TSP.2012.2212886 10.1007/978-3-642-15939-8_17 10.1109/TSP.2014.2345355 10.1145/1273496.1273520 10.1109/PCS.2010.5702565 10.1109/TSP.2013.2238935 10.1109/MSP.2012.2235192 10.1109/TSP.2014.2332441 10.1016/j.acha.2010.04.005 10.1109/ICASSP.2015.7178669 10.1093/biomet/asm018 10.1109/ISBI.2011.5872835 10.1109/ICASSP.2013.6638232 10.1214/13-AOS1162 10.1109/TSP.2012.2188718 10.1007/978-3-540-45167-9_12 10.1109/TSP.2011.2107908 10.1016/j.neuroimage.2013.07.019 10.1109/ISBI.2013.6556550 10.1016/j.jcss.2007.08.006 10.1007/s11222-007-9033-z 10.1017/CBO9780511810800 10.1109/TSP.2015.2424203 10.1201/9780203492024 10.1126/science.286.5439.509 10.1109/SSP.2012.6319640 10.1002/9781119970583 10.1007/978-3-642-38868-2_1 10.1109/TPAMI.2013.50 10.1109/ICASSP.2012.6288775 10.1016/j.acha.2006.04.004 10.1017/CBO9780511809071 10.1109/ICASSP.2012.6288639 10.1016/j.acha.2006.03.004 10.1214/009053606000000281 10.1109/TIT.2013.2252233 10.1109/LSP.2012.2230165 10.1007/11503415_32 10.1214/08-EJS176 10.1111/j.1467-9868.2005.00503.x 10.1111/1467-9868.00196 10.1017/CBO9780511804441 10.1109/TSP.2011.2158428 10.1561/2200000016 10.1016/j.acha.2015.02.005 10.1145/1553374.1553400 10.1007/978-1-84800-155-8_7
ContentType	Journal Article
DBID	97E RIA RIE AAYXX CITATION
DOI	10.1109/TSP.2016.2602809
DatabaseName	IEEE All-Society Periodicals Package (ASPP) 2005–Present IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE Electronic Library (IEL) CrossRef
DatabaseTitle	CrossRef
DatabaseTitleList
Database_xml	– sequence: 1 dbid: RIE name: IEEE Xplore url: https://ieeexplore.ieee.org/ sourceTypes: Publisher
DeliveryMethod	fulltext_linktorsrc
Discipline	Engineering
EISSN	1941-0476
EndPage	6173
ExternalDocumentID	10_1109_TSP_2016_2602809 7552590
Genre	orig-research
GrantInformation_xml	– fundername: Swiss National Science Foundation grantid: 200021_135493 funderid: 10.13039/501100001711 – fundername: Swiss National Science Foundation funderid: 10.13039/501100001711 – fundername: Hasler Foundation, Switzerland funderid: 10.13039/501100003475 – fundername: LOGAN
GroupedDBID	-~X .DC 0R~ 29I 4.4 5GY 6IK 85S 97E AAJGR AARMG AASAJ AAWTH ABAZT ABQJQ ABVLG ACGFO ACIWK ACNCT AENEX AGQYO AGSQL AHBIQ AJQPL AKQYR ALMA_UNASSIGNED_HOLDINGS ASUFR ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ CS3 EBS EJD F5P HZ~ IFIPE IPLJI JAVBF LAI MS~ O9- OCL P2P RIA RIE RNS TAE TN5 3EH 53G 5VS AAYXX ABFSI ACKIV AETIX AI. AIBXA AKJIK ALLEH CITATION E.L H~9 ICLAB IFJZH VH1
ID	FETCH-LOGICAL-c371t-cc634f36f0ce4122711874b34c01319b1d3dff853118de5585dc3e6fcb2a6d253
IEDL.DBID	RIE
ISICitedReferencesCount	446
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000386232300007&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	1053-587X
IngestDate	Sat Nov 29 04:10:41 EST 2025 Tue Nov 18 22:18:35 EST 2025 Tue Aug 26 16:43:03 EDT 2025
IsDoiOpenAccess	false
IsOpenAccess	true
IsPeerReviewed	true
IsScholarly	true
Issue	23
Language	English
License	https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c371t-cc634f36f0ce4122711874b34c01319b1d3dff853118de5585dc3e6fcb2a6d253
OpenAccessLink	https://infoscience.epfl.ch/handle/20.500.14299/105002
PageCount	14
ParticipantIDs	crossref_citationtrail_10_1109_TSP_2016_2602809 crossref_primary_10_1109_TSP_2016_2602809 ieee_primary_7552590
PublicationCentury	2000
PublicationDate	2016-Dec.1, 2016-12-00
PublicationDateYYYYMMDD	2016-12-01
PublicationDate_xml	– month: 12 year: 2016 text: 2016-Dec.1, day: 01
PublicationDecade	2010
PublicationTitle	IEEE transactions on signal processing
PublicationTitleAbbrev	TSP
PublicationYear	2016
Publisher	IEEE
Publisher_xml	– name: IEEE
References	ref13 ref56 ref15 ref14 ref53 ref52 ref55 ref11 ref54 ref10 grant (ref57) 2013 banerjee (ref38) 2008; 9 ref17 ref16 zhu (ref59) 2003 ref19 ref18 zhou (ref4) 0 ng (ref63) 0 ref51 (ref64) 0 ref46 ref48 (ref65) 0 ref47 ref44 ref43 barabási (ref61) 1999; 286 ref49 ref7 ref9 ref3 ref6 ref5 ref40 roweis (ref50) 1997 ref35 ref34 ref37 ref36 (ref66) 0 ref31 ref30 ravikumar (ref41) 0 ref32 grant (ref58) 2008 ref2 ref1 ref39 erd?s (ref60) 1960; 5 hsieh (ref42) 0 (ref62) 0 argyriou (ref33) 0 ref24 ref23 ref26 ref25 ref20 ref22 ref21 lake (ref8) 0 chung (ref45) 1997 ref28 ref27 ref29 gavish (ref12) 0
References_xml	– start-page: 367 year: 0 ident: ref12 article-title: Multiscale wavelets on trees, graphs and high dimensional data: Theory and applications to semi supervised learning publication-title: Proc 27th Int Conf Mach Learn – ident: ref39 doi: 10.1093/biostatistics/kxm045 – start-page: 67 year: 0 ident: ref33 article-title: Combining graph Laplacians for semi-supervised learning publication-title: Proc Adv Neural Inf Process Syst 18 – start-page: 2330 year: 0 ident: ref42 article-title: Sparse inverse covariance matrix estimation using quadratic approximation publication-title: Proc Adv Neural Inf Process Syst 24 – volume: 9 start-page: 485 year: 2008 ident: ref38 article-title: Model selection through sparse maximum likelihood estimation for multivariate Gaussian or binary data publication-title: J Mach Learn Res – ident: ref47 doi: 10.1002/9780470316894 – start-page: 849 year: 0 ident: ref63 article-title: On spectral clustering: Analysis and an algorithm publication-title: Proc Adv Neural Inf Process Syst 14 – ident: ref5 doi: 10.1109/TSP.2012.2212886 – ident: ref35 doi: 10.1007/978-3-642-15939-8_17 – ident: ref24 doi: 10.1109/TSP.2014.2345355 – start-page: 778 year: 0 ident: ref8 article-title: Discovering structure by learning sparse graph publication-title: Proc 32nd Annu Meeting Cogn Sci Soc – start-page: 1329 year: 0 ident: ref41 article-title: Model selection in Gaussian graphical models: High-dimensional consistency of $\ell _1$ -regularized MLE publication-title: Proc Adv Neural Inf Process Syst 21 – ident: ref34 doi: 10.1145/1273496.1273520 – ident: ref21 doi: 10.1109/PCS.2010.5702565 – ident: ref2 doi: 10.1109/TSP.2013.2238935 – ident: ref1 doi: 10.1109/MSP.2012.2235192 – year: 1997 ident: ref50 article-title: EM algorithms for PCA and sensible PCA – ident: ref18 doi: 10.1109/TSP.2014.2332441 – ident: ref13 doi: 10.1016/j.acha.2010.04.005 – ident: ref6 doi: 10.1109/ICASSP.2015.7178669 – ident: ref37 doi: 10.1093/biomet/asm018 – ident: ref31 doi: 10.1109/ISBI.2011.5872835 – ident: ref23 doi: 10.1109/ICASSP.2013.6638232 – ident: ref43 doi: 10.1214/13-AOS1162 – ident: ref15 doi: 10.1109/TSP.2012.2188718 – ident: ref3 doi: 10.1007/978-3-540-45167-9_12 – ident: ref51 doi: 10.1109/TSP.2011.2107908 – ident: ref32 doi: 10.1016/j.neuroimage.2013.07.019 – ident: ref29 doi: 10.1109/ISBI.2013.6556550 – ident: ref27 doi: 10.1016/j.jcss.2007.08.006 – ident: ref49 doi: 10.1007/s11222-007-9033-z – ident: ref53 doi: 10.1017/CBO9780511810800 – ident: ref16 doi: 10.1109/TSP.2015.2424203 – ident: ref44 doi: 10.1201/9780203492024 – volume: 286 start-page: 509 year: 1999 ident: ref61 article-title: Emergence of scaling in random networks publication-title: Science doi: 10.1126/science.286.5439.509 – year: 2013 ident: ref57 publication-title: CVX MATLAB Software for Disciplined Convex Programming – ident: ref9 doi: 10.1109/SSP.2012.6319640 – ident: ref46 doi: 10.1002/9781119970583 – year: 0 ident: ref66 – ident: ref22 doi: 10.1007/978-3-642-38868-2_1 – ident: ref7 doi: 10.1109/TPAMI.2013.50 – ident: ref10 doi: 10.1109/ICASSP.2012.6288775 – year: 0 ident: ref65 – ident: ref11 doi: 10.1016/j.acha.2006.04.004 – ident: ref56 doi: 10.1017/CBO9780511809071 – ident: ref17 doi: 10.1109/ICASSP.2012.6288639 – year: 0 ident: ref64 – ident: ref26 doi: 10.1016/j.acha.2006.03.004 – year: 0 ident: ref62 – ident: ref36 doi: 10.1214/009053606000000281 – ident: ref20 doi: 10.1109/TIT.2013.2252233 – ident: ref28 doi: 10.1109/LSP.2012.2230165 – ident: ref25 doi: 10.1007/11503415_32 – ident: ref40 doi: 10.1214/08-EJS176 – year: 2003 ident: ref59 article-title: Semi-supervised learning: From Gaussian fields to Gaussian processes – ident: ref52 doi: 10.1111/j.1467-9868.2005.00503.x – ident: ref48 doi: 10.1111/1467-9868.00196 – ident: ref54 doi: 10.1017/CBO9780511804441 – ident: ref14 doi: 10.1109/TSP.2011.2158428 – volume: 5 start-page: 17 year: 1960 ident: ref60 article-title: On the evolution of random graphs publication-title: Publ Math Inst Hung Acad Sci – ident: ref55 doi: 10.1561/2200000016 – ident: ref19 doi: 10.1016/j.acha.2015.02.005 – ident: ref30 doi: 10.1145/1553374.1553400 – year: 1997 ident: ref45 publication-title: Spectral Graph Theory – start-page: 95 year: 2008 ident: ref58 article-title: Graph implementations for nonsmooth convex programs publication-title: Recent Advances in Learning and Control (Lecture Notes in Control and Information Sciences) doi: 10.1007/978-1-84800-155-8_7 – start-page: 132 year: 0 ident: ref4 article-title: A regularization framework for learning from graph data publication-title: Proc ICML Workshop Statistical Relational Learning
SSID	ssj0014496
Score	2.6776571
Snippet	The construction of a meaningful graph plays a crucial role in the success of many graph-based representations and algorithms for handling structured data,...
SourceID	crossref ieee
SourceType	Enrichment Source Index Database Publisher
StartPage	6160
SubjectTerms	Analytical models factor analysis Gaussian prior graph signal processing Kernel Laplace equations Laplacian matrix learning representation theory Signal processing Signal processing algorithms Signal representation Topology
Title	Learning Laplacian Matrix in Smooth Graph Signal Representations
URI	https://ieeexplore.ieee.org/document/7552590
Volume	64
WOSCitedRecordID	wos000386232300007&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVIEE databaseName: IEEE Xplore customDbUrl: eissn: 1941-0476 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0014496 issn: 1053-587X databaseCode: RIE dateStart: 19910101 isFulltext: true titleUrlDefault: https://ieeexplore.ieee.org/ providerName: IEEE
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3NS8MwFA9zeNCDX1OcX-TgRbBb16RNelPE6WGO4SbsVtqXZAy0k32If755aVd2EMFbCUko76W895rf-_0IuRY8S7Gf0gtEGHpcao2Ut8xDqrpAREZKcKolPdHvy_E4HtTIbdULo7V24DPdwkd3l69msMJfZW27nc3WbYG-JYQoerWqGwPOnRaXTReYF0oxXl9J-nF7NBwghitq2dw9kAg93AhBG5oqLqR09__3Mgdkr0wd6X3h60NS0_kR2d0gFGyQu5IudUJ7KaKtrO_pC5Lwf9NpTocfM-sX-oQc1XQ4neBurw4JWzYg5Ytj8tZ9HD08e6VGggdMdJYeQMS4YZHxQfNOEAiUD-cZ44BEOnHWUUwZY2OyHVc6tMWBAqYjA1mQRioI2Qmp57NcnxKqwH6-GTe-ShU3GqQfGqyGpAAb50E0SXtttgRKAnHUsXhPXCHhx4k1dIKGTkpDN8lNteKzIM_4Y24DbVzNK8179vvwOdnBxQWu5ILUl_OVviTb8LWcLuZX7mT8AIvltKg
linkProvider	IEEE
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LS8NAEF5KFdSDryrW5x68CKZNdjfZ5KaItWJaiq3QW0j2UQqaSh_iz3dnm4YeRPAWls0QZhJmJvvN9yF0zVmWwjylQ7jvOyxUCihvqQNUdYQHOgyFVS2JebcbDodRr4Juy1kYpZQFn6kGXNqzfDkRC_hV1jTmTLVuGvQNnzHiLae1yjMDxqwalykYqOOHfLg6lHSj5qDfAxRX0DDVOwkBfLiWhNZUVWxSae3973H20W5RPOL7ZbQPUEXlh2hnjVKwhu4KwtQRjlPAW5no4w7Q8H_jcY77HxMTGfwELNW4Px6BtVeLhS1GkPLZEXprPQ4e2k6hkuAIyr25I0RAmaaBdoViHiEcBMRZRpkAKp0o8ySVWpusbNal8k17IAVVgRYZSQNJfHqMqvkkVycIS2E-4IxpV6aSaSVC19fQD4VcmEwveB01V25LREEhDkoW74ltJdwoMY5OwNFJ4eg6uinv-FzSZ_yxtwY-LvcV7j39ffkKbbUHnTiJn7svZ2gbDC1RJueoOp8u1AXaFF_z8Wx6ad-SHyAJt-8
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Learning+Laplacian+Matrix+in+Smooth+Graph+Signal+Representations&rft.jtitle=IEEE+transactions+on+signal+processing&rft.au=Xiaowen+Dong&rft.au=Thanou%2C+Dorina&rft.au=Frossard%2C+Pascal&rft.au=Vandergheynst%2C+Pierre&rft.date=2016-12-01&rft.pub=IEEE&rft.issn=1053-587X&rft.volume=64&rft.issue=23&rft.spage=6160&rft.epage=6173&rft_id=info:doi/10.1109%2FTSP.2016.2602809&rft.externalDocID=7552590
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1053-587X&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1053-587X&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1053-587X&client=summon