sampling & community structure in densely connected networks - PowerPoint PPT Presentation

sampling & community structure in densely connected networks Sune Lehmann , YY Ahn and JP Bagrow Technical University of Denmark

Yong-­‑Yeol ¡Ahn Jim ¡Bagrow

pervasive overlap sampling metadata

Illustra6on: ¡Newman ¡& ¡Girvan. ¡PRE ¡69, ¡026113 ¡(2004)

Alice_Martucci Caroline_Buckee Kaspar_Bredahl_Rasmussen Trevor_Gillaspy Skyler_Place Dorthe_Sandager_Bilde Anmol_Madan Pascal_Braun Annelise_Maren_Kromann Jure_Leskovec Nathan_Eagle Jim_Bagrow Zehui_Qu Rikke_Thorsteinsson Annamaria_Talas Marie_Louise_Scharff_Grandorf Ida_Marie_Heerfordt Jonas_Jakobsen Agi_Petroczky Rikke_Hadrup Benny_Lautrup Kristian_Ingemann_Petersen Sebastian_Ahnert Maximilian_Schich Albert-Laszlo_Barabasi Cesar_A._Hidalgo Aaron_Clauset Julian_Candia Ronaldo_Menezes Pu_WangMichele_Coscia Suzanne_Aleva Yong-Yeol_Ahn Kristoffer_Gravgaard Vinko_Zlatic* Morten_Felding Dennis_Meyhoff_Brink Joakim_Grundahl Jose*_Fernando_Mendes Peder_Holm-Pedersen Dirk_Brockmann Gourab_Ghoshal Palle_Hyldga*rd_Poulsen *****_****Dashun_Wang Mette_Miriam_Rakel_Bo*ll Chaoming_Song Niels_Arne_Dam Line_Friis_Frederiksen Peter_Csermely Signe_Torsbjerg_J*rgensen Janet_Kelley Sabrina_Rabello Ginestra_Bianconi Nicolle_Haley Gert_Gadkj*r_Nielsen Ida_Solhaug Gert_Nielsen Anne-Ruxandra_Carvunis Marta_C._Gonzalez Laura_Kirch_Kirkegaard Petter_Holme Sameet_Sreenivasan Jozsef_Baranyi Stig_Aagaard Rut_Jesus Nikolaj_Beuschel Joa*o_Gama_Oliveira Nitesh_Chawla Takashi_Iba Sang_Hoon_Lee Luigi_Cuccia Mads_Olesen Karina_Louise_Petersen Hans_Laurberg Kristian_West Martin_Schwartz Aaron_Petersen_DiBona Morten_Hansen Dan_Romescu Kaare_Brandt_Petersen Rasmus_Elsborg_Madsen Mikael_*rting_Kristiansen Morten_Houmann_Jensen Sebastian_Bernhardsson Jonas_Mengel-From Lasse_M*lgaard Michael_Syskind_Pedersen Finn_A*rup_Nielsen Anders_Meng Torben_Jensen Steen_Thomsen Ella_Caroline_DiBona Erik_Christensen Kristian_Krohn_Djurhuus Erik_West Tue_Lehn-Schi*ler Mikkel_N._Schmidt J*rgen_Jensen Esben_Sverdrup-Jensen Mikael_Caroc_Warner Ole_Jensen Morten_Morup Mikkel_Nissen Anders_Petersen Jan_Larsen Niels_Henrik_Bohl_Pontoppidan Brian_Larsen Sofie_Falbe Christina_Egelund_Pedersen Thomas_R*nn Louise_Fynbo_Jensen Ling_Feng Lone_N*rgaard_Skoven Kristoffer_Hougaard_Madsen Mads_Dyrholm Torbj*rn_Jensen James_Kang Michael_Nyhus_Andreasen Frank_*stergaard Anders_Vedel_Holst Christian_Nyhus_Andreasen Stine_Bang_Iversen S*ren_Stenild_Juhl Mads_Hofmeister Simon_Falbe-Hansen Mikkel_S*ndergaard Katrine_Bj*rnlund Sarah_Wasana Lek-Heng_Lim Johan_Hjortsberg Kasper_Vedel Helene_Christensen Anne_Lynge_Agerb*k Christian_Jensen Andreas_Toft_S*rensen Lisa_Agerb*k Mogens_Skot-Hansen Christian_Christiansen Andreas_Holst_Andersen Mikkjal_Gulklett Carsten_Henriksen Maria_Glinvad S*ren_Iversen Anders_Iversen Jens_Kj*rsgaard Tim_SweeneyShannon_Walkley Carly_Wilcox Peter_Langen Karen_Agerb*k_J*rgensen Mette_Agerb*k_Kj*ller Torbj*rn_Porsmose_Rokamp Jessie_Hudecek_Kj*rsgaard Rikke_Ankerstjerne_Schmidt Renee_Randall S*ren_McLaks_Lehmann Peter_Lehmann_Syre_Fin Lis_Agerb*k_J*rgensen Karina_Kj*r Karin_Agerb*k Kalle_Hennie James_SweeneyColeen_Filipinas Lauren_Knight_Lewicki Kira_Clausen Lars_Lehmann_Hunnam Jacob_Berg Nina_Adelaide_Skeem_Geist B*rge_Lehmann Jesper_Levinsen S*ren_Kj*rsgaard Kirsten_Boelskifte Mikis_Theodorakis_Lehmann Michael_Tronskov Signe_Lehmann Sanne_Lehmann_Nielsen Lene_Lehmann Winnie_R*dkj*r Helle_Lehmann_Becker Steen_Lehmann

Caroline_Buckee Trevor_Gillaspy Skyler_Place Anmol_Madan Pascal_Braun Jure_Leskovec Nathan_Eagle Jim_Bagrow Zehui_Qu Annamaria_Talas Agi_Petroczky Sebastian_Ahnert Albert-Laszlo_Barabasi Maximilian_Schich Cesar_A._Hidalgo Aaron_Clauset Julian_Candia Ronaldo_Menezes Pu_WangMichele_Coscia Suzanne_Aleva Yong-Yeol_Ahn Vinko_Zlatic* Jose*_Fernando_Mendes Dirk_Brockmann Gourab_Ghoshal *****_****Dashun_Wang Mette_Miriam_Rakel_Bo*ll Chaoming_Song Peter_Csermely Janet_Kelley Sabrina_Rabello Ginestra_Bianconi Nicolle_Haley Anne-Ruxandra_Carvunis Marta_C._Gonzalez Petter_Holme Sameet_Sreenivasan Jozsef_Baranyi Rut_Jesus Takashi_Iba Joa*o_Gama_Oliveira Nitesh_Chawla Sang_Hoon_Lee Luigi_Cuccia Mads_Olesen Martin_Schwartz Dan_Romescu Sebastian_Bernhardsson Jonas_Mengel-From Lasse_M*lgaard Torben_Jensen J*rgen_Jensen Mikael_Caroc_Warner Ole_Jensen Anders_Petersen Brian_Larsen

Alice_Martucci Kaspar_Bredahl_Rasmussen Dorthe_Sandager_Bilde Annelise_Maren_Kromann Rikke_Thorsteinsson Marie_Louise_Scharff_Grandorf Ida_Marie_Heerfordt Jonas_Jakobsen Rikke_Hadrup Benny_Lautrup Kristian_Ingemann_Petersen Kristoffer_Gravgaard Dennis_Meyhoff_Brink Morten_Felding Joakim_Grundahl Peder_Holm-Pedersen Palle_Hyldga*rd_Poulsen Niels_Arne_Dam Line_Friis_Frederiksen Signe_Torsbjerg_J*rgensen Gert_Gadkj*r_Nielsen Ida_Solhaug Gert_Nielsen Laura_Kirch_Kirkegaard Stig_Aagaard Nikolaj_Beuschel Karina_Louise_Petersen Kristian_West Aaron_Petersen_DiBona Mikael_*rting_Kristiansen Steen_Thomsen Ella_Caroline_DiBona Erik_Christensen Kristian_Krohn_Djurhuus Erik_West Esben_Sverdrup-Jensen Mikkel_Nissen

Martin_Schwartz Dan_Romescu Morten_Houmann_Jensen Sebastian_Bernhardsson Jonas_Mengel-From Torben_Jensen J*rgen_Jensen Mikael_Caroc_Warner Ole_Jensen Brian_Larsen Louise_Fynbo_Jensen Lone_N*rgaard_Skoven Torbj*rn_Jensen Sarah_Wasana Katrine_Bj*rnlund Anne_Lynge_Agerb*k Lisa_Agerb*k Carsten_Henriksen Tim_SweeneyShannon_Walkley Karen_Agerb*k_J*rgensen Mette_Agerb*k_Kj*ller S*ren_McLaks_Lehmann Peter_Lehmann_Syre_Fin Lis_Agerb*k_J*rgensen Karin_Agerb*k James_SweeneyColeen_Filipinas Lauren_Knight_Lewicki Lars_Lehmann_Hunnam B*rge_Lehmann Mikis_Theodorakis_Lehmann Signe_Lehmann Sanne_Lehmann_Nielsen Lene_Lehmann Winnie_R*dkj*r Helle_Lehmann_Becker Steen_Lehmann

10 3 metabolites number of ATP 10 2 ADP H 2 O, H + P i 10 1 10 0 0 50 100 150 200 number of communities per metabolite 1 10 2 10 3

A B

A B

Hierarchy and community structure were thought to be two sides of the same story Clauset, Moore, Newman. Nature 453, 98 (2008)

X Hierarchy and community structure were thought to be two sides of the same story Clauset, Moore, Newman. Nature 453, 98 (2008)

Even in the case when nodes belong to multiple communities, their links can be well categorized.

n + ( i ) ≡ { x | d ( i, x ) ≤ 1 } S ( e ik , e jk ) = | n + ( i ) ∩ n + ( j ) | | n + ( i ) ∪ n + ( j ) | A B C e ik e jk c c k i j a a b b S ( e ac , e bc ) = 1 S ( e ac , e bc ) = 1 3

LinkComm R Package by Alex T. Kalinka

− m c − ( n c − 1) D c = n c ( n c − 1) − ( n c − 1) 2 − m c � = D M D c c 2 m c − ( n c − 1) � = m c ( n c − 1)( n c − 1) 2 M c

BROOM PAINT SWEEP PAINTER GROOM PAINTING BRUSH HAIR TOOTHBRUSH COMB HAIRSPRAY TOOTHPASTE • SUNSET , SUNRISE, ORANGE • SUNSET , SUNRISE, RED • SUNSET , SUNRISE, PRETTY, BEAUTIFUL • SUNSET , SUNRISE, MOON • SUNSET , SUNRISE, BEACH • SUNSET , SUNRISE, SUN, DAWN, DUSK, SUNSHINE • SUNSET , SUNRISE, DAWN, DUSK, AFTERNOON, EVENING

LinkComm R Package by Alex T. Kalinka (Pavel Tomancak's group)

LinkComm R Package by Alex T. Kalinka (Pavel Tomancak's group)

LinkComm R Package by Alex T. Kalinka (Pavel Tomancak's group)

LinkComm R Package by Alex T. Kalinka (Pavel Tomancak's group)

LinkComm R Package by Alex T. Kalinka (Pavel Tomancak's group)

pervasive overlap sampling metadata

Building a (synthetic) benchmark graph assumes a model. A specific view of the community structure.

A synthetic graph cannot be used to compare methods with different models of community structure.

Problem : A synthetic graph cannot be used to compare methods with different models of community structure. Solution : Use metadata to test the detected structure.

Community quality Amazon.com Community coverage no membership Subjects Subjects HIV / AIDS Medical Africa - General Africa Africa History Subjects HIV / AIDS Medical Nonfiction / General Infectious Diseases high coverage low coverage Overlap quality Metabolic network Overlap coverage community memberships Acetyl-CoA 1. Glycolysis / Gluconeogenesis 2. TCA cycle 3. Fatty acid biosynthesis 4. ... Many pathway Memberships high overlap IDP (Inosine diphosphate) 1. Purine metaboilsm Few pathway Memberships high overlap coverage low overlap coverage low overlap

Amazon.com Community quality Community coverage Subjects Subjects HIV / AIDS Medical Africa - General Africa Africa History Subjects HIV / AIDS Medical Nonfiction / General Infectious Diseases Overlap quality Overlap coverage

Community coverage no membership ects S Medical al Infectious Diseases high coverage low coverage rk Overlap coverage community

Nonfiction / General Infectious Diseases Metabolic network Overlap quality Overlap coverage Acetyl-CoA 1. Glycolysis / Gluconeogenesis 2. TCA cycle 3. Fatty acid biosynthesis 4. ... Many pathway Memberships high overlap IDP (Inosine diphosphate) 1. Purine metaboilsm Few pathway Memberships low overlap

Infectious Diseases high coverage low coverage lic network Overlap coverage community memberships high overlap coverage low overlap coverage