File Coverage

blib/lib/NNexus/Classification.pm

Criterion	Covered	Total	%
statement	86	96	89.5
branch	15	24	62.5
condition	9	14	64.2
subroutine	9	10	90.0
pod	2	6	33.3
total	121	150	80.6

# /=====================================================================\ #
# |  NNexus Autolinker                                                  | #
# | Named Entity Classification Module                                  | #
# |=====================================================================| #
# | Part of the Planetary project: http://trac.mathweb.org/planetary    | #
# |  Research software, produced as part of work done by:               | #
# |  the KWARC group at Jacobs University                               | #
# | Copyright (c) 2012                                                  | #
# | Released under the MIT License (MIT)                                | #
# |---------------------------------------------------------------------| #
# | Adapted from the original NNexus code by                            | #
# |                                  James Gardner and Aaron Krowne     | #
# |---------------------------------------------------------------------| #
# | Deyan Ginev                   #_#     | #
# | http://kwarc.info/people/dginev                            (o o)    | #
# \=========================================================ooo==U==ooo=/ #
package NNexus::Classification;
use strict;
use warnings;
use Exporter;
our @ISA = qw(Exporter);
our @EXPORT_OK = qw(msc_similarity disambiguate);
use List::Util qw(max min);

# Let's do things differently here.
# We will use Jan Wilken Doerrie's MSC similarity metric:
# "we defined the similarity between two categories as the size of the
#   intersections divided by the size of the union over the ZBL dataset"
our $msc_similarities = [ # 63x63 matrix, top-level MSC 2000 categories
  [1.00000000,0.08157364,0.05611695,0.01857567,0.00526125,0.00493453,0.02162828,0.01738086,0.01488942,0.01995192,0.01850128,0.01315144,0.01112859,0.00875912,0.00258325,0.01958233,0.01059040,0.02694878,0.00814224,0.01508530,0.00391065,0.01222424,0.00659643,0.01744963,0.02033044,0.01715241,0.00549930,0.00368565,0.00844784,0.01205280,0.00590242,0.00640019,0.00470555,0.01450557,0.01117073,0.01519435,0.01915299,0.00949692,0.02112821,0.01075672,0.00831446,0.01284788,0.02376349,0.01846751,0.02192419,0.02827359,0.06235569,0.01871924,0.02326626,0.02549734,0.01149905,0.00904571,0.02978857,0.01858157,0.01913664,0.00986617,0.00980736,0.02622097,0.02015345,0.02370473,0.02309777,0.02525110,0.06049483],
  [0.08157364,1.00000000,0.04843149,0.00532875,0.00205666,0.00135896,0.01867335,0.01162555,0.00454580,0.00914432,0.00561143,0.00339066,0.00233557,0.00318598,0.00112062,0.00596528,0.00474509,0.01721411,0.00592865,0.00682061,0.00180499,0.00344266,0.00441784,0.00357584,0.00276735,0.00367641,0.00180428,0.00557237,0.00315267,0.00397678,0.00230947,0.00158525,0.00194050,0.00436769,0.00245270,0.00323992,0.03266539,0.00462011,0.00786873,0.00592230,0.00625668,0.00554406,0.00367927,0.00894575,0.00961623,0.00339433,0.00442661,0.02332687,0.00304362,0.00367554,0.00783214,0.00359950,0.01357759,0.00583133,0.01961088,0.03410275,0.00370477,0.00360240,0.00517674,0.00367842,0.00215416,0.00470674,0.02079996],
  [0.05611695,0.04843149,1.00000000,0.01860533,0.09942421,0.05170597,0.01116272,0.02366804,0.01088601,0.00678883,0.00619870,0.01188854,0.00194541,0.03826328,0.00037826,0.03378654,0.00411333,0.01952391,0.02813212,0.00144777,0.00048211,0.00200346,0.00019596,0.00120727,0.00040013,0.00283891,0.00242860,0.00174449,0.00086392,0.00117239,0.00139450,0.00026806,0.00036410,0.01135132,0.00259196,0.00098411,0.00869706,0.00278418,0.00065182,0.04870472,0.00162055,0.00190805,0.00122017,0.01033098,0.00408488,0.00158937,0.11329349,0.00131901,0.00031955,0.00016804,0.00014428,0.00025776,0.01361661,0.00071465,0.00278636,0.00058838,0.00033706,0.01095038,0.02561634,0.00333059,0.00669844,0.02532072,0.00174317],
  [0.01857567,0.00532875,0.01860533,1.00000000,0.03854465,0.00695286,0.06147985,0.00381552,0.01111890,0.01036229,0.04460750,0.01316603,0.01265964,0.00515676,0.00079911,0.07192152,0.00451860,0.00357714,0.00334221,0.00286208,0.00143900,0.00147393,0.02179999,0.00186239,0.00088413,0.00484911,0.00313808,0.00180966,0.00263198,0.00221683,0.00284620,0.00101324,0.00022575,0.00341334,0.00269952,0.00114372,0.05704468,0.04862097,0.00177969,0.00785647,0.00544478,0.01902742,0.00199649,0.02516203,0.01832947,0.00795814,0.07579728,0.00124556,0.00085965,0.00014810,0.00034212,0.00039567,0.00564823,0.01156505,0.00036484,0.00003067,0.00026446,0.04216157,0.01448784,0.02353333,0.00356946,0.04458390,0.00179613],
  [0.00526125,0.00205666,0.09942421,0.03854465,1.00000000,0.13498574,0.00433243,0.01252955,0.02119390,0.00273427,0.01431677,0.03376084,0.00576282,0.05441052,0.00177224,0.05178723,0.00922929,0.00392307,0.01936738,0.00051527,0.00099050,0.00025145,0.00058066,0.00029417,0.00013702,0.00106777,0.00244524,0.00110532,0.00055186,0.00040533,0.00124399,0.00035144,0.00010310,0.01638482,0.00445366,0.00120617,0.01113947,0.01531835,0.00039070,0.06202833,0.00706150,0.00336538,0.00045634,0.00300478,0.00139167,0.00075193,0.01245292,0.00033423,0.00002379,0.00001954,0.00003722,0.00006753,0.00970181,0.00050743,0.00086061,0.00000000,0.00009151,0.00290705,0.00745701,0.00204881,0.00119390,0.02242817,0.00025653],
  [0.00493453,0.00135896,0.05170597,0.00695286,0.13498574,1.00000000,0.00108207,0.00591517,0.00605827,0.00141397,0.00741604,0.02646703,0.01336303,0.06039531,0.00035010,0.06902687,0.00574293,0.00052350,0.00053657,0.00002714,0.00000000,0.00000000,0.00005061,0.00000000,0.00003237,0.00004214,0.00101535,0.00008925,0.00014061,0.00003739,0.00007630,0.00016497,0.00004694,0.00062654,0.00021500,0.00000000,0.00378012,0.00184760,0.00017622,0.00733195,0.00199509,0.00039905,0.00009479,0.00026701,0.00007847,0.00065581,0.00679404,0.00022507,0.00002622,0.00001058,0.00000000,0.00009166,0.00075771,0.00011908,0.00010628,0.00000000,0.00000000,0.00028208,0.00056563,0.00035722,0.00077455,0.00193900,0.00064115],
  [0.02162828,0.01867335,0.01116272,0.06147985,0.00433243,0.00108207,1.00000000,0.07510125,0.02964458,0.12328037,0.02564406,0.01861066,0.01072190,0.00610098,0.01736422,0.04876552,0.03999814,0.01013660,0.01648549,0.02365574,0.00114353,0.01283800,0.04351610,0.00310510,0.00250883,0.01927488,0.00578289,0.01215249,0.00733156,0.01013116,0.00939150,0.00237590,0.00047886,0.00438082,0.00267569,0.00027081,0.01065916,0.02057247,0.00373513,0.00293046,0.00387222,0.00807042,0.00871024,0.00918703,0.00147008,0.01090241,0.01622746,0.00087207,0.00010859,0.00011596,0.00047994,0.00016857,0.00977301,0.00545278,0.00160478,0.00010979,0.00000000,0.00213201,0.00103991,0.00105356,0.00090291,0.04688816,0.00337673],
  [0.01738086,0.01162555,0.02366804,0.00381552,0.01252955,0.00591517,0.07510125,1.00000000,0.10327601,0.05552831,0.02090534,0.04187867,0.00738352,0.01105315,0.01170594,0.02435063,0.00429508,0.03557033,0.00178563,0.02655667,0.00033904,0.00973898,0.00672954,0.00693442,0.00078453,0.00241796,0.00796306,0.00207254,0.00332360,0.00160225,0.00290728,0.00200535,0.00017666,0.00755212,0.00168273,0.00028101,0.01917842,0.00421842,0.00106842,0.00377618,0.00492809,0.00231786,0.00275841,0.00050158,0.00015461,0.00975019,0.00727802,0.00089392,0.00012882,0.00002086,0.00009797,0.00021588,0.00095943,0.00042942,0.00054114,0.00007965,0.00000000,0.00062483,0.00020720,0.00027694,0.00276635,0.00486968,0.00339206],
  [0.01488942,0.00454580,0.01088601,0.01111890,0.02119390,0.00605827,0.02964458,0.10327601,1.00000000,0.14900523,0.02532176,0.09917895,0.01360819,0.05210757,0.01503290,0.03515368,0.00379712,0.00287966,0.00067947,0.00302452,0.00014375,0.02226528,0.00235095,0.00174760,0.00080893,0.00196637,0.00355291,0.00048213,0.00217216,0.00078930,0.00063203,0.00112325,0.00006953,0.00426375,0.00128080,0.00022091,0.00456440,0.00935890,0.00140085,0.00611161,0.01957090,0.00565262,0.00378400,0.00031160,0.00065168,0.00249695,0.00858768,0.00057049,0.00008359,0.00002941,0.00011305,0.00010245,0.00105292,0.00026795,0.00014010,0.00000000,0.00027875,0.00106974,0.00004685,0.00060664,0.00289897,0.00612092,0.00117948],
  [0.01995192,0.00914432,0.00678883,0.01036229,0.00273427,0.00141397,0.12328037,0.05552831,0.14900523,1.00000000,0.01372342,0.04089925,0.03216888,0.03963411,0.03271138,0.04915837,0.02431038,0.00392283,0.00104910,0.02161542,0.00081625,0.17399932,0.01041594,0.00381929,0.00396809,0.01526674,0.00204542,0.00011577,0.00177630,0.00079854,0.00312736,0.00160699,0.00015678,0.00310573,0.00173009,0.00057235,0.02585302,0.01645332,0.03430529,0.00272510,0.03361024,0.04910434,0.03047494,0.00050122,0.00031984,0.00272203,0.00552471,0.00299371,0.00008030,0.00011027,0.00051862,0.00008856,0.02816400,0.00223054,0.00878367,0.00005787,0.00002673,0.00080236,0.00028778,0.00047446,0.00134026,0.01790618,0.00051373],
  [0.01850128,0.00561143,0.00619870,0.04460750,0.01431677,0.00741604,0.02564406,0.02090534,0.02532176,0.01372342,1.00000000,0.04495687,0.01809097,0.00825840,0.00188975,0.03007862,0.00764406,0.01730886,0.00282589,0.01172287,0.00164933,0.00389351,0.01197920,0.01455147,0.00347447,0.00669667,0.01056136,0.00352644,0.00909528,0.01061630,0.00248232,0.00446782,0.00385592,0.01283188,0.03121173,0.00698622,0.02200911,0.01214765,0.01022627,0.00180644,0.00246790,0.00323702,0.00523446,0.01917991,0.01575161,0.06158560,0.00760292,0.00694049,0.00478471,0.00082096,0.00367486,0.00057709,0.01518055,0.01160495,0.00572667,0.00021805,0.00098801,0.01278296,0.00415772,0.00773684,0.04709159,0.01208866,0.00336093],
  [0.01315144,0.00339066,0.01188854,0.01316603,0.03376084,0.02646703,0.01861066,0.04187867,0.09917895,0.04089925,0.04495687,1.00000000,0.13736403,0.11612482,0.02659091,0.12470886,0.01323026,0.00047464,0.00044968,0.00112657,0.00009768,0.00573489,0.00318360,0.00051594,0.00070273,0.00211532,0.00196784,0.00059630,0.00037158,0.00027242,0.00282797,0.00033981,0.00015541,0.01651029,0.00546494,0.00018146,0.00558436,0.00267307,0.00489924,0.00526033,0.01933054,0.01241364,0.00974384,0.00055166,0.00006572,0.00038290,0.00337312,0.00055779,0.00002137,0.00000000,0.00000000,0.00000000,0.02064372,0.00222026,0.00081263,0.00003506,0.00000000,0.00023440,0.00009475,0.00013492,0.00134141,0.00240426,0.00027885],
  [0.01112859,0.00233557,0.00194541,0.01265964,0.00576282,0.01336303,0.01072190,0.00738352,0.01360819,0.03216888,0.01809097,0.13736403,1.00000000,0.03104971,0.00777443,0.05533815,0.10059134,0.00042804,0.00058611,0.00250784,0.00021171,0.01568708,0.02072003,0.00317848,0.00615162,0.02370322,0.00575064,0.00032687,0.00036216,0.00062237,0.00832029,0.00094027,0.00022213,0.02323206,0.00493813,0.00064563,0.01001453,0.00277862,0.03036682,0.00078355,0.01349284,0.02104511,0.03578595,0.00150099,0.00051297,0.00038859,0.00126309,0.00544643,0.00013874,0.00025775,0.00085371,0.00031220,0.10424722,0.01947444,0.00894971,0.00018670,0.00000000,0.00040926,0.00020963,0.00277772,0.00225085,0.00098062,0.00005553],
  [0.00875912,0.00318598,0.03826328,0.00515676,0.05441052,0.06039531,0.00610098,0.01105315,0.05210757,0.03963411,0.00825840,0.11612482,0.03104971,1.00000000,0.05955507,0.03995468,0.01494897,0.00099281,0.00313536,0.00031539,0.00028115,0.00767646,0.00029001,0.00020468,0.00041422,0.00140823,0.00028409,0.00044925,0.00042652,0.00006426,0.00205914,0.00012121,0.00003894,0.01414366,0.00140343,0.00026078,0.00422643,0.00332764,0.00447246,0.04956246,0.12995965,0.03171323,0.01188014,0.00057622,0.00013891,0.00014967,0.01075779,0.00056373,0.00007438,0.00001011,0.00004264,0.00003817,0.00792679,0.00036874,0.00104283,0.00000000,0.00000000,0.00023474,0.00106642,0.00086267,0.00166201,0.00145186,0.00008213],
  [0.00258325,0.00112062,0.00037826,0.00079911,0.00177224,0.00035010,0.01736422,0.01170594,0.01503290,0.03271138,0.00188975,0.02659091,0.00777443,0.05955507,1.00000000,0.01562602,0.00983284,0.00014027,0.00041045,0.00035932,0.00000000,0.00281889,0.00183886,0.00012794,0.00019978,0.00122685,0.00022561,0.00000000,0.00000000,0.00012876,0.00093168,0.00000000,0.00011200,0.01759005,0.00173629,0.00005821,0.00064098,0.00152619,0.00245656,0.00099108,0.05874367,0.01961069,0.01879199,0.00010133,0.00001166,0.00000000,0.00002908,0.00028928,0.00000000,0.00000000,0.00000000,0.00000000,0.00347836,0.00033174,0.00080709,0.00000000,0.00000000,0.00001225,0.00001882,0.00002594,0.00015389,0.00002476,0.00022975],
  [0.01958233,0.00596528,0.03378654,0.07192152,0.05178723,0.06902687,0.04876552,0.02435063,0.03515368,0.04915837,0.03007862,0.12470886,0.05533815,0.03995468,0.01562602,1.00000000,0.06595953,0.00136487,0.00350335,0.01802493,0.00096360,0.00909453,0.00515694,0.00092596,0.00073283,0.00797362,0.00525956,0.00057556,0.00034906,0.00149558,0.01390702,0.00054471,0.00018725,0.00700920,0.00276790,0.00021263,0.05220301,0.01430250,0.01125201,0.01183416,0.03213102,0.06774395,0.00526822,0.00410551,0.00065532,0.00117392,0.01695153,0.00125465,0.00081774,0.00016668,0.00056620,0.00011811,0.01195643,0.00888301,0.00146184,0.00014386,0.00001942,0.00067740,0.00087217,0.00157362,0.00068008,0.01158942,0.00059678],
  [0.01059040,0.00474509,0.00411333,0.00451860,0.00922929,0.00574293,0.03999814,0.00429508,0.00379712,0.02431038,0.00764406,0.01323026,0.10059134,0.01494897,0.00983284,0.06595953,1.00000000,0.00328817,0.02482425,0.00616447,0.00591990,0.03196992,0.02214633,0.00303539,0.00808711,0.02152074,0.00508249,0.00264278,0.00161911,0.01106370,0.21195908,0.00576058,0.00091710,0.03571950,0.01124942,0.00191355,0.01234284,0.00343306,0.04837319,0.04712816,0.01933463,0.04609447,0.04692010,0.00572997,0.00019301,0.00129479,0.00076547,0.00962075,0.00104078,0.00109856,0.00264999,0.00041869,0.05004606,0.00436722,0.00915766,0.00048918,0.00030055,0.00011663,0.00039512,0.00076144,0.00225356,0.00133797,0.00017619],
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  [0.02622097,0.00360240,0.01095038,0.04216157,0.00290705,0.00028208,0.00213201,0.00062483,0.00106974,0.00080236,0.01278296,0.00023440,0.00040926,0.00023474,0.00001225,0.00067740,0.00011663,0.01441252,0.00228709,0.00063688,0.00026597,0.00024719,0.00047399,0.00441917,0.00400217,0.00436409,0.00121366,0.00023733,0.00682661,0.00080150,0.00003481,0.00061039,0.00078414,0.00805088,0.01077644,0.12164423,0.00130272,0.02302896,0.00065248,0.00526645,0.00062218,0.00047698,0.00434502,0.08263703,0.03587032,0.10620462,0.07395106,0.00279354,0.00682948,0.00222538,0.00285431,0.00159134,0.00130397,0.00411594,0.00002962,0.00016611,0.00189372,1.00000000,0.11510114,0.01939883,0.05791038,0.02146187,0.00081616],
  [0.02015345,0.00517674,0.02561634,0.01448784,0.00745701,0.00056563,0.00103991,0.00020720,0.00004685,0.00028778,0.00415772,0.00009475,0.00020963,0.00106642,0.00001882,0.00087217,0.00039512,0.00342977,0.00542576,0.00013513,0.00018976,0.00005833,0.00054415,0.00655674,0.00554911,0.01243201,0.00499164,0.00023313,0.00119168,0.00089756,0.00005202,0.00109380,0.00283927,0.00339569,0.00514171,0.04318634,0.00055026,0.00358856,0.00072151,0.00864329,0.00101418,0.00042981,0.00288680,0.05462587,0.07669852,0.01714580,0.02744583,0.00132169,0.00084406,0.00088424,0.00095862,0.00073817,0.00314726,0.00532310,0.00019234,0.00007172,0.00133057,0.11510114,1.00000000,0.03310225,0.04122635,0.01095066,0.00273120],
  [0.02370473,0.00367842,0.00333059,0.02353333,0.00204881,0.00035722,0.00105356,0.00027694,0.00060664,0.00047446,0.00773684,0.00013492,0.00277772,0.00086267,0.00002594,0.00157362,0.00076144,0.00180629,0.00281322,0.00050885,0.00073762,0.00012964,0.00170902,0.10888766,0.05259490,0.07245937,0.02679881,0.00033997,0.00224231,0.00500701,0.00053387,0.01472719,0.02753618,0.00165429,0.00978555,0.02021245,0.00199908,0.00321930,0.00266505,0.00143054,0.00051524,0.00396239,0.00374848,0.04486943,0.05432662,0.04982741,0.04985920,0.00759703,0.01766422,0.02395618,0.01814512,0.02505985,0.00615594,0.02350313,0.00044672,0.00084973,0.00722112,0.01939883,0.03310225,1.00000000,0.05860653,0.02368163,0.00127072],
  [0.02309777,0.00215416,0.00669844,0.00356946,0.00119390,0.00077455,0.00090291,0.00276635,0.00289897,0.00134026,0.04709159,0.00134141,0.00225085,0.00166201,0.00015389,0.00068008,0.00225356,0.00600656,0.00247036,0.00794608,0.00035807,0.00082056,0.00370215,0.08290100,0.02729086,0.04159908,0.01159190,0.00068031,0.00897971,0.00921155,0.00066170,0.00625958,0.00716731,0.00734813,0.01815607,0.13947737,0.00033131,0.00172338,0.00213053,0.00235497,0.00104060,0.00254832,0.00593906,0.06067439,0.03723326,0.03309934,0.03208429,0.05759177,0.01920178,0.00662449,0.00698152,0.00600777,0.00281269,0.00355548,0.00046079,0.00050277,0.00391637,0.05791038,0.04122635,0.05860653,1.00000000,0.05373646,0.00045164],
  [0.02525110,0.00470674,0.02532072,0.04458390,0.02242817,0.00193900,0.04688816,0.00486968,0.00612092,0.01790618,0.01208866,0.00240426,0.00098062,0.00145186,0.00002476,0.01158942,0.00133797,0.00517165,0.00861962,0.00238844,0.00090650,0.00037605,0.00409053,0.00726229,0.00299233,0.01913399,0.00893648,0.00083669,0.00852850,0.03720525,0.00349448,0.00628051,0.00222120,0.00457324,0.00403095,0.00631943,0.01332835,0.00418654,0.00120634,0.00149506,0.00035737,0.00057251,0.00111861,0.02265862,0.02739749,0.02584118,0.09567894,0.00232030,0.00094351,0.00103668,0.01188710,0.00288950,0.02691022,0.01051787,0.00436314,0.00202156,0.00331270,0.02146187,0.01095066,0.02368163,0.05373646,1.00000000,0.00093386],
  [0.06049483,0.02079996,0.00174317,0.00179613,0.00025653,0.00064115,0.00337673,0.00339206,0.00117948,0.00051373,0.00336093,0.00027885,0.00005553,0.00008213,0.00022975,0.00059678,0.00017619,0.00897340,0.00110538,0.00064367,0.00010881,0.00015148,0.00128667,0.00045993,0.00016756,0.00060123,0.00031932,0.00214654,0.00045398,0.00026633,0.00011249,0.00050588,0.00000000,0.00019363,0.00012445,0.00011909,0.01469944,0.00271172,0.00078964,0.00034901,0.00013958,0.00059960,0.00021871,0.00113842,0.00155304,0.00083280,0.00264640,0.00078112,0.00012488,0.00018821,0.00161540,0.00068166,0.00068706,0.00054470,0.00308205,0.00600214,0.00091412,0.00081616,0.00273120,0.00127072,0.00045164,0.00093386,1.00000000]
];

# Precompute Logs, make a finite penalty for 0 entries, where logs would be undefined
sub log10 { log($_[0])/log(10); }
our $msc_log_similarities = [map {[map {$_ ? log($_) : undef} @$_]} @$msc_similarities];
our $underflow_penalty = min(grep {defined} map {@$_} @$msc_log_similarities) - 1;
# We only do this once, so no need to overoptimize
$msc_log_similarities = [map {[map {$_ ? log($_) : $underflow_penalty} @$_]} @$msc_similarities];

our $msc_to_array_index = {
  '00'=>0, '01'=>1, '03'=>2, '05'=>3, '06'=>4, '08'=>5, 11=>6, 12=>7, 13=>8, 14=>9, 15=>10,
  16=>11, 17=>12, 18=>13, 19=>14, 20=>15, 22=>16, 26=>17, 28=>18, 30=>19, 31=>20,
  32=>21, 33=>22, 34=>23, 35=>24, 37=>25, 39=>26, 40=>27, 41=>28, 42=>29, 43=>30,
  44=>31, 45=>32, 46=>33, 47=>34, 49=>35, 51=>36, 52=>37, 53=>38, 54=>39, 55=>40,
  57=>41, 58=>42, 60=>43, 62=>44, 65=>45, 68=>46, 70=>47, 74=>48, 76=>49, 78=>50,
  80=>51, 81=>52, 82=>53, 83=>54, 85=>55, 86=>56, 90=>57, 91=>58, 92=>59, 93=>60,
  94=>61, 97=>62 };

# Until we have some metric that determines the term-likelihood of a given word,
# we will use a simple threshold on the number of characters in a concept,
# bailing out on words that are not long enough, as they are most likely to
# have informal uses. For the moment, 7 seems a good value.
our $word_length_threshold = 7;
sub msc_to_array_index { defined $_[0] ? $msc_to_array_index->{"".substr($_[0],0,2)} : undef; }
sub msc_similarity {
  my ($category1, $category2) = @_;
  # Top-level MSC categories only at the moment:
  my $index1 = msc_to_array_index($category1);
  my $index2 = msc_to_array_index($category2);
  ((defined $index1) && (defined $index2)) ?
  # Well-defined, lookup in matrix
  return $msc_similarities->[$index1]
                          ->[$index2] :
  # Ill-defined means no similarity
  return 0; }

# Discover the most similar cluster of concepts
sub disambiguate {
  my ($candidates,%options) = @_;
  my %category_view = ();
  #print STDERR "\n Text length: ",($options{text_length}||0),"\n";
  # Algorithm:
  if ($options{include_all}) {
    return $candidates; }
  # 0. Dropping anything uncategorized:
  @$candidates = grep {$_->{scheme} eq 'msc'} @$candidates; # TODO: Map everything into MSC!
  @$candidates = grep {$_->{category} !~ /^XX/} @$candidates; # TODO: Can we do something with uncategorized concepts?
  @$candidates = grep {length($_->{concept}) >= $word_length_threshold} @$candidates; # TEMPORARY: We really need term-likelihood here
  # 1. group by top-level MSC category and point into the original candidates array
  print STDERR "[NNexus::Classification] Eligible concepts: ",scalar(@$candidates),"\n" if $options{verbosity};
  foreach my $index(0..$#$candidates) {
    my $candidate = $candidates->[$index];
    my $link = $candidate->{link};
    my $msc_index = msc_to_array_index($candidate->{category});
    # 1.0. Skip fine-grained distinctions on the MSC class from the same URL (for now at least)
    #      45H07 and 45H05 are just "45" with the current metric, so we only need one of them
    next if ($link && (grep {($candidates->[$_]->{link}||'') eq $link} @{$category_view{$msc_index}}));
    # 1.1. also, use the similarity indeces, for faster lookups
    push @{$category_view{$msc_index}}, $index;
  }
  # 2. Greedy search through the ordered %category_view:
  # 2.1. Precompute category weights (sum of length of concepts)
  my @category_keys = keys %category_view;
  my %category_weights = map {$_ => (weigh_category($category_view{$_},$candidates))} @category_keys;
  # 2.2. Order by weights
  my @ordered_categories = sort {$category_weights{$b} cmp $category_weights{$a}} @category_keys;
  # 2.3. Precompute concept sizes in each category (for greedy cutoff)
  my %category_sizes = map {$_ => scalar(@{$category_view{$_}})} @category_keys;
  # print STDERR Dumper(\%category_view);
  # print STDERR Dumper(\%category_weights);
  # print STDERR Dumper(\%category_sizes);
  # So: maximize the sum of lengths of all concepts currently grouped and all log_similarities!
  my $max_clique = maximize_clique(weights=>\%category_weights,sizes=>\%category_sizes,queue=>\@ordered_categories, );
  # Grab the corresponding candidates from %category_view, and then splice the $candidates array:
  my @final_candidates_indexes = map { @{$category_view{$_}} } @{$max_clique->{clique}};
  my @final_candidates = map {$candidates->[$_]} sort {$a<=>$b} @final_candidates_indexes;
  print STDERR "[NNexus::Classification] Disambiguated concepts: ",scalar(@final_candidates),"\n" if $options{verbosity};
  return \@final_candidates; # mockup
}

sub weigh_category {
  my ($concept_indexes,$candidates) = @_;
  my $weight = 0;
  # - Weigh by: the (sum of lengths)/4 of all concepts in the category
  foreach my $index(@$concept_indexes) {
    my $current_concept = $candidates->[$index]->{concept};
    my $current_weight = length($current_concept) - $word_length_threshold;
    # Possible Alternatives: geometric via division:
    # my $current_weight = length($current_concept) / $word_length_threshold;
    $weight += $current_weight;
  }
  # Concepts of length 4 or less are less "termy" than longer concepts.
  # TODO: How certain are we? If we're really certain long phrases are termy, we can subtract 4 rather than divide.
  #       Though subtracting 4 is unintelligent... maybe using the "number of words" in a concept?
  #$weight = $weight / 4;
  return $weight; }

sub maximize_clique {
  my (%options) = @_;
  my ($weights, $sizes, $queue, $score, $size, $clique) = map {$options{$_}} qw(weights sizes queue score size clique);
  my @traversal_queue = @$queue;
  return {score=>$score,size=>$size,clique=>$clique} unless @traversal_queue; # Base case
  my $greedy_bound = 0;
  $score //= 0;
  $size //= 0;
  $clique //= [];
  my @candidate_cliques= $score ? ({score=>$score,size=>$size,clique=>$clique}) : ();
  # 2 entries in category 10 , and 4 entries in category 80 = 2^((length(a1)+length(a2)+...)/4)*sim(10,80)
  #
  # 2 in 10, 4 in 80, 3 in 53 = 2^(sum of lengths / 4)*sim(10,80) *sim(10,53) * sim(53,80)
  # Take logs to simplify:
  # (sum of lengths) / 4 -log(sim(10,80)) -log(sim(10,53)) -log(sim(53,80))
  while(@traversal_queue) {
    # Next extension index:
    my $next_index = shift @traversal_queue;
    last if $sizes->{$next_index} < $greedy_bound; # Greedy, don't go beyond the bound
    my $next_weight = $weights->{$next_index};
    my $next_size = $sizes->{$next_index};
    my $similarity_score=0;
    my $well_defined = 1;
    foreach my $category_index(@$clique) {
      my $similarity = $msc_log_similarities->[$next_index]->[$category_index];
      if (! $similarity) {
        # Ill-defined, skip the $next_index
        $well_defined = 0;
        last;
      }
      $similarity_score += $similarity;
    }
    next if (! $well_defined);
    my $extended_score = $score + $next_weight + $similarity_score; # ?!
    my $extended_size = $size + $next_size;
    # DEPRECATED: Maximizing score
     next if $extended_score < $score; # No improvement, next
    # NEW: Maximizing clique, while keeping a positive score
    #next if $extended_score <= 0;
    # Improvement! Update the score and clique
    my $extended_clique = [@$clique,$next_index];
    push @candidate_cliques, maximize_clique(weights=>$weights, sizes=>$sizes, queue=>\@traversal_queue,
                                             score=>$extended_score, size=>$extended_size, clique=>$extended_clique);
    # Heuristic: Let's be greedy here to save time. The moment a category with size N can be added
    #  to the current cluster, don't look in categories of size N-1 or smaller in the current merge pass
    #  (of course we look at them as further additions to the now extended cluster)
    # Update the greedy bound:
    $greedy_bound = $sizes->{$next_index};
  }

  # DEPRECATED: Maximizing score
  # # We've gathered a number of candidate cliques, return the best scoring one:
   @candidate_cliques = sort { $b->{score} <=> $a->{score} } @candidate_cliques;
  # We've gathered a number of candidate cliques, return the one with most concepts:
  #@candidate_cliques = sort { $b->{size} <=> $a->{size} } @candidate_cliques;

  return $candidate_cliques[0];
}

1;
__END__