Clarification of behaviour for recursive line generation

[avyavkumar]

Hi,

While generating lines for 768 dimensional data with a large number of classes (1609), the following lines were gotten using find_lines_R_multiD using k=~800

[array([2, 2]) array([581, 780, 275]) array([26, 26]) array([7, 7])
 array([603, 158]) array([9, 9]) array([11, 11]) array([12, 12])
 array([1023,   13,  912]) array([590, 478])
 array([  15,  806,  171, 1536, 1392,  172,  888,  387]) array([16, 16])
 array([258, 258])
 array([  10,   62,  434, 1476, 1335,  672,  830,  400,  784,   19,   23,
        1205,  395,  889,  697,  676,  131, 1129])
 array([ 557, 1409,  219, 1183, 1444,  242])
 array([ 633,  783,  124,  517, 1046,   39,   22, 1161, 1202,   42,  534,
         714, 1070,  553,  491])
 array([ 937,  786, 1222]) array([597,  24]) array([29, 29])
 array([31, 31]) array([ 845,  973,   55,  361,  249, 1006,  169])
 array([579, 383]) array([34, 34]) array([36, 36]) array([37, 37])
 array([  93,  345,  530,  907,  441,   96,  389,  291,  663,  730, 1505,
        1336, 1345,  694])
 array([41, 41]) array([1447,  378]) array([  43,   43, 1162])
 array([44, 44]) array([1519,   45]) array([47, 47])
 array([ 904, 1072, 1346,  438,  447,  881,  167,  442,  198,  617,  168,
        1203,  921,   48,  945,  803, 1155, 1424])
 array([50, 50]) array([1272, 1313, 1187,  338]) array([53, 53])
 array([ 196,  854, 1290,  632,   54,  449]) array([744, 113])
 array([843, 785,  32, 364, 837]) array([59, 59]) array([799, 615])
 array([464, 203]) array([575, 409]) array([227,  38])
 array([1528,  723, 1445,  408,   68,  761,  283]) array([452, 321])
 array([1412,  386,  278,  506, 1466,  545]) array([77, 77])
 array([ 682,   78, 1538, 1556,  469]) array([585, 450])
 array([ 481,  382,  327,  920, 1218, 1270,  448,  767, 1554, 1201, 1382,
        1374, 1425,   82,  623, 1060,  148,  548,  958,  743])
 array([605, 399,  83, 511]) array([ 813,  343,  108,  966, 1565,  572])
 array([775, 751]) array([444, 153]) array([1240,   91,  844,  587,  302])
 array([718, 483]) array([490,  95]) array([630, 254,  71])
 array([691, 111]) array([571, 102]) array([101, 101]) array([103, 103])
 array([104, 104]) array([374, 374]) array([170, 170]) array([112, 112])
 array([1367,  115]) array([1471,  118,  432, 1354, 1125,  234, 1495])
 array([119, 119]) array([245, 812, 735, 120, 948]) array([121, 121])
 array([644, 558]) array([528, 528]) array([126, 126]) array([792, 792])
 array([ 81, 816, 507,  25,  30]) array([296, 296]) array([130, 130])
 array([ 514, 1434,  132]) array([133, 133]) array([608, 536])
 array([137, 137]) array([138, 138])
 array([ 638,  320,  906,  915,    1,   67, 1073,  527,  698,  642,  602,
         708,  294,  727,  873,  725,  419,  724,    6,  420,  567,   35,
        1366,  688,  776,  367,  140,  216,  415,  898,  531,  946, 1225,
         252,  957,  277,  394,    0,  263,   51,   52,  731, 1546,  446,
         641,  716,  900,   88,  304, 1330,  974, 1259,   49,  328,  815,
         348,  467, 1234,  455,  351,   80,  544, 1082, 1074,  217,  869,
        1059, 1478, 1261,  612, 1583,  625,  324,  695,  139,  681,  496,
         872,  679,   64,  692,  944,  188,  522,  281, 1062, 1545, 1574,
          28,  894, 1561, 1524,  860,  319,  354,  337,  839, 1145,  502,
         418,  668, 1567,  151,  346,  225,  919,  684,  410,  891,   18,
         927, 1050, 1208, 1220,  458,  505, 1110, 1590, 1094,  311, 1507,
        1178,  793,  308, 1362,  817, 1267, 1585,  713,  941,  707,  764,
         289,  908,  256, 1204, 1468, 1509,  466, 1598,  513,  800,  660,
         229,  629,  593,  685,  573, 1182,  542,  240, 1053,  192,  565,
         220,  350, 1496, 1464,  582, 1163,  290, 1104,  288,  570,  779,
        1106, 1340, 1258,  204, 1214,  190, 1426,  230,  214, 1431, 1298,
         122,  100, 1433, 1236, 1602,  954,  300, 1278,  849,   92,  495,
         982,  175,   69, 1482,  379,  622,  482, 1274, 1390,  989,  871,
         566,  251,  955, 1407, 1308,  895,  330, 1099,  257,  413, 1215,
         390,  634,  934,  835,  569,  516, 1085,  174,  365, 1479,  651,
         584, 1301,  696, 1530,  404, 1031,  236, 1173,  454,  286,  377,
        1241,  355, 1238,  986,  261,  564,  244,  671,  134, 1591, 1189,
        1132, 1030, 1075,  589,  653,  309,  690,  712])
 array([141, 141])
 array([ 762,  142,  601,  260,  159,  271,   86,  719,  358, 1310,  852])
 array([1408,  143])
 array([ 193,  808,  850, 1533,  842,  902,   94,  144,  269,  828,  421,
         221, 1436,  233,  347,  451,  381,  739,   66,  733,  195,  384,
         962])
 array([ 152,  145,   74,  604,  181, 1317, 1055,  248])
 array([1487,  238, 1143,  146,  189, 1275,  988, 1102,  429])
 array([ 182,   56,  788,  616, 1223, 1087, 1097,  885,  994,  425,  314,
        1322,  149,  117,  201,  431])
 array([ 675,  606,  594,  437,  747, 1532,  561, 1227,  185, 1558, 1522,
        1276,  778, 1153, 1315,  591, 1078])
 array([855, 239])
 array([ 678, 1216,  191,  840,  901,   60,  546,  480,   61,  334,  128,
         123,  529, 1320, 1321,  899, 1467, 1212, 1089,  753,  315, 1377,
          65,  155,  521, 1124])
 array([156, 156])
 array([ 453, 1361,  157,  515,  184,  703,  317, 1430,  576, 1356])
 array([160, 160]) array([161, 161]) array([ 209,  162,  423, 1432])
 array([ 646, 1526, 1008,  463,  715]) array([166, 166]) array([661, 661])
 array([722, 722]) array([285,  90])
 array([ 176,  807,  611, 1399,  975, 1175])
 array([178, 882, 884, 457, 187]) array([179, 179]) array([180, 180])
 array([440, 435]) array([1038,  183, 1262, 1531]) array([186, 186])
 array([298, 200]) array([459, 459]) array([235, 235])
 array([547, 401, 360]) array([ 877,  199,  554,  658, 1047, 1029])
 array([ 202,  202, 1380]) array([1112,  472,  639,  206])
 array([ 537,  215,  650,  373,  609,  376,  610, 1372,  532,  648, 1523,
         154,  657, 1489,  136, 1400,  293, 1460,  997, 1194,  107, 1357])
 array([1224,  211])
 array([ 323,  411,   99, 1364, 1457,  868,  693,  362,  771])
 array([1135, 1383,  114]) array([748, 476, 526]) array([223, 223])
 array([226, 226]) array([ 795,  231,  998, 1448, 1402,   79,  272,  498])
 array([232, 232]) array([237, 237]) array([1245,  802, 1101])
 array([243, 243]) array([600, 600]) array([942, 247, 588, 928, 680])
 array([250, 250]) array([ 656,  991, 1488, 1353, 1048, 1391, 1348,  523])
 array([255,  70]) array([259, 259])
 array([ 829,  823,  559,  598, 1580,  306, 1014, 1061,  331,  683,  880,
         177, 1256, 1548,  535, 1133,  706,  487,   76, 1011, 1517,  222,
         494, 1396,  369,  687, 1254, 1166,  810, 1088,  329, 1077, 1253,
         150, 1415, 1344, 1360, 1600,  325,  628,   27,  110,   98, 1325,
         287, 1035,   87,  832, 1116, 1307,  923,  393,   57,  673,  241,
          73, 1056, 1324, 1441, 1285,  782,  512,  677,  665,  949,  335,
         412,  282,  951])
 array([264, 264]) array([266, 266]) array([1393,  777]) array([268, 268])
 array([818, 818]) array([276, 276]) array([910, 709, 841])
 array([ 147,  279,  574, 1484,  210]) array([307, 307])
 array([ 556,  599,  652,  265,  717,  388, 1388,   17,  356,  774, 1499,
        1450, 1306, 1198, 1562, 1200,  500,  436,  274,    8, 1470,   89,
        1504,  280,  284, 1076,  607,    5,  127, 1271, 1027])
 array([1036,  292]) array([805, 805]) array([825, 825]) array([752, 736])
 array([301, 301]) array([826, 826]) array([310, 310]) array([313, 313])
 array([704, 342, 791, 643]) array([318, 318]) array([322, 322])
 array([ 352,  163,  749,  391,  772, 1206,  109,   63,  406, 1150])
 array([336, 336]) array([732, 732]) array([339, 339])
 array([896, 363, 543, 809, 341]) array([ 953, 1022,  763])
 array([797, 797])
 array([1327, 1057,  702,  647, 1492,  586,  848, 1370,  533,  759])
 array([ 939,  787, 1179, 1510,  398,  353, 1594, 1159,  766])
 array([621,  40]) array([357, 357]) array([1389,  701,  380])
 array([368, 368]) array([372, 372])
 array([ 164,  740,  375,  550,  492, 1001, 1474,  909,  486])
 array([1323, 1049, 1242,  857,  562]) array([385, 385])
 array([ 207,  801,  662,  838,  208,  964, 1233,  538,  911,  851,  552,
        1597,  965,  983,  853, 1032, 1015,   21,  359, 1114,  981,  595,
         416, 1054, 1572])
 array([ 396, 1020, 1421,  689,  541,  370])
 array([ 686, 1248,  212,  746,  253,  105,  194, 1064, 1456,  620,   97,
         822,  568,  861, 1009,  303,  397, 1304, 1287,  878])
 array([539, 539]) array([407, 407]) array([1117,  224]) array([781, 781])
 array([705, 461]) array([424, 424]) array([549, 549])
 array([1213,  426,  426, 1566]) array([430, 430])
 array([  46,  728,   72, 1148,  205,  267,  789,  197,  846,  627,  773,
        1581,  297, 1086,  299,  443, 1575, 1485, 1529, 1156])
 array([669, 666]) array([711, 475, 305]) array([456, 456])
 array([460, 460]) array([471, 471]) array([473, 473])
 array([ 619,  824,  654,  470,  738, 1294,  770,  580,  757, 1568,  968,
         729, 1527,  635])
 array([479, 479]) array([758, 405]) array([484, 484]) array([485, 485])
 array([1142,  497, 1542, 1595,  246,  433]) array([499, 499])
 array([ 344,  519,  734,  489,  930,  349, 1514, 1333,  504,  636,  428,
        1028, 1219,  984,  106, 1319,  741,  560, 1543,  555])
 array([509, 509]) array([1039,  510,  833]) array([520, 520])
 array([745, 745]) array([ 551, 1418,  804, 1394,  518])
 array([  58,  819,  796,  814, 1569,  943]) array([1113,  821])
 array([856, 856, 577]) array([659, 659]) array([640, 640])
 array([596, 596]) array([811, 887, 614, 631]) array([624, 624])
 array([649, 649]) array([667, 392]) array([1378, 1000, 1363,  769,  798])
 array([710, 710]) array([720, 720]) array([737, 737])
 array([1401,  754,  445, 1286,  858]) array([756, 756])
 array([1540,  836,  578, 1026])
 array([ 270,  863,  173,  890,  862, 1586, 1314,  503,  864,  403,  563,
        1557,   14,    4,  700])
 array([865, 865]) array([866, 866]) array([867, 867]) array([870, 870])
 array([874, 874]) array([875, 875]) array([876, 876]) array([879, 879])
 array([883, 883]) array([892, 892]) array([1334,  893]) array([897, 897])
 array([903, 903]) array([905, 905]) array([913, 913]) array([918, 918])
 array([922, 922]) array([924, 924]) array([925, 925]) array([926, 926])
 array([929, 929]) array([1341,  931]) array([932, 932]) array([933, 933])
 array([936, 936]) array([940, 940]) array([947, 947]) array([950, 950])
 array([956, 956]) array([985, 960]) array([961, 961]) array([963, 963])
 array([967, 967]) array([969, 592]) array([971, 971])
 array([1025,  972,  295]) array([976, 976, 699]) array([977, 977])
 array([978, 978]) array([ 979,  917,  422, 1051,  540]) array([980, 980])
 array([987, 987]) array([990, 990]) array([992, 992]) array([993, 993])
 array([995, 995]) array([996, 996]) array([999, 999]) array([1002, 1002])
 array([1003, 1003]) array([1004, 1004]) array([1005, 1005])
 array([1007, 1007]) array([1010, 1010]) array([1012, 1012])
 array([1013, 1013]) array([1016, 1016]) array([1018, 1018])
 array([1019, 1019]) array([1021, 1021]) array([1033, 1033])
 array([1034, 1034,  674]) array([1037, 1037]) array([1040, 1040])
 array([1041, 1041]) array([1042, 1042]) array([1043, 1043])
 array([1044, 1044]) array([1045, 1045]) array([1052, 1052])
 array([1071, 1058]) array([1063, 1063]) array([1066, 1066])
 array([1067, 1067]) array([1068, 1068]) array([1069, 1069])
 array([1079, 1079]) array([1080, 1080]) array([1081, 1081])
 array([1573, 1065, 1083]) array([1579, 1584, 1084])
 array([  84, 1090, 1090,   85]) array([1091, 1091]) array([1092, 1092])
 array([1093, 1093]) array([1095, 1095]) array([1103, 1103])
 array([1105, 1105]) array([1107, 1107]) array([1109, 1109])
 array([1111, 1111]) array([1115, 1115]) array([1118, 1118])
 array([1120, 1120]) array([1121, 1188, 1279, 1331, 1490, 1190,  218])
 array([1122, 1122]) array([1512, 1126,  721]) array([1127, 1172,  402])
 array([1128, 1128]) array([508, 165]) array([1130, 1130])
 array([1131, 1131]) array([1134, 1134]) array([1136,  645,  332])
 array([1137, 1137]) array([1138, 1138]) array([1139, 1477,  655,  914])
 array([1140, 1140])
 array([ 312, 1283,  794, 1459,  750,  366,  618,   33,  116, 1537, 1541,
        1193, 1358,  427,  670,  135, 1098, 1151,  952,  583, 1469, 1555,
         760,  465, 1601, 1462,  213, 1508,  228, 1096, 1384,  462, 1266,
        1141,  742,    3,  959, 1452, 1186, 1397,  439,  488])
 array([1144, 1144]) array([1146, 1146]) array([1147, 1147])
 array([1149, 1149]) array([1152, 1152]) array([1154, 1154])
 array([1157, 1157]) array([1589, 1158]) array([1160, 1160])
 array([1164, 1164]) array([1167, 1167]) array([1168, 1168])
 array([1169, 1169]) array([1170, 1170]) array([1463, 1171])
 array([1176, 1176]) array([1177, 1177]) array([ 501, 1449,  414,  273])
 array([1180, 1180]) array([1181, 1181]) array([1185, 1185])
 array([1191, 1191]) array([1192, 1192]) array([1195, 1195])
 array([1196, 1196]) array([1199, 1199]) array([1207, 1207])
 array([1209, 1209]) array([1210, 1210]) array([1211, 1211])
 array([1217, 1217]) array([1221, 1221])
 array([1292,  938,  831, 1226,  417]) array([1228, 1228])
 array([1229, 1229]) array([ 125, 1230,  637, 1252,  834])
 array([1231, 1231]) array([1232, 1232]) array([1235, 1235])
 array([1239, 1239]) array([1243, 1243]) array([1244, 1244])
 array([1246, 1246]) array([1247, 1247]) array([1249, 1249])
 array([1250, 1250]) array([1251, 1251]) array([1255, 1255])
 array([ 371, 1295, 1257,  326]) array([1260, 1260]) array([1263, 1263])
 array([1264, 1264]) array([1265, 1265]) array([1268, 1268])
 array([1269, 1269]) array([1273, 1273]) array([1277, 1277])
 array([1280, 1280]) array([1282, 1282]) array([1284, 1284])
 array([1288, 1288]) array([1289, 1289]) array([1291, 1291])
 array([1293, 1293]) array([1296,  477]) array([1297, 1297])
 array([1299, 1299]) array([1302, 1302]) array([1303, 1303])
 array([1305, 1305]) array([1309, 1309]) array([1311, 1311])
 array([1312, 1312]) array([1316, 1316]) array([1318, 1318])
 array([1498,  847]) array([1326, 1326]) array([1328, 1328])
 array([1329, 1329]) array([1332, 1332]) array([1337,  827])
 array([1338, 1338]) array([1339, 1339]) array([1342, 1342])
 array([1343, 1343]) array([1347, 1347]) array([1349,  493])
 array([1350, 1350]) array([1351, 1351]) array([1352, 1352])
 array([1359, 1359]) array([1365, 1365]) array([1368, 1368])
 array([1369, 1369]) array([1371, 1371]) array([1373, 1373])
 array([1375, 1375])
 array([ 768,  726, 1017,  886,  316,  790, 1281,  935,  340, 1119, 1237,
        1123, 1197,  765,  664, 1491,  468, 1355, 1376,  333,  613, 1483,
        1174,  525,  916, 1443, 1024,  970, 1184,  859, 1472, 1300, 1454,
         820])
 array([1379, 1379]) array([1381, 1381,   75]) array([1385, 1385])
 array([1386, 1386]) array([1387,  626]) array([1599, 1395])
 array([1398, 1398]) array([1403, 1403]) array([1404, 1404])
 array([1405,  755, 1165,  474, 1417,  524, 1535,   20,  129, 1473, 1100])
 array([1406, 1406]) array([1410, 1410]) array([1411, 1411])
 array([1413, 1413]) array([1414, 1414]) array([1416, 1416])
 array([1419, 1419]) array([1420, 1420]) array([1422, 1422])
 array([1423, 1423]) array([1427, 1427]) array([1428, 1428])
 array([1429, 1429]) array([1435, 1435]) array([1437, 1437])
 array([1438, 1438]) array([1439, 1439]) array([1440, 1440])
 array([1442, 1442]) array([1446, 1446]) array([1451, 1451])
 array([1453, 1453, 1108]) array([1455, 1455]) array([1458, 1458])
 array([1461, 1461]) array([1465, 1465]) array([1475, 1475])
 array([1480, 1480]) array([1481, 1481]) array([1486, 1486])
 array([1493, 1493]) array([1494, 1494]) array([1497, 1497])
 array([1500, 1500]) array([1501, 1501]) array([1502, 1502])
 array([1503, 1503]) array([1506, 1506]) array([1511, 1511])
 array([1513, 1513]) array([1515, 1515]) array([1516, 1516])
 array([1518, 1518]) array([1520, 1520]) array([1521, 1521])
 array([1525, 1525]) array([1534, 1534]) array([1539, 1539])
 array([1544, 1544]) array([1547, 1547]) array([1549, 1549])
 array([1550, 1550]) array([1551, 1551]) array([1552,  262])
 array([1553, 1553]) array([1559, 1559]) array([1560, 1560])
 array([1563, 1563]) array([1564, 1564]) array([1570, 1570])
 array([1571, 1571]) array([1576, 1576]) array([1577, 1577])
 array([1578, 1578]) array([1582, 1582]) array([1587, 1587])
 array([1588, 1588]) array([1592, 1592]) array([1593, 1593])
 array([1596, 1596])]

A lot of lines consist of a single point (which seems geometrically incorrect) even though they have two endpoints. Can you (a) let me know if this is expected and (b) if not, possible workarounds around this issue? Thanks!

[ilia10000]

I think it's plausible that lines could end up being single points though this of course isn't desirable. It may come about as a result of trying to avoid lines that overlap in which case it's indeed reasonable. However, if the points can easily be joined by a line that doesn't overlap with other lines then something is going wrong.