1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699
|
"""
Generate samples of synthetic data sets.
"""
# Authors: B. Thirion, G. Varoquaux, A. Gramfort, V. Michel, O. Grisel,
# G. Louppe, J. Nothman
# License: BSD 3 clause
import numbers
import array
import numpy as np
from scipy import linalg
import scipy.sparse as sp
from ..preprocessing import MultiLabelBinarizer
from ..utils import check_array, check_random_state
from ..utils import shuffle as util_shuffle
from ..utils.fixes import _Iterable as Iterable
from ..utils.random import sample_without_replacement
from ..externals import six
map = six.moves.map
zip = six.moves.zip
def _generate_hypercube(samples, dimensions, rng):
"""Returns distinct binary samples of length dimensions
"""
if dimensions > 30:
return np.hstack([rng.randint(2, size=(samples, dimensions - 30)),
_generate_hypercube(samples, 30, rng)])
out = sample_without_replacement(2 ** dimensions, samples,
random_state=rng).astype(dtype='>u4',
copy=False)
out = np.unpackbits(out.view('>u1')).reshape((-1, 32))[:, -dimensions:]
return out
def make_classification(n_samples=100, n_features=20, n_informative=2,
n_redundant=2, n_repeated=0, n_classes=2,
n_clusters_per_class=2, weights=None, flip_y=0.01,
class_sep=1.0, hypercube=True, shift=0.0, scale=1.0,
shuffle=True, random_state=None):
"""Generate a random n-class classification problem.
This initially creates clusters of points normally distributed (std=1)
about vertices of an ``n_informative``-dimensional hypercube with sides of
length ``2*class_sep`` and assigns an equal number of clusters to each
class. It introduces interdependence between these features and adds
various types of further noise to the data.
Without shuffling, ``X`` horizontally stacks features in the following
order: the primary ``n_informative`` features, followed by ``n_redundant``
linear combinations of the informative features, followed by ``n_repeated``
duplicates, drawn randomly with replacement from the informative and
redundant features. The remaining features are filled with random noise.
Thus, without shuffling, all useful features are contained in the columns
``X[:, :n_informative + n_redundant + n_repeated]``.
Read more in the :ref:`User Guide <sample_generators>`.
Parameters
----------
n_samples : int, optional (default=100)
The number of samples.
n_features : int, optional (default=20)
The total number of features. These comprise ``n_informative``
informative features, ``n_redundant`` redundant features,
``n_repeated`` duplicated features and
``n_features-n_informative-n_redundant-n_repeated`` useless features
drawn at random.
n_informative : int, optional (default=2)
The number of informative features. Each class is composed of a number
of gaussian clusters each located around the vertices of a hypercube
in a subspace of dimension ``n_informative``. For each cluster,
informative features are drawn independently from N(0, 1) and then
randomly linearly combined within each cluster in order to add
covariance. The clusters are then placed on the vertices of the
hypercube.
n_redundant : int, optional (default=2)
The number of redundant features. These features are generated as
random linear combinations of the informative features.
n_repeated : int, optional (default=0)
The number of duplicated features, drawn randomly from the informative
and the redundant features.
n_classes : int, optional (default=2)
The number of classes (or labels) of the classification problem.
n_clusters_per_class : int, optional (default=2)
The number of clusters per class.
weights : list of floats or None (default=None)
The proportions of samples assigned to each class. If None, then
classes are balanced. Note that if ``len(weights) == n_classes - 1``,
then the last class weight is automatically inferred.
More than ``n_samples`` samples may be returned if the sum of
``weights`` exceeds 1.
flip_y : float, optional (default=0.01)
The fraction of samples whose class are randomly exchanged. Larger
values introduce noise in the labels and make the classification
task harder.
class_sep : float, optional (default=1.0)
The factor multiplying the hypercube size. Larger values spread
out the clusters/classes and make the classification task easier.
hypercube : boolean, optional (default=True)
If True, the clusters are put on the vertices of a hypercube. If
False, the clusters are put on the vertices of a random polytope.
shift : float, array of shape [n_features] or None, optional (default=0.0)
Shift features by the specified value. If None, then features
are shifted by a random value drawn in [-class_sep, class_sep].
scale : float, array of shape [n_features] or None, optional (default=1.0)
Multiply features by the specified value. If None, then features
are scaled by a random value drawn in [1, 100]. Note that scaling
happens after shifting.
shuffle : boolean, optional (default=True)
Shuffle the samples and the features.
random_state : int, RandomState instance or None (default)
Determines random number generation for dataset creation. Pass an int
for reproducible output across multiple function calls.
See :term:`Glossary <random_state>`.
Returns
-------
X : array of shape [n_samples, n_features]
The generated samples.
y : array of shape [n_samples]
The integer labels for class membership of each sample.
Notes
-----
The algorithm is adapted from Guyon [1] and was designed to generate
the "Madelon" dataset.
References
----------
.. [1] I. Guyon, "Design of experiments for the NIPS 2003 variable
selection benchmark", 2003.
See also
--------
make_blobs: simplified variant
make_multilabel_classification: unrelated generator for multilabel tasks
"""
generator = check_random_state(random_state)
# Count features, clusters and samples
if n_informative + n_redundant + n_repeated > n_features:
raise ValueError("Number of informative, redundant and repeated "
"features must sum to less than the number of total"
" features")
# Use log2 to avoid overflow errors
if n_informative < np.log2(n_classes * n_clusters_per_class):
raise ValueError("n_classes * n_clusters_per_class must"
" be smaller or equal 2 ** n_informative")
if weights and len(weights) not in [n_classes, n_classes - 1]:
raise ValueError("Weights specified but incompatible with number "
"of classes.")
n_useless = n_features - n_informative - n_redundant - n_repeated
n_clusters = n_classes * n_clusters_per_class
if weights and len(weights) == (n_classes - 1):
weights = weights + [1.0 - sum(weights)]
if weights is None:
weights = [1.0 / n_classes] * n_classes
weights[-1] = 1.0 - sum(weights[:-1])
# Distribute samples among clusters by weight
n_samples_per_cluster = []
for k in range(n_clusters):
n_samples_per_cluster.append(int(n_samples * weights[k % n_classes]
/ n_clusters_per_class))
for i in range(n_samples - sum(n_samples_per_cluster)):
n_samples_per_cluster[i % n_clusters] += 1
# Initialize X and y
X = np.zeros((n_samples, n_features))
y = np.zeros(n_samples, dtype=np.int)
# Build the polytope whose vertices become cluster centroids
centroids = _generate_hypercube(n_clusters, n_informative,
generator).astype(float)
centroids *= 2 * class_sep
centroids -= class_sep
if not hypercube:
centroids *= generator.rand(n_clusters, 1)
centroids *= generator.rand(1, n_informative)
# Initially draw informative features from the standard normal
X[:, :n_informative] = generator.randn(n_samples, n_informative)
# Create each cluster; a variant of make_blobs
stop = 0
for k, centroid in enumerate(centroids):
start, stop = stop, stop + n_samples_per_cluster[k]
y[start:stop] = k % n_classes # assign labels
X_k = X[start:stop, :n_informative] # slice a view of the cluster
A = 2 * generator.rand(n_informative, n_informative) - 1
X_k[...] = np.dot(X_k, A) # introduce random covariance
X_k += centroid # shift the cluster to a vertex
# Create redundant features
if n_redundant > 0:
B = 2 * generator.rand(n_informative, n_redundant) - 1
X[:, n_informative:n_informative + n_redundant] = \
np.dot(X[:, :n_informative], B)
# Repeat some features
if n_repeated > 0:
n = n_informative + n_redundant
indices = ((n - 1) * generator.rand(n_repeated) + 0.5).astype(np.intp)
X[:, n:n + n_repeated] = X[:, indices]
# Fill useless features
if n_useless > 0:
X[:, -n_useless:] = generator.randn(n_samples, n_useless)
# Randomly replace labels
if flip_y >= 0.0:
flip_mask = generator.rand(n_samples) < flip_y
y[flip_mask] = generator.randint(n_classes, size=flip_mask.sum())
# Randomly shift and scale
if shift is None:
shift = (2 * generator.rand(n_features) - 1) * class_sep
X += shift
if scale is None:
scale = 1 + 100 * generator.rand(n_features)
X *= scale
if shuffle:
# Randomly permute samples
X, y = util_shuffle(X, y, random_state=generator)
# Randomly permute features
indices = np.arange(n_features)
generator.shuffle(indices)
X[:, :] = X[:, indices]
return X, y
def make_multilabel_classification(n_samples=100, n_features=20, n_classes=5,
n_labels=2, length=50, allow_unlabeled=True,
sparse=False, return_indicator='dense',
return_distributions=False,
random_state=None):
"""Generate a random multilabel classification problem.
For each sample, the generative process is:
- pick the number of labels: n ~ Poisson(n_labels)
- n times, choose a class c: c ~ Multinomial(theta)
- pick the document length: k ~ Poisson(length)
- k times, choose a word: w ~ Multinomial(theta_c)
In the above process, rejection sampling is used to make sure that
n is never zero or more than `n_classes`, and that the document length
is never zero. Likewise, we reject classes which have already been chosen.
Read more in the :ref:`User Guide <sample_generators>`.
Parameters
----------
n_samples : int, optional (default=100)
The number of samples.
n_features : int, optional (default=20)
The total number of features.
n_classes : int, optional (default=5)
The number of classes of the classification problem.
n_labels : int, optional (default=2)
The average number of labels per instance. More precisely, the number
of labels per sample is drawn from a Poisson distribution with
``n_labels`` as its expected value, but samples are bounded (using
rejection sampling) by ``n_classes``, and must be nonzero if
``allow_unlabeled`` is False.
length : int, optional (default=50)
The sum of the features (number of words if documents) is drawn from
a Poisson distribution with this expected value.
allow_unlabeled : bool, optional (default=True)
If ``True``, some instances might not belong to any class.
sparse : bool, optional (default=False)
If ``True``, return a sparse feature matrix
.. versionadded:: 0.17
parameter to allow *sparse* output.
return_indicator : 'dense' (default) | 'sparse' | False
If ``dense`` return ``Y`` in the dense binary indicator format. If
``'sparse'`` return ``Y`` in the sparse binary indicator format.
``False`` returns a list of lists of labels.
return_distributions : bool, optional (default=False)
If ``True``, return the prior class probability and conditional
probabilities of features given classes, from which the data was
drawn.
random_state : int, RandomState instance or None (default)
Determines random number generation for dataset creation. Pass an int
for reproducible output across multiple function calls.
See :term:`Glossary <random_state>`.
Returns
-------
X : array of shape [n_samples, n_features]
The generated samples.
Y : array or sparse CSR matrix of shape [n_samples, n_classes]
The label sets.
p_c : array, shape [n_classes]
The probability of each class being drawn. Only returned if
``return_distributions=True``.
p_w_c : array, shape [n_features, n_classes]
The probability of each feature being drawn given each class.
Only returned if ``return_distributions=True``.
"""
generator = check_random_state(random_state)
p_c = generator.rand(n_classes)
p_c /= p_c.sum()
cumulative_p_c = np.cumsum(p_c)
p_w_c = generator.rand(n_features, n_classes)
p_w_c /= np.sum(p_w_c, axis=0)
def sample_example():
_, n_classes = p_w_c.shape
# pick a nonzero number of labels per document by rejection sampling
y_size = n_classes + 1
while (not allow_unlabeled and y_size == 0) or y_size > n_classes:
y_size = generator.poisson(n_labels)
# pick n classes
y = set()
while len(y) != y_size:
# pick a class with probability P(c)
c = np.searchsorted(cumulative_p_c,
generator.rand(y_size - len(y)))
y.update(c)
y = list(y)
# pick a non-zero document length by rejection sampling
n_words = 0
while n_words == 0:
n_words = generator.poisson(length)
# generate a document of length n_words
if len(y) == 0:
# if sample does not belong to any class, generate noise word
words = generator.randint(n_features, size=n_words)
return words, y
# sample words with replacement from selected classes
cumulative_p_w_sample = p_w_c.take(y, axis=1).sum(axis=1).cumsum()
cumulative_p_w_sample /= cumulative_p_w_sample[-1]
words = np.searchsorted(cumulative_p_w_sample, generator.rand(n_words))
return words, y
X_indices = array.array('i')
X_indptr = array.array('i', [0])
Y = []
for i in range(n_samples):
words, y = sample_example()
X_indices.extend(words)
X_indptr.append(len(X_indices))
Y.append(y)
X_data = np.ones(len(X_indices), dtype=np.float64)
X = sp.csr_matrix((X_data, X_indices, X_indptr),
shape=(n_samples, n_features))
X.sum_duplicates()
if not sparse:
X = X.toarray()
# return_indicator can be True due to backward compatibility
if return_indicator in (True, 'sparse', 'dense'):
lb = MultiLabelBinarizer(sparse_output=(return_indicator == 'sparse'))
Y = lb.fit([range(n_classes)]).transform(Y)
elif return_indicator is not False:
raise ValueError("return_indicator must be either 'sparse', 'dense' "
'or False.')
if return_distributions:
return X, Y, p_c, p_w_c
return X, Y
def make_hastie_10_2(n_samples=12000, random_state=None):
"""Generates data for binary classification used in
Hastie et al. 2009, Example 10.2.
The ten features are standard independent Gaussian and
the target ``y`` is defined by::
y[i] = 1 if np.sum(X[i] ** 2) > 9.34 else -1
Read more in the :ref:`User Guide <sample_generators>`.
Parameters
----------
n_samples : int, optional (default=12000)
The number of samples.
random_state : int, RandomState instance or None (default)
Determines random number generation for dataset creation. Pass an int
for reproducible output across multiple function calls.
See :term:`Glossary <random_state>`.
Returns
-------
X : array of shape [n_samples, 10]
The input samples.
y : array of shape [n_samples]
The output values.
References
----------
.. [1] T. Hastie, R. Tibshirani and J. Friedman, "Elements of Statistical
Learning Ed. 2", Springer, 2009.
See also
--------
make_gaussian_quantiles: a generalization of this dataset approach
"""
rs = check_random_state(random_state)
shape = (n_samples, 10)
X = rs.normal(size=shape).reshape(shape)
y = ((X ** 2.0).sum(axis=1) > 9.34).astype(np.float64)
y[y == 0.0] = -1.0
return X, y
def make_regression(n_samples=100, n_features=100, n_informative=10,
n_targets=1, bias=0.0, effective_rank=None,
tail_strength=0.5, noise=0.0, shuffle=True, coef=False,
random_state=None):
"""Generate a random regression problem.
The input set can either be well conditioned (by default) or have a low
rank-fat tail singular profile. See :func:`make_low_rank_matrix` for
more details.
The output is generated by applying a (potentially biased) random linear
regression model with `n_informative` nonzero regressors to the previously
generated input and some gaussian centered noise with some adjustable
scale.
Read more in the :ref:`User Guide <sample_generators>`.
Parameters
----------
n_samples : int, optional (default=100)
The number of samples.
n_features : int, optional (default=100)
The number of features.
n_informative : int, optional (default=10)
The number of informative features, i.e., the number of features used
to build the linear model used to generate the output.
n_targets : int, optional (default=1)
The number of regression targets, i.e., the dimension of the y output
vector associated with a sample. By default, the output is a scalar.
bias : float, optional (default=0.0)
The bias term in the underlying linear model.
effective_rank : int or None, optional (default=None)
if not None:
The approximate number of singular vectors required to explain most
of the input data by linear combinations. Using this kind of
singular spectrum in the input allows the generator to reproduce
the correlations often observed in practice.
if None:
The input set is well conditioned, centered and gaussian with
unit variance.
tail_strength : float between 0.0 and 1.0, optional (default=0.5)
The relative importance of the fat noisy tail of the singular values
profile if `effective_rank` is not None.
noise : float, optional (default=0.0)
The standard deviation of the gaussian noise applied to the output.
shuffle : boolean, optional (default=True)
Shuffle the samples and the features.
coef : boolean, optional (default=False)
If True, the coefficients of the underlying linear model are returned.
random_state : int, RandomState instance or None (default)
Determines random number generation for dataset creation. Pass an int
for reproducible output across multiple function calls.
See :term:`Glossary <random_state>`.
Returns
-------
X : array of shape [n_samples, n_features]
The input samples.
y : array of shape [n_samples] or [n_samples, n_targets]
The output values.
coef : array of shape [n_features] or [n_features, n_targets], optional
The coefficient of the underlying linear model. It is returned only if
coef is True.
"""
n_informative = min(n_features, n_informative)
generator = check_random_state(random_state)
if effective_rank is None:
# Randomly generate a well conditioned input set
X = generator.randn(n_samples, n_features)
else:
# Randomly generate a low rank, fat tail input set
X = make_low_rank_matrix(n_samples=n_samples,
n_features=n_features,
effective_rank=effective_rank,
tail_strength=tail_strength,
random_state=generator)
# Generate a ground truth model with only n_informative features being non
# zeros (the other features are not correlated to y and should be ignored
# by a sparsifying regularizers such as L1 or elastic net)
ground_truth = np.zeros((n_features, n_targets))
ground_truth[:n_informative, :] = 100 * generator.rand(n_informative,
n_targets)
y = np.dot(X, ground_truth) + bias
# Add noise
if noise > 0.0:
y += generator.normal(scale=noise, size=y.shape)
# Randomly permute samples and features
if shuffle:
X, y = util_shuffle(X, y, random_state=generator)
indices = np.arange(n_features)
generator.shuffle(indices)
X[:, :] = X[:, indices]
ground_truth = ground_truth[indices]
y = np.squeeze(y)
if coef:
return X, y, np.squeeze(ground_truth)
else:
return X, y
def make_circles(n_samples=100, shuffle=True, noise=None, random_state=None,
factor=.8):
"""Make a large circle containing a smaller circle in 2d.
A simple toy dataset to visualize clustering and classification
algorithms.
Read more in the :ref:`User Guide <sample_generators>`.
Parameters
----------
n_samples : int, optional (default=100)
The total number of points generated. If odd, the inner circle will
have one point more than the outer circle.
shuffle : bool, optional (default=True)
Whether to shuffle the samples.
noise : double or None (default=None)
Standard deviation of Gaussian noise added to the data.
random_state : int, RandomState instance or None (default)
Determines random number generation for dataset shuffling and noise.
Pass an int for reproducible output across multiple function calls.
See :term:`Glossary <random_state>`.
factor : 0 < double < 1 (default=.8)
Scale factor between inner and outer circle.
Returns
-------
X : array of shape [n_samples, 2]
The generated samples.
y : array of shape [n_samples]
The integer labels (0 or 1) for class membership of each sample.
"""
if factor >= 1 or factor < 0:
raise ValueError("'factor' has to be between 0 and 1.")
n_samples_out = n_samples // 2
n_samples_in = n_samples - n_samples_out
generator = check_random_state(random_state)
# so as not to have the first point = last point, we set endpoint=False
linspace_out = np.linspace(0, 2 * np.pi, n_samples_out, endpoint=False)
linspace_in = np.linspace(0, 2 * np.pi, n_samples_in, endpoint=False)
outer_circ_x = np.cos(linspace_out)
outer_circ_y = np.sin(linspace_out)
inner_circ_x = np.cos(linspace_in) * factor
inner_circ_y = np.sin(linspace_in) * factor
X = np.vstack([np.append(outer_circ_x, inner_circ_x),
np.append(outer_circ_y, inner_circ_y)]).T
y = np.hstack([np.zeros(n_samples_out, dtype=np.intp),
np.ones(n_samples_in, dtype=np.intp)])
if shuffle:
X, y = util_shuffle(X, y, random_state=generator)
if noise is not None:
X += generator.normal(scale=noise, size=X.shape)
return X, y
def make_moons(n_samples=100, shuffle=True, noise=None, random_state=None):
"""Make two interleaving half circles
A simple toy dataset to visualize clustering and classification
algorithms. Read more in the :ref:`User Guide <sample_generators>`.
Parameters
----------
n_samples : int, optional (default=100)
The total number of points generated.
shuffle : bool, optional (default=True)
Whether to shuffle the samples.
noise : double or None (default=None)
Standard deviation of Gaussian noise added to the data.
random_state : int, RandomState instance or None (default)
Determines random number generation for dataset shuffling and noise.
Pass an int for reproducible output across multiple function calls.
See :term:`Glossary <random_state>`.
Returns
-------
X : array of shape [n_samples, 2]
The generated samples.
y : array of shape [n_samples]
The integer labels (0 or 1) for class membership of each sample.
"""
n_samples_out = n_samples // 2
n_samples_in = n_samples - n_samples_out
generator = check_random_state(random_state)
outer_circ_x = np.cos(np.linspace(0, np.pi, n_samples_out))
outer_circ_y = np.sin(np.linspace(0, np.pi, n_samples_out))
inner_circ_x = 1 - np.cos(np.linspace(0, np.pi, n_samples_in))
inner_circ_y = 1 - np.sin(np.linspace(0, np.pi, n_samples_in)) - .5
X = np.vstack([np.append(outer_circ_x, inner_circ_x),
np.append(outer_circ_y, inner_circ_y)]).T
y = np.hstack([np.zeros(n_samples_out, dtype=np.intp),
np.ones(n_samples_in, dtype=np.intp)])
if shuffle:
X, y = util_shuffle(X, y, random_state=generator)
if noise is not None:
X += generator.normal(scale=noise, size=X.shape)
return X, y
def make_blobs(n_samples=100, n_features=2, centers=None, cluster_std=1.0,
center_box=(-10.0, 10.0), shuffle=True, random_state=None):
"""Generate isotropic Gaussian blobs for clustering.
Read more in the :ref:`User Guide <sample_generators>`.
Parameters
----------
n_samples : int or array-like, optional (default=100)
If int, it is the total number of points equally divided among
clusters.
If array-like, each element of the sequence indicates
the number of samples per cluster.
n_features : int, optional (default=2)
The number of features for each sample.
centers : int or array of shape [n_centers, n_features], optional
(default=None)
The number of centers to generate, or the fixed center locations.
If n_samples is an int and centers is None, 3 centers are generated.
If n_samples is array-like, centers must be
either None or an array of length equal to the length of n_samples.
cluster_std : float or sequence of floats, optional (default=1.0)
The standard deviation of the clusters.
center_box : pair of floats (min, max), optional (default=(-10.0, 10.0))
The bounding box for each cluster center when centers are
generated at random.
shuffle : boolean, optional (default=True)
Shuffle the samples.
random_state : int, RandomState instance or None (default)
Determines random number generation for dataset creation. Pass an int
for reproducible output across multiple function calls.
See :term:`Glossary <random_state>`.
Returns
-------
X : array of shape [n_samples, n_features]
The generated samples.
y : array of shape [n_samples]
The integer labels for cluster membership of each sample.
Examples
--------
>>> from sklearn.datasets.samples_generator import make_blobs
>>> X, y = make_blobs(n_samples=10, centers=3, n_features=2,
... random_state=0)
>>> print(X.shape)
(10, 2)
>>> y
array([0, 0, 1, 0, 2, 2, 2, 1, 1, 0])
>>> X, y = make_blobs(n_samples=[3, 3, 4], centers=None, n_features=2,
... random_state=0)
>>> print(X.shape)
(10, 2)
>>> y
array([0, 1, 2, 0, 2, 2, 2, 1, 1, 0])
See also
--------
make_classification: a more intricate variant
"""
generator = check_random_state(random_state)
if isinstance(n_samples, numbers.Integral):
# Set n_centers by looking at centers arg
if centers is None:
centers = 3
if isinstance(centers, numbers.Integral):
n_centers = centers
centers = generator.uniform(center_box[0], center_box[1],
size=(n_centers, n_features))
else:
centers = check_array(centers)
n_features = centers.shape[1]
n_centers = centers.shape[0]
else:
# Set n_centers by looking at [n_samples] arg
n_centers = len(n_samples)
if centers is None:
centers = generator.uniform(center_box[0], center_box[1],
size=(n_centers, n_features))
try:
assert len(centers) == n_centers
except TypeError:
raise ValueError("Parameter `centers` must be array-like. "
"Got {!r} instead".format(centers))
except AssertionError:
raise ValueError("Length of `n_samples` not consistent"
" with number of centers. Got n_samples = {} "
"and centers = {}".format(n_samples, centers))
else:
centers = check_array(centers)
n_features = centers.shape[1]
# stds: if cluster_std is given as list, it must be consistent
# with the n_centers
if (hasattr(cluster_std, "__len__") and len(cluster_std) != n_centers):
raise ValueError("Length of `clusters_std` not consistent with "
"number of centers. Got centers = {} "
"and cluster_std = {}".format(centers, cluster_std))
if isinstance(cluster_std, numbers.Real):
cluster_std = np.full(len(centers), cluster_std)
X = []
y = []
if isinstance(n_samples, Iterable):
n_samples_per_center = n_samples
else:
n_samples_per_center = [int(n_samples // n_centers)] * n_centers
for i in range(n_samples % n_centers):
n_samples_per_center[i] += 1
for i, (n, std) in enumerate(zip(n_samples_per_center, cluster_std)):
X.append(generator.normal(loc=centers[i], scale=std,
size=(n, n_features)))
y += [i] * n
X = np.concatenate(X)
y = np.array(y)
if shuffle:
total_n_samples = np.sum(n_samples)
indices = np.arange(total_n_samples)
generator.shuffle(indices)
X = X[indices]
y = y[indices]
return X, y
def make_friedman1(n_samples=100, n_features=10, noise=0.0, random_state=None):
"""Generate the "Friedman #1" regression problem
This dataset is described in Friedman [1] and Breiman [2].
Inputs `X` are independent features uniformly distributed on the interval
[0, 1]. The output `y` is created according to the formula::
y(X) = 10 * sin(pi * X[:, 0] * X[:, 1]) + 20 * (X[:, 2] - 0.5) ** 2 \
+ 10 * X[:, 3] + 5 * X[:, 4] + noise * N(0, 1).
Out of the `n_features` features, only 5 are actually used to compute
`y`. The remaining features are independent of `y`.
The number of features has to be >= 5.
Read more in the :ref:`User Guide <sample_generators>`.
Parameters
----------
n_samples : int, optional (default=100)
The number of samples.
n_features : int, optional (default=10)
The number of features. Should be at least 5.
noise : float, optional (default=0.0)
The standard deviation of the gaussian noise applied to the output.
random_state : int, RandomState instance or None (default)
Determines random number generation for dataset noise. Pass an int
for reproducible output across multiple function calls.
See :term:`Glossary <random_state>`.
Returns
-------
X : array of shape [n_samples, n_features]
The input samples.
y : array of shape [n_samples]
The output values.
References
----------
.. [1] J. Friedman, "Multivariate adaptive regression splines", The Annals
of Statistics 19 (1), pages 1-67, 1991.
.. [2] L. Breiman, "Bagging predictors", Machine Learning 24,
pages 123-140, 1996.
"""
if n_features < 5:
raise ValueError("n_features must be at least five.")
generator = check_random_state(random_state)
X = generator.rand(n_samples, n_features)
y = 10 * np.sin(np.pi * X[:, 0] * X[:, 1]) + 20 * (X[:, 2] - 0.5) ** 2 \
+ 10 * X[:, 3] + 5 * X[:, 4] + noise * generator.randn(n_samples)
return X, y
def make_friedman2(n_samples=100, noise=0.0, random_state=None):
"""Generate the "Friedman #2" regression problem
This dataset is described in Friedman [1] and Breiman [2].
Inputs `X` are 4 independent features uniformly distributed on the
intervals::
0 <= X[:, 0] <= 100,
40 * pi <= X[:, 1] <= 560 * pi,
0 <= X[:, 2] <= 1,
1 <= X[:, 3] <= 11.
The output `y` is created according to the formula::
y(X) = (X[:, 0] ** 2 + (X[:, 1] * X[:, 2] \
- 1 / (X[:, 1] * X[:, 3])) ** 2) ** 0.5 + noise * N(0, 1).
Read more in the :ref:`User Guide <sample_generators>`.
Parameters
----------
n_samples : int, optional (default=100)
The number of samples.
noise : float, optional (default=0.0)
The standard deviation of the gaussian noise applied to the output.
random_state : int, RandomState instance or None (default)
Determines random number generation for dataset noise. Pass an int
for reproducible output across multiple function calls.
See :term:`Glossary <random_state>`.
Returns
-------
X : array of shape [n_samples, 4]
The input samples.
y : array of shape [n_samples]
The output values.
References
----------
.. [1] J. Friedman, "Multivariate adaptive regression splines", The Annals
of Statistics 19 (1), pages 1-67, 1991.
.. [2] L. Breiman, "Bagging predictors", Machine Learning 24,
pages 123-140, 1996.
"""
generator = check_random_state(random_state)
X = generator.rand(n_samples, 4)
X[:, 0] *= 100
X[:, 1] *= 520 * np.pi
X[:, 1] += 40 * np.pi
X[:, 3] *= 10
X[:, 3] += 1
y = (X[:, 0] ** 2
+ (X[:, 1] * X[:, 2] - 1 / (X[:, 1] * X[:, 3])) ** 2) ** 0.5 \
+ noise * generator.randn(n_samples)
return X, y
def make_friedman3(n_samples=100, noise=0.0, random_state=None):
"""Generate the "Friedman #3" regression problem
This dataset is described in Friedman [1] and Breiman [2].
Inputs `X` are 4 independent features uniformly distributed on the
intervals::
0 <= X[:, 0] <= 100,
40 * pi <= X[:, 1] <= 560 * pi,
0 <= X[:, 2] <= 1,
1 <= X[:, 3] <= 11.
The output `y` is created according to the formula::
y(X) = arctan((X[:, 1] * X[:, 2] - 1 / (X[:, 1] * X[:, 3])) \
/ X[:, 0]) + noise * N(0, 1).
Read more in the :ref:`User Guide <sample_generators>`.
Parameters
----------
n_samples : int, optional (default=100)
The number of samples.
noise : float, optional (default=0.0)
The standard deviation of the gaussian noise applied to the output.
random_state : int, RandomState instance or None (default)
Determines random number generation for dataset noise. Pass an int
for reproducible output across multiple function calls.
See :term:`Glossary <random_state>`.
Returns
-------
X : array of shape [n_samples, 4]
The input samples.
y : array of shape [n_samples]
The output values.
References
----------
.. [1] J. Friedman, "Multivariate adaptive regression splines", The Annals
of Statistics 19 (1), pages 1-67, 1991.
.. [2] L. Breiman, "Bagging predictors", Machine Learning 24,
pages 123-140, 1996.
"""
generator = check_random_state(random_state)
X = generator.rand(n_samples, 4)
X[:, 0] *= 100
X[:, 1] *= 520 * np.pi
X[:, 1] += 40 * np.pi
X[:, 3] *= 10
X[:, 3] += 1
y = np.arctan((X[:, 1] * X[:, 2] - 1 / (X[:, 1] * X[:, 3])) / X[:, 0]) \
+ noise * generator.randn(n_samples)
return X, y
def make_low_rank_matrix(n_samples=100, n_features=100, effective_rank=10,
tail_strength=0.5, random_state=None):
"""Generate a mostly low rank matrix with bell-shaped singular values
Most of the variance can be explained by a bell-shaped curve of width
effective_rank: the low rank part of the singular values profile is::
(1 - tail_strength) * exp(-1.0 * (i / effective_rank) ** 2)
The remaining singular values' tail is fat, decreasing as::
tail_strength * exp(-0.1 * i / effective_rank).
The low rank part of the profile can be considered the structured
signal part of the data while the tail can be considered the noisy
part of the data that cannot be summarized by a low number of linear
components (singular vectors).
This kind of singular profiles is often seen in practice, for instance:
- gray level pictures of faces
- TF-IDF vectors of text documents crawled from the web
Read more in the :ref:`User Guide <sample_generators>`.
Parameters
----------
n_samples : int, optional (default=100)
The number of samples.
n_features : int, optional (default=100)
The number of features.
effective_rank : int, optional (default=10)
The approximate number of singular vectors required to explain most of
the data by linear combinations.
tail_strength : float between 0.0 and 1.0, optional (default=0.5)
The relative importance of the fat noisy tail of the singular values
profile.
random_state : int, RandomState instance or None (default)
Determines random number generation for dataset creation. Pass an int
for reproducible output across multiple function calls.
See :term:`Glossary <random_state>`.
Returns
-------
X : array of shape [n_samples, n_features]
The matrix.
"""
generator = check_random_state(random_state)
n = min(n_samples, n_features)
# Random (ortho normal) vectors
u, _ = linalg.qr(generator.randn(n_samples, n), mode='economic')
v, _ = linalg.qr(generator.randn(n_features, n), mode='economic')
# Index of the singular values
singular_ind = np.arange(n, dtype=np.float64)
# Build the singular profile by assembling signal and noise components
low_rank = ((1 - tail_strength) *
np.exp(-1.0 * (singular_ind / effective_rank) ** 2))
tail = tail_strength * np.exp(-0.1 * singular_ind / effective_rank)
s = np.identity(n) * (low_rank + tail)
return np.dot(np.dot(u, s), v.T)
def make_sparse_coded_signal(n_samples, n_components, n_features,
n_nonzero_coefs, random_state=None):
"""Generate a signal as a sparse combination of dictionary elements.
Returns a matrix Y = DX, such as D is (n_features, n_components),
X is (n_components, n_samples) and each column of X has exactly
n_nonzero_coefs non-zero elements.
Read more in the :ref:`User Guide <sample_generators>`.
Parameters
----------
n_samples : int
number of samples to generate
n_components : int,
number of components in the dictionary
n_features : int
number of features of the dataset to generate
n_nonzero_coefs : int
number of active (non-zero) coefficients in each sample
random_state : int, RandomState instance or None (default)
Determines random number generation for dataset creation. Pass an int
for reproducible output across multiple function calls.
See :term:`Glossary <random_state>`.
Returns
-------
data : array of shape [n_features, n_samples]
The encoded signal (Y).
dictionary : array of shape [n_features, n_components]
The dictionary with normalized components (D).
code : array of shape [n_components, n_samples]
The sparse code such that each column of this matrix has exactly
n_nonzero_coefs non-zero items (X).
"""
generator = check_random_state(random_state)
# generate dictionary
D = generator.randn(n_features, n_components)
D /= np.sqrt(np.sum((D ** 2), axis=0))
# generate code
X = np.zeros((n_components, n_samples))
for i in range(n_samples):
idx = np.arange(n_components)
generator.shuffle(idx)
idx = idx[:n_nonzero_coefs]
X[idx, i] = generator.randn(n_nonzero_coefs)
# encode signal
Y = np.dot(D, X)
return map(np.squeeze, (Y, D, X))
def make_sparse_uncorrelated(n_samples=100, n_features=10, random_state=None):
"""Generate a random regression problem with sparse uncorrelated design
This dataset is described in Celeux et al [1]. as::
X ~ N(0, 1)
y(X) = X[:, 0] + 2 * X[:, 1] - 2 * X[:, 2] - 1.5 * X[:, 3]
Only the first 4 features are informative. The remaining features are
useless.
Read more in the :ref:`User Guide <sample_generators>`.
Parameters
----------
n_samples : int, optional (default=100)
The number of samples.
n_features : int, optional (default=10)
The number of features.
random_state : int, RandomState instance or None (default)
Determines random number generation for dataset creation. Pass an int
for reproducible output across multiple function calls.
See :term:`Glossary <random_state>`.
Returns
-------
X : array of shape [n_samples, n_features]
The input samples.
y : array of shape [n_samples]
The output values.
References
----------
.. [1] G. Celeux, M. El Anbari, J.-M. Marin, C. P. Robert,
"Regularization in regression: comparing Bayesian and frequentist
methods in a poorly informative situation", 2009.
"""
generator = check_random_state(random_state)
X = generator.normal(loc=0, scale=1, size=(n_samples, n_features))
y = generator.normal(loc=(X[:, 0] +
2 * X[:, 1] -
2 * X[:, 2] -
1.5 * X[:, 3]), scale=np.ones(n_samples))
return X, y
def make_spd_matrix(n_dim, random_state=None):
"""Generate a random symmetric, positive-definite matrix.
Read more in the :ref:`User Guide <sample_generators>`.
Parameters
----------
n_dim : int
The matrix dimension.
random_state : int, RandomState instance or None (default)
Determines random number generation for dataset creation. Pass an int
for reproducible output across multiple function calls.
See :term:`Glossary <random_state>`.
Returns
-------
X : array of shape [n_dim, n_dim]
The random symmetric, positive-definite matrix.
See also
--------
make_sparse_spd_matrix
"""
generator = check_random_state(random_state)
A = generator.rand(n_dim, n_dim)
U, s, V = linalg.svd(np.dot(A.T, A))
X = np.dot(np.dot(U, 1.0 + np.diag(generator.rand(n_dim))), V)
return X
def make_sparse_spd_matrix(dim=1, alpha=0.95, norm_diag=False,
smallest_coef=.1, largest_coef=.9,
random_state=None):
"""Generate a sparse symmetric definite positive matrix.
Read more in the :ref:`User Guide <sample_generators>`.
Parameters
----------
dim : integer, optional (default=1)
The size of the random matrix to generate.
alpha : float between 0 and 1, optional (default=0.95)
The probability that a coefficient is zero (see notes). Larger values
enforce more sparsity.
norm_diag : boolean, optional (default=False)
Whether to normalize the output matrix to make the leading diagonal
elements all 1
smallest_coef : float between 0 and 1, optional (default=0.1)
The value of the smallest coefficient.
largest_coef : float between 0 and 1, optional (default=0.9)
The value of the largest coefficient.
random_state : int, RandomState instance or None (default)
Determines random number generation for dataset creation. Pass an int
for reproducible output across multiple function calls.
See :term:`Glossary <random_state>`.
Returns
-------
prec : sparse matrix of shape (dim, dim)
The generated matrix.
Notes
-----
The sparsity is actually imposed on the cholesky factor of the matrix.
Thus alpha does not translate directly into the filling fraction of
the matrix itself.
See also
--------
make_spd_matrix
"""
random_state = check_random_state(random_state)
chol = -np.eye(dim)
aux = random_state.rand(dim, dim)
aux[aux < alpha] = 0
aux[aux > alpha] = (smallest_coef
+ (largest_coef - smallest_coef)
* random_state.rand(np.sum(aux > alpha)))
aux = np.tril(aux, k=-1)
# Permute the lines: we don't want to have asymmetries in the final
# SPD matrix
permutation = random_state.permutation(dim)
aux = aux[permutation].T[permutation]
chol += aux
prec = np.dot(chol.T, chol)
if norm_diag:
# Form the diagonal vector into a row matrix
d = np.diag(prec).reshape(1, prec.shape[0])
d = 1. / np.sqrt(d)
prec *= d
prec *= d.T
return prec
def make_swiss_roll(n_samples=100, noise=0.0, random_state=None):
"""Generate a swiss roll dataset.
Read more in the :ref:`User Guide <sample_generators>`.
Parameters
----------
n_samples : int, optional (default=100)
The number of sample points on the S curve.
noise : float, optional (default=0.0)
The standard deviation of the gaussian noise.
random_state : int, RandomState instance or None (default)
Determines random number generation for dataset creation. Pass an int
for reproducible output across multiple function calls.
See :term:`Glossary <random_state>`.
Returns
-------
X : array of shape [n_samples, 3]
The points.
t : array of shape [n_samples]
The univariate position of the sample according to the main dimension
of the points in the manifold.
Notes
-----
The algorithm is from Marsland [1].
References
----------
.. [1] S. Marsland, "Machine Learning: An Algorithmic Perspective",
Chapter 10, 2009.
http://seat.massey.ac.nz/personal/s.r.marsland/Code/10/lle.py
"""
generator = check_random_state(random_state)
t = 1.5 * np.pi * (1 + 2 * generator.rand(1, n_samples))
x = t * np.cos(t)
y = 21 * generator.rand(1, n_samples)
z = t * np.sin(t)
X = np.concatenate((x, y, z))
X += noise * generator.randn(3, n_samples)
X = X.T
t = np.squeeze(t)
return X, t
def make_s_curve(n_samples=100, noise=0.0, random_state=None):
"""Generate an S curve dataset.
Read more in the :ref:`User Guide <sample_generators>`.
Parameters
----------
n_samples : int, optional (default=100)
The number of sample points on the S curve.
noise : float, optional (default=0.0)
The standard deviation of the gaussian noise.
random_state : int, RandomState instance or None (default)
Determines random number generation for dataset creation. Pass an int
for reproducible output across multiple function calls.
See :term:`Glossary <random_state>`.
Returns
-------
X : array of shape [n_samples, 3]
The points.
t : array of shape [n_samples]
The univariate position of the sample according to the main dimension
of the points in the manifold.
"""
generator = check_random_state(random_state)
t = 3 * np.pi * (generator.rand(1, n_samples) - 0.5)
x = np.sin(t)
y = 2.0 * generator.rand(1, n_samples)
z = np.sign(t) * (np.cos(t) - 1)
X = np.concatenate((x, y, z))
X += noise * generator.randn(3, n_samples)
X = X.T
t = np.squeeze(t)
return X, t
def make_gaussian_quantiles(mean=None, cov=1., n_samples=100,
n_features=2, n_classes=3,
shuffle=True, random_state=None):
r"""Generate isotropic Gaussian and label samples by quantile
This classification dataset is constructed by taking a multi-dimensional
standard normal distribution and defining classes separated by nested
concentric multi-dimensional spheres such that roughly equal numbers of
samples are in each class (quantiles of the :math:`\chi^2` distribution).
Read more in the :ref:`User Guide <sample_generators>`.
Parameters
----------
mean : array of shape [n_features], optional (default=None)
The mean of the multi-dimensional normal distribution.
If None then use the origin (0, 0, ...).
cov : float, optional (default=1.)
The covariance matrix will be this value times the unit matrix. This
dataset only produces symmetric normal distributions.
n_samples : int, optional (default=100)
The total number of points equally divided among classes.
n_features : int, optional (default=2)
The number of features for each sample.
n_classes : int, optional (default=3)
The number of classes
shuffle : boolean, optional (default=True)
Shuffle the samples.
random_state : int, RandomState instance or None (default)
Determines random number generation for dataset creation. Pass an int
for reproducible output across multiple function calls.
See :term:`Glossary <random_state>`.
Returns
-------
X : array of shape [n_samples, n_features]
The generated samples.
y : array of shape [n_samples]
The integer labels for quantile membership of each sample.
Notes
-----
The dataset is from Zhu et al [1].
References
----------
.. [1] J. Zhu, H. Zou, S. Rosset, T. Hastie, "Multi-class AdaBoost", 2009.
"""
if n_samples < n_classes:
raise ValueError("n_samples must be at least n_classes")
generator = check_random_state(random_state)
if mean is None:
mean = np.zeros(n_features)
else:
mean = np.array(mean)
# Build multivariate normal distribution
X = generator.multivariate_normal(mean, cov * np.identity(n_features),
(n_samples,))
# Sort by distance from origin
idx = np.argsort(np.sum((X - mean[np.newaxis, :]) ** 2, axis=1))
X = X[idx, :]
# Label by quantile
step = n_samples // n_classes
y = np.hstack([np.repeat(np.arange(n_classes), step),
np.repeat(n_classes - 1, n_samples - step * n_classes)])
if shuffle:
X, y = util_shuffle(X, y, random_state=generator)
return X, y
def _shuffle(data, random_state=None):
generator = check_random_state(random_state)
n_rows, n_cols = data.shape
row_idx = generator.permutation(n_rows)
col_idx = generator.permutation(n_cols)
result = data[row_idx][:, col_idx]
return result, row_idx, col_idx
def make_biclusters(shape, n_clusters, noise=0.0, minval=10,
maxval=100, shuffle=True, random_state=None):
"""Generate an array with constant block diagonal structure for
biclustering.
Read more in the :ref:`User Guide <sample_generators>`.
Parameters
----------
shape : iterable (n_rows, n_cols)
The shape of the result.
n_clusters : integer
The number of biclusters.
noise : float, optional (default=0.0)
The standard deviation of the gaussian noise.
minval : int, optional (default=10)
Minimum value of a bicluster.
maxval : int, optional (default=100)
Maximum value of a bicluster.
shuffle : boolean, optional (default=True)
Shuffle the samples.
random_state : int, RandomState instance or None (default)
Determines random number generation for dataset creation. Pass an int
for reproducible output across multiple function calls.
See :term:`Glossary <random_state>`.
Returns
-------
X : array of shape `shape`
The generated array.
rows : array of shape (n_clusters, X.shape[0],)
The indicators for cluster membership of each row.
cols : array of shape (n_clusters, X.shape[1],)
The indicators for cluster membership of each column.
References
----------
.. [1] Dhillon, I. S. (2001, August). Co-clustering documents and
words using bipartite spectral graph partitioning. In Proceedings
of the seventh ACM SIGKDD international conference on Knowledge
discovery and data mining (pp. 269-274). ACM.
See also
--------
make_checkerboard
"""
generator = check_random_state(random_state)
n_rows, n_cols = shape
consts = generator.uniform(minval, maxval, n_clusters)
# row and column clusters of approximately equal sizes
row_sizes = generator.multinomial(n_rows,
np.repeat(1.0 / n_clusters,
n_clusters))
col_sizes = generator.multinomial(n_cols,
np.repeat(1.0 / n_clusters,
n_clusters))
row_labels = np.hstack(list(np.repeat(val, rep) for val, rep in
zip(range(n_clusters), row_sizes)))
col_labels = np.hstack(list(np.repeat(val, rep) for val, rep in
zip(range(n_clusters), col_sizes)))
result = np.zeros(shape, dtype=np.float64)
for i in range(n_clusters):
selector = np.outer(row_labels == i, col_labels == i)
result[selector] += consts[i]
if noise > 0:
result += generator.normal(scale=noise, size=result.shape)
if shuffle:
result, row_idx, col_idx = _shuffle(result, random_state)
row_labels = row_labels[row_idx]
col_labels = col_labels[col_idx]
rows = np.vstack([row_labels == c for c in range(n_clusters)])
cols = np.vstack([col_labels == c for c in range(n_clusters)])
return result, rows, cols
def make_checkerboard(shape, n_clusters, noise=0.0, minval=10,
maxval=100, shuffle=True, random_state=None):
"""Generate an array with block checkerboard structure for
biclustering.
Read more in the :ref:`User Guide <sample_generators>`.
Parameters
----------
shape : iterable (n_rows, n_cols)
The shape of the result.
n_clusters : integer or iterable (n_row_clusters, n_column_clusters)
The number of row and column clusters.
noise : float, optional (default=0.0)
The standard deviation of the gaussian noise.
minval : int, optional (default=10)
Minimum value of a bicluster.
maxval : int, optional (default=100)
Maximum value of a bicluster.
shuffle : boolean, optional (default=True)
Shuffle the samples.
random_state : int, RandomState instance or None (default)
Determines random number generation for dataset creation. Pass an int
for reproducible output across multiple function calls.
See :term:`Glossary <random_state>`.
Returns
-------
X : array of shape `shape`
The generated array.
rows : array of shape (n_clusters, X.shape[0],)
The indicators for cluster membership of each row.
cols : array of shape (n_clusters, X.shape[1],)
The indicators for cluster membership of each column.
References
----------
.. [1] Kluger, Y., Basri, R., Chang, J. T., & Gerstein, M. (2003).
Spectral biclustering of microarray data: coclustering genes
and conditions. Genome research, 13(4), 703-716.
See also
--------
make_biclusters
"""
generator = check_random_state(random_state)
if hasattr(n_clusters, "__len__"):
n_row_clusters, n_col_clusters = n_clusters
else:
n_row_clusters = n_col_clusters = n_clusters
# row and column clusters of approximately equal sizes
n_rows, n_cols = shape
row_sizes = generator.multinomial(n_rows,
np.repeat(1.0 / n_row_clusters,
n_row_clusters))
col_sizes = generator.multinomial(n_cols,
np.repeat(1.0 / n_col_clusters,
n_col_clusters))
row_labels = np.hstack(list(np.repeat(val, rep) for val, rep in
zip(range(n_row_clusters), row_sizes)))
col_labels = np.hstack(list(np.repeat(val, rep) for val, rep in
zip(range(n_col_clusters), col_sizes)))
result = np.zeros(shape, dtype=np.float64)
for i in range(n_row_clusters):
for j in range(n_col_clusters):
selector = np.outer(row_labels == i, col_labels == j)
result[selector] += generator.uniform(minval, maxval)
if noise > 0:
result += generator.normal(scale=noise, size=result.shape)
if shuffle:
result, row_idx, col_idx = _shuffle(result, random_state)
row_labels = row_labels[row_idx]
col_labels = col_labels[col_idx]
rows = np.vstack([row_labels == label
for label in range(n_row_clusters)
for _ in range(n_col_clusters)])
cols = np.vstack([col_labels == label
for _ in range(n_row_clusters)
for label in range(n_col_clusters)])
return result, rows, cols
|