Newer
Older
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
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Pandas"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Pandas is a data analysis library focussed on the cleaning and exploration of tabular data.\n",
"\n",
"Some useful links are:\n",
"- [main website](https://pandas.pydata.org)\n",
"- [documentation](http://pandas.pydata.org/pandas-docs/stable/)<sup>1</sup>\n",
"- [Python Data Science Handbook](https://jakevdp.github.io/PythonDataScienceHandbook/)<sup>1</sup> by Jake van der Plas\n",
"\n",
"<sup>1</sup> This tutorial borrows heavily from the pandas documentation and the Python Data Science Handbook"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"%pylab inline\n",
"import pandas as pd # pd is the usual abbreviation for pandas\n",
"import seaborn as sns # seaborn is the main plotting library for Pandas\n",
"import statsmodels.api as sm # statsmodels fits linear models to pandas data\n",
"import statsmodels.formula.api as smf\n",
"from IPython.display import Image\n",
"sns.set() # use the prettier seaborn plotting settings rather than the default matplotlib one"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Loading in data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Pandas supports a wide range of I/O tools to load from text files, binary files, and SQL databases. You can find a table with all formats [here](http://pandas.pydata.org/pandas-docs/stable/io.html)."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic = pd.read_csv('https://raw.githubusercontent.com/mwaskom/seaborn-data/master/titanic.csv')\n",
"titanic"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This loads the data into a [DataFrame](https://pandas.pydata.org/pandas-docs/version/0.21/generated/pandas.DataFrame.html) object, which is the main object we will be interacting with in pandas. It represents a table of data.\n",
"\n",
"The other file formats all start with `pd.read_{format}`. Note that we can provide the URL to the dataset, rather than download it beforehand.\n",
"\n",
"We can write out the dataset using `dataframe.to_{format}(<filename)`:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic.to_csv('titanic_copy.csv', index=False) # we set index to False to prevent pandas from storing the row names"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If you can not connect to the internet, you can run the command below to load this locally stored titanic dataset"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"titanic = pd.read_csv('09_pandas/titanic.csv')\n",
"titanic"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that the titanic dataset was also available to us as one of the standard datasets included with seaborn. We could load it from there using"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"sns.load_dataset('titanic')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Dataframes can also be created from other python objects, using pd.DataFrame.from_{other type}. The most useful of these is from_dict, which converts a mapping of the columns to a pandas DataFrame (i.e., table).\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"pd.DataFrame.from_dict({\n",
" 'random numbers': np.random.rand(5),\n",
" 'sequence (int)': np.arange(5),\n",
" 'sequence (float)': np.linspace(0, 5, 5),\n",
" 'letters': list('abcde'),\n",
" 'constant_value': 'same_value'\n",
"})"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For many applications (e.g., ICA, machine learning input) you might want to extract your data as a numpy array. The underlying numpy array can be accessed using the `values` attribute"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic.values"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that the type of the returned array is the most common type (in this case object). If you just want the numeric parts of the table you can use `select_dtype`, which selects specific columns based on their dtype:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic.select_dtypes(include=np.number).values"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that the numpy array has no information on the column names or row indices.\n",
"\n",
"Alternatively, when you want to include the categorical variables in your later analysis (e.g., for machine learning), you can extract dummy variables using: "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"pd.get_dummies(titanic)"
]
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
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Accessing parts of the data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[Documentation on indexing](http://pandas.pydata.org/pandas-docs/stable/indexing.html)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Selecting columns by name"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Single columns can be selected using the normal python indexing:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic['embark_town']"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If the column names are simple strings (not required) we can also access it directly as an attribute"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic.embark_town"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that this returns a pandas [Series](https://pandas.pydata.org/pandas-docs/version/0.23.4/generated/pandas.Series.html) rather than a DataFrame object. A Series is simply a 1-dimensional array representing a single column.\n",
"\n",
"Multiple columns can be returned by providing a list of columns names. This will return a DataFrame:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic[['class', 'alive']]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that you have to provide a list here (square brackets). If you provide a tuple (round brackets) pandas will think you are trying to access a single column that has that tuple as a name:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic[('class', 'alive')]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this case there is no column called ('class', 'alive') leading to an error. Later on we will see some uses to having columns named like this."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Indexing rows by name or integer"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Individual rows can be accessed based on their name (i.e., the index) or integer (i.e., which row it is in). In our current table this will give the same results. To ensure that these are different, let's sort our titanic dataset based on the passenger fare:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic_sorted = titanic.sort_values('fare')\n",
"titanic_sorted"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that the re-sorting did not change the values in the index (i.e., left-most column).\n",
"\n",
"We can select the first row of this newly sorted table using iloc"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic_sorted.iloc[0]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can select the row with the index 0 using"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic_sorted.loc[0]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that this gives the same passenger as the first row of the initial table before sorting"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic.iloc[0]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Another common way to access the first or last N rows of a table is using the head/tail methods"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic_sorted.head(3)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic_sorted.tail(3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that nearly all methods in pandas return a new Dataframe, which means that we can easily call another method on them"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic_sorted.tail(10).head(5) # select the first 5 of the last 10 passengers in the database"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic_sorted.iloc[-10:-5] # alternative way to get the same passengers"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Exercise: use sorting and tail/head or indexing to find the 10 youngest passengers on the titanic. Try to do this on a single line by chaining calls to the titanic dataframe object"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic.sort_values..."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Indexing rows by value"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"One final way to select specific columns is by their value"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic[titanic.sex == 'female'] # selects all females"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# select all passengers older than 60 who departed from Southampton\n",
"titanic[(titanic.age > 60) & (titanic['embark_town'] == 'Southampton')]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that this required typing \"titanic\" quite often. A quicker way to get the same result is using the `query` method, which is described in detail [here](http://pandas.pydata.org/pandas-docs/stable/indexing.html#the-query-method) (note that using the `query` method is also faster and uses a lot less memory).\n",
"\n",
"> You may have trouble using the query method with columns which have a name that cannot be used as a Python identifier."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic.query('(age > 60) & (embark_town == \"Southampton\")')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Particularly useful when selecting data like this is the `isna` method which finds all missing data"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic[~titanic.age.isna()] # select first few passengers whose age is not N/A"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This removing of missing numbers is so common that it has is own method"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic.dropna() # drops all passengers that have some datapoint missing"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic.dropna(subset=['age', 'fare']) # Only drop passengers with missing ages or fares"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Exercise: use sorting, indexing by value, dropna and tail/head or indexing to find the 10 oldest female passengers on the titanic. Try to do this on a single line by chaining calls to the titanic dataframe object"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic..."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Plotting the data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Before we start analyzing the data, let's play around with visualizing it. \n",
"\n",
"Pandas does have some basic built-in plotting options:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic.fare.hist(bins=20, log=True)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic.age.plot()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Individual columns are essentially 1D arrays, so we can use them as such in matplotlib"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"plt.scatter(titanic.age, titanic.fare)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"However, for most purposes much nicer plots can be obtained using [Seaborn](https://seaborn.pydata.org). Seaborn has support to produce plots showing the [univariate](https://seaborn.pydata.org/tutorial/distributions.html#plotting-univariate-distributions) or [bivariate](https://seaborn.pydata.org/tutorial/distributions.html#plotting-bivariate-distributions) distribution of data in a single or a grid of plots.\n",
"\n",
"Most of the seaborn plotting functions expect to get a pandas dataframe (although they will work with Numpy arrays as well). So we can plot age vs. fare like:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"sns.jointplot('age', 'fare', data=titanic)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Exercise: check the documentation from `sns.jointplot` (hover the mouse over the text \"jointplot\" and press shift-tab) to find out how to turn the scatter plot into a density (kde) map"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"sns.jointplot('age', 'fare', data=titanic, ...)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here is just a brief example of how we can use multiple columns to illustrate the data in more detail"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"sns.relplot(x='age', y='fare', col='class', hue='sex', data=titanic,\n",
" col_order=('First', 'Second', 'Third'))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Exercise: Split the plot above into two rows with the first row including the passengers who survived and the second row those who did not (you might have to check the documentation again by using shift-tab while overing the mouse over `relplot`) "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"sns.relplot(x='age', y='fare', col='class', hue='sex', data=titanic,\n",
" col_order=('First', 'Second', 'Third')...)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"One of the nice thing of Seaborn is how easy it is to update how these plots look. You can read more about that [here](https://seaborn.pydata.org/tutorial/aesthetics.html). For example, to increase the font size to get a plot more approriate for a talk, you can use:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"sns.set_context('talk')\n",
"sns.violinplot(x='class', y='age', hue='sex', data=titanic, split=True, \n",
" order=('First', 'Second', 'Third'))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Summarizing the data (mean, std, etc.)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There are a large number of built-in methods to summarize the observations in a Pandas dataframe. Most of these will return a Series with the columns names as index:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic.mean()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic.quantile(0.75)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"One very useful one is `describe`, which gives an overview of many common summary measures"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic.describe()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that non-numeric columns are ignored when summarizing data in this way.\n",
"\n",
"We can also define our own functions to apply to the columns (in this case we have to explicitly set the data types)."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def mad(series):\n",
" \"\"\"\n",
" Computes the median absolute deviatation (MAD)\n",
" \n",
" This is a outlier-resistant measure of the standard deviation\n",
" \"\"\"\n",
" no_nan = series.dropna()\n",
" return np.median(abs(no_nan - np.nanmedian(no_nan)))\n",
"\n",
"titanic.select_dtypes(np.number).apply(mad)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also provide multiple functions to the `apply` method (note that functions can be provided as strings)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic.select_dtypes(np.number).apply(['mean', np.median, np.std, mad])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Grouping by"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"One of the more powerful features of is `groupby`, which splits the dataset on a categorical variable. The book contains a clear tutorial on that feature [here](https://jakevdp.github.io/PythonDataScienceHandbook/03.08-aggregation-and-grouping.html). You can check the pandas documentation [here](http://pandas.pydata.org/pandas-docs/stable/groupby.html) for a more formal introduction. One simple use is just to put it into a loop"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"for cls, part_table in titanic.groupby('class'):\n",
" print(f'Mean fare in {cls.lower()} class: {part_table.fare.mean()}')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"However, it is more often combined with one of the aggregation functions discussed above as illustrated in this figure from the [Python data science handbook](https://jakevdp.github.io/PythonDataScienceHandbook/06.00-figure-code.html#Split-Apply-Combine)\n",
"\n",
""
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic.groupby('class').mean()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also group by multiple variables at once"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic.groupby(['class', 'survived']).mean() # as always in pandas supply multiple column names as lists, not tuples"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"When grouping it can help to use the `cut` method to split a continuous variable into a categorical one"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic.groupby(['class', pd.cut(titanic.age, bins=(0, 18, 50, np.inf))]).mean()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can use the `aggregate` method to apply a different function to each series"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic.groupby(['class', 'survived']).aggregate((np.median, mad))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that both the index (on the left) and the column names (on the top) now have multiple levels. Such a multi-level index is referred to as `MultiIndex`. This does complicate selecting specific columns/rows. You can read more of using `MultiIndex` [here](http://pandas.pydata.org/pandas-docs/stable/advanced.html).\n",
"\n",
"The short version is that columns can be selected using direct indexing (as discussed above)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"df_full = titanic.groupby(['class', 'survived']).aggregate((np.median, mad))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"df_full[('age', 'median')] # selects median age column; note that the round brackets are optional"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"df_full['age'] # selects both age columns"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Remember that indexing based on the index was done through `loc`. The rest is the same as for the columns above"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"df_full.loc[('First', 0)]"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"df_full.loc['First']\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"More advanced use of the `MultiIndex` is possible through `xs`:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"df_full.xs(0, level='survived') # selects all the zero's from the survived index"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"df_full.xs('mad', axis=1, level=1) # selects mad from the second level in the columns (i.e., axis=1) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Reshaping tables"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If we were interested in how the survival rate depends on the class and sex of the passengers we could simply use a groupby:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic.groupby(['class', 'sex']).survived.mean()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"However, this single-column table is difficult to read. The reason for this is that the indexing is multi-leveled (called `MultiIndex` in pandas), while there is only a single column. We would like to move one of the levels in the index to the columns. This can be done using `stack`/`unstack`:\n",
"- `unstack`: Moves one levels in the index to the columns\n",
"- `stack`: Moves one of levels in the columns to the index"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic.groupby(['class', 'sex']).survived.mean().unstack('sex')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The former table, where the different groups are defined in different rows, is often referred to as long-form. After unstacking the table is often referred to as wide-form as the different group (sex in this case) is now represented as different columns. In pandas some operations are easier on long-form tables (e.g., `groupby`) while others require wide_form tables (e.g., making scatter plots of two variables). You can go back and forth using `unstack` or `stack` as illustrated above, but as this is a crucial part of pandas there are many alternatives, such as `pivot_table`, `melt`, and `wide_to_long`, which we will discuss below.\n",
"\n",
"We can prettify the table further using seaborn"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"ax = sns.heatmap(titanic.groupby(['class', 'sex']).survived.mean().unstack('sex'), \n",
" annot=True)\n",
"ax.set_title('survival rate')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that there are also many ways to produce prettier tables in pandas (e.g., color all the negative values). This is documented [here](http://pandas.pydata.org/pandas-docs/stable/style.html)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Because this stacking/unstacking is fairly common after a groupby operation, there is a shortcut for it: `pivot_table`"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic.pivot_table('survived', 'class', 'sex')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As usual in pandas, where we can also provide multiple column names"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"sns.heatmap(titanic.pivot_table('survived', ['class', 'embark_town'], ['sex', pd.cut(titanic.age, (0, 18, np.inf))]), annot=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also change the function to be used to aggregate the data"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"sns.heatmap(titanic.pivot_table('survived', ['class', 'embark_town'], ['sex', pd.cut(titanic.age, (0, 18, np.inf))], \n",
" aggfunc='count'), annot=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As in `groupby` the aggregation function can be a string of a common aggregation function, or any function that should be applied.\n",
"\n",
"We can even apply different aggregate functions to different columns"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"titanic.pivot_table(index='class', columns='sex', \n",
" aggfunc={'survived': 'count', 'fare': np.mean}) # compute number of survivors and mean fare\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The opposite of `pivot_table` is `melt`. This can be used to change a wide-form table into a long-form table. This is not particularly useful on the titanic dataset, so let's create a new table where this might be useful. Let's say we have a dataset listing the FA and MD values in various WM tracts:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"tracts = ('Corpus callosum', 'Internal capsule', 'SLF', 'Arcuate fasciculus')\n",
"df_wide = pd.DataFrame.from_dict(dict({'subject': list('ABCDEFGHIJ')}, **{\n",
" f'FA({tract})': np.random.rand(10) for tract in tracts }, **{\n",
" f'MD({tract})': np.random.rand(10) * 1e-3 for tract in tracts\n",
"}))\n",
"df_wide"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This wide-form table (i.e., all the information is in different columns) makes it hard to select just all the FA values or only the values associated with the SLF. For this it would be easier to lismt all the values in a single column. Most of the tools discussed above (e.g., `group_by` or `seaborn` plotting) work better with long-form data, which we can obtain from `melt`: "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"df_long = df_wide.melt('subject', var_name='measurement', value_name='dti_value')\n",
"df_long.head(12)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can see that `melt` took all the columns (we could also have specified a specific sub-set) and returned each measurement as a seperate row. We probably want to seperate the measurement column into the measurement type (FA or MD) and the tract name. Many string manipulation function are available in the `DataFrame` object under `DataFrame.str` ([tutorial](http://pandas.pydata.org/pandas-docs/stable/text.html))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"df_long['variable'] = df_long.measurement.str.slice(0, 2) # first two letters correspond to FA or MD\n",
"df_long['tract'] = df_long.measurement.str.slice(3, -1) # fourth till the second-to-last letter correspond to the tract\n",
"df_long.head(12)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Finally we probably do want the FA and MD variables as different columns. \n",
"\n",
"*Exercise*: Use `pivot_table` or `stack`/`unstack` to create a column for MD and FA."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"df_unstacked = df_long."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can now use the tools discussed above to visualize the table (`seaborn`) or to group the table based on tract (`groupby` or `pivot_table`)."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# feel free to analyze this random data in more detail"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In general pandas is better at handling long-form than wide-form data, although for better visualization of the data an intermediate format is often best. One exception is calculating a covariance (`DataFrame.cov`) or correlation (`DataFrame.corr`) matrices which computes the correlation between each column:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"sns.heatmap(df_wide.corr(), cmap=sns.diverging_palette(240, 10, s=99, n=300), )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Linear fitting (statsmodels)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Linear fitting between the different columns is available through the [statsmodels](https://www.statsmodels.org/stable/index.html) library. A nice way to play around with a wide variety of possible models is to use R-style functions. The usage of the functions in stastmodels is described [here](https://www.statsmodels.org/dev/example_formulas.html). You can find a more detailed description of the R-style functions [here](https://patsy.readthedocs.io/en/latest/formulas.html#the-formula-language). \n",
"\n",
"In short these functions describe the linear model as a string. For example, \"y ~ x + a + x * a\" fits the variable `y` as a function of `x`, `a`, and the interaction between `x` and `a`. The intercept is included by default (you can add \"+ 0\" to remove it)."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"result = smf.logit('survived ~ age + sex + age * sex', data=titanic).fit()\n",
"print(result.summary())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that statsmodels understands categorical variables and automatically replaces them with dummy variables.\n",
"\n",
"Above we used logistic regression, which is appropriate for the binary survival rate. A wide variety of linear models are available. Let's try a GLM, but assume that the fare is drawn from a Gamma distribution:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"age_dmean = titanic.age - titanic.age.mean()\n",
"result = smf.glm('fare ~ age_dmean + embark_town', data=titanic).fit()\n",
"print(result.summary())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Cherbourg passengers clearly paid a lot more...\n",
"\n",
"\n",
"Note that we did not actually add the age_dmean to the dataframe. Statsmodels (or more precisely the underlying [patsy](https://patsy.readthedocs.io/en/latest/) library) automatically extracted this from our environment. This can lead to confusing behaviour..."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# More reading"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Other useful features\n",
"- [Concatenating](https://jakevdp.github.io/PythonDataScienceHandbook/03.06-concat-and-append.html) and [merging](https://jakevdp.github.io/PythonDataScienceHandbook/03.07-merge-and-join.html) of tables\n",
"- [Lots of](http://pandas.pydata.org/pandas-docs/stable/basics.html#dt-accessor) [time](http://pandas.pydata.org/pandas-docs/stable/timeseries.html) [series](http://pandas.pydata.org/pandas-docs/stable/timedeltas.html) support\n",
"- [Rolling Window functions](http://pandas.pydata.org/pandas-docs/stable/computation.html#window-functions) for after you have meaningfully sorted your data\n",
"- and much, much more"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.2"
},
"toc": {
"colors": {
"hover_highlight": "#DAA520",
"running_highlight": "#FF0000",
"selected_highlight": "#FFD700"
},
"moveMenuLeft": true,
"nav_menu": {
"height": "225px",
"width": "252px"
},
"navigate_menu": true,
"number_sections": true,
"sideBar": true,
"threshold": 4,
"toc_cell": false,
"toc_section_display": "block",
"toc_window_display": false
}
},
"nbformat": 4,
"nbformat_minor": 2
}