-
Notifications
You must be signed in to change notification settings - Fork 81
/
Copy pathplot_cyclical_feature_engineering.html
2167 lines (2096 loc) · 152 KB
/
plot_cyclical_feature_engineering.html
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
<!DOCTYPE html>
<!-- data-theme below is forced to be "light" but should be changed if we use pydata-theme-sphinx in the future -->
<!--[if IE 8]><html class="no-js lt-ie9" lang="en" data-content_root="../../" data-theme="light"> <![endif]-->
<!--[if gt IE 8]><!--> <html class="no-js" lang="en" data-content_root="../../" data-theme="light"> <!--<![endif]-->
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1" />
<meta property="og:title" content="Time-related feature engineering" />
<meta property="og:type" content="website" />
<meta property="og:url" content="https://scikit-learn/stable/auto_examples/applications/plot_cyclical_feature_engineering.html" />
<meta property="og:site_name" content="scikit-learn" />
<meta property="og:description" content="This notebook introduces different strategies to leverage time-related features for a bike sharing demand regression task that is highly dependent on business cycles (days, weeks, months) and yearl..." />
<meta property="og:image" content="https://scikit-learn.org/stable/_static/scikit-learn-logo-small.png" />
<meta property="og:image:alt" content="scikit-learn" />
<meta name="description" content="This notebook introduces different strategies to leverage time-related features for a bike sharing demand regression task that is highly dependent on business cycles (days, weeks, months) and yearl..." />
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Time-related feature engineering — scikit-learn 1.4.2 documentation</title>
<link rel="canonical" href="https://scikit-learn.org/stable/auto_examples/applications/plot_cyclical_feature_engineering.html" />
<link rel="shortcut icon" href="../../_static/favicon.ico"/>
<link rel="stylesheet" href="../../_static/css/vendor/bootstrap.min.css" type="text/css" />
<link rel="stylesheet" href="../../_static/pygments.css" type="text/css" />
<link rel="stylesheet" href="../../_static/css/theme.css" type="text/css" />
<link rel="stylesheet" href="../../_static/copybutton.css" type="text/css" />
<link rel="stylesheet" href="../../_static/plot_directive.css" type="text/css" />
<link rel="stylesheet" href="../../https://fonts.googleapis.com/css?family=Vibur" type="text/css" />
<link rel="stylesheet" href="../../_static/jupyterlite_sphinx.css" type="text/css" />
<link rel="stylesheet" href="../../_static/sg_gallery.css" type="text/css" />
<link rel="stylesheet" href="../../_static/sg_gallery-binder.css" type="text/css" />
<link rel="stylesheet" href="../../_static/sg_gallery-dataframe.css" type="text/css" />
<link rel="stylesheet" href="../../_static/sg_gallery-rendered-html.css" type="text/css" />
<link rel="stylesheet" href="../../_static/css/theme.css" type="text/css" />
<script id="documentation_options" data-url_root="../../" src="../../_static/documentation_options.js"></script>
<script src="../../_static/js/vendor/jquery-3.6.3.slim.min.js"></script>
<script src="../../_static/js/details-permalink.js"></script>
</head>
<body>
<nav id="navbar" class="sk-docs-navbar navbar navbar-expand-md navbar-light bg-light py-0">
<div class="container-fluid sk-docs-container px-0">
<a class="navbar-brand py-0" href="../../index.html">
<img
class="sk-brand-img"
src="../../_static/scikit-learn-logo-small.png"
alt="logo"/>
</a>
<button
id="sk-navbar-toggler"
class="navbar-toggler"
type="button"
data-toggle="collapse"
data-target="#navbarSupportedContent"
aria-controls="navbarSupportedContent"
aria-expanded="false"
aria-label="Toggle navigation"
>
<span class="navbar-toggler-icon"></span>
</button>
<div class="sk-navbar-collapse collapse navbar-collapse" id="navbarSupportedContent">
<ul class="navbar-nav mr-auto">
<li class="nav-item">
<a class="sk-nav-link nav-link" href="../../install.html">Install</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link" href="../../user_guide.html">User Guide</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link" href="../../modules/classes.html">API</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link" href="../index.html">Examples</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link" target="_blank" rel="noopener noreferrer" href="https://blog.scikit-learn.org/">Community</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../getting_started.html" >Getting Started</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../tutorial/index.html" >Tutorial</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../whats_new/v1.4.html" >What's new</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../glossary.html" >Glossary</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="https://scikit-learn.org/dev/developers/index.html" target="_blank" rel="noopener noreferrer">Development</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../faq.html" >FAQ</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../support.html" >Support</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../related_projects.html" >Related packages</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../roadmap.html" >Roadmap</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../governance.html" >Governance</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../about.html" >About us</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="https://github.com/scikit-learn/scikit-learn" >GitHub</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="https://scikit-learn.org/dev/versions.html" >Other Versions and Download</a>
</li>
<li class="nav-item dropdown nav-more-item-dropdown">
<a class="sk-nav-link nav-link dropdown-toggle" href="#" id="navbarDropdown" role="button" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false">More</a>
<div class="dropdown-menu" aria-labelledby="navbarDropdown">
<a class="sk-nav-dropdown-item dropdown-item" href="../../getting_started.html" >Getting Started</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../tutorial/index.html" >Tutorial</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../whats_new/v1.4.html" >What's new</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../glossary.html" >Glossary</a>
<a class="sk-nav-dropdown-item dropdown-item" href="https://scikit-learn.org/dev/developers/index.html" target="_blank" rel="noopener noreferrer">Development</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../faq.html" >FAQ</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../support.html" >Support</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../related_projects.html" >Related packages</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../roadmap.html" >Roadmap</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../governance.html" >Governance</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../about.html" >About us</a>
<a class="sk-nav-dropdown-item dropdown-item" href="https://github.com/scikit-learn/scikit-learn" >GitHub</a>
<a class="sk-nav-dropdown-item dropdown-item" href="https://scikit-learn.org/dev/versions.html" >Other Versions and Download</a>
</div>
</li>
</ul>
<div id="searchbox" role="search">
<div class="searchformwrapper">
<form class="search" action="../../search.html" method="get">
<input class="sk-search-text-input" type="text" name="q" aria-labelledby="searchlabel" />
<input class="sk-search-text-btn" type="submit" value="Go" />
</form>
</div>
</div>
</div>
</div>
</nav>
<div class="d-flex" id="sk-doc-wrapper">
<input type="checkbox" name="sk-toggle-checkbox" id="sk-toggle-checkbox">
<label id="sk-sidemenu-toggle" class="sk-btn-toggle-toc btn sk-btn-primary" for="sk-toggle-checkbox">Toggle Menu</label>
<div id="sk-sidebar-wrapper" class="border-right">
<div class="sk-sidebar-toc-wrapper">
<div class="btn-group w-100 mb-2" role="group" aria-label="rellinks">
<a href="plot_species_distribution_modeling.html" role="button" class="btn sk-btn-rellink py-1" sk-rellink-tooltip="Species distribution modeling">Prev</a><a href="index.html" role="button" class="btn sk-btn-rellink py-1" sk-rellink-tooltip="Examples based on real world datasets">Up</a>
<a href="plot_topics_extraction_with_nmf_lda.html" role="button" class="btn sk-btn-rellink py-1" sk-rellink-tooltip="Topic extraction with Non-negative Matrix Factorization and Latent Dirichlet Allocation">Next</a>
</div>
<div class="alert alert-danger p-1 mb-2" role="alert">
<p class="text-center mb-0">
<strong>scikit-learn 1.4.2</strong><br/>
<a href="https://scikit-learn.org/dev/versions.html">Other versions</a>
</p>
</div>
<div class="alert alert-warning p-1 mb-2" role="alert">
<p class="text-center mb-0">
Please <a class="font-weight-bold" href="../../about.html#citing-scikit-learn"><string>cite us</string></a> if you use the software.
</p>
</div>
<div class="sk-sidebar-toc">
<ul>
<li><a class="reference internal" href="#">Time-related feature engineering</a><ul>
<li><a class="reference internal" href="#data-exploration-on-the-bike-sharing-demand-dataset">Data exploration on the Bike Sharing Demand dataset</a></li>
<li><a class="reference internal" href="#time-based-cross-validation">Time-based cross-validation</a></li>
<li><a class="reference internal" href="#gradient-boosting">Gradient Boosting</a></li>
<li><a class="reference internal" href="#naive-linear-regression">Naive linear regression</a></li>
<li><a class="reference internal" href="#time-steps-as-categories">Time-steps as categories</a></li>
<li><a class="reference internal" href="#trigonometric-features">Trigonometric features</a></li>
<li><a class="reference internal" href="#periodic-spline-features">Periodic spline features</a></li>
<li><a class="reference internal" href="#qualitative-analysis-of-the-impact-of-features-on-linear-model-predictions">Qualitative analysis of the impact of features on linear model predictions</a></li>
<li><a class="reference internal" href="#modeling-pairwise-interactions-with-splines-and-polynomial-features">Modeling pairwise interactions with splines and polynomial features</a></li>
<li><a class="reference internal" href="#modeling-non-linear-feature-interactions-with-kernels">Modeling non-linear feature interactions with kernels</a></li>
<li><a class="reference internal" href="#concluding-remarks">Concluding remarks</a></li>
</ul>
</li>
</ul>
</div>
</div>
</div>
<div id="sk-page-content-wrapper">
<div class="sk-page-content container-fluid body px-md-3" role="main">
<div class="sphx-glr-download-link-note admonition note">
<p class="admonition-title">Note</p>
<p><a class="reference internal" href="#sphx-glr-download-auto-examples-applications-plot-cyclical-feature-engineering-py"><span class="std std-ref">Go to the end</span></a>
to download the full example code or to run this example in your browser via JupyterLite or Binder</p>
</div>
<section class="sphx-glr-example-title" id="time-related-feature-engineering">
<span id="sphx-glr-auto-examples-applications-plot-cyclical-feature-engineering-py"></span><h1>Time-related feature engineering<a class="headerlink" href="#time-related-feature-engineering" title="Link to this heading">¶</a></h1>
<p>This notebook introduces different strategies to leverage time-related features
for a bike sharing demand regression task that is highly dependent on business
cycles (days, weeks, months) and yearly season cycles.</p>
<p>In the process, we introduce how to perform periodic feature engineering using
the <a class="reference internal" href="../../modules/generated/sklearn.preprocessing.SplineTransformer.html#sklearn.preprocessing.SplineTransformer" title="sklearn.preprocessing.SplineTransformer"><code class="xref py py-class docutils literal notranslate"><span class="pre">sklearn.preprocessing.SplineTransformer</span></code></a> class and its
<code class="docutils literal notranslate"><span class="pre">extrapolation="periodic"</span></code> option.</p>
<section id="data-exploration-on-the-bike-sharing-demand-dataset">
<h2>Data exploration on the Bike Sharing Demand dataset<a class="headerlink" href="#data-exploration-on-the-bike-sharing-demand-dataset" title="Link to this heading">¶</a></h2>
<p>We start by loading the data from the OpenML repository.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.datasets.fetch_openml.html#sklearn.datasets.fetch_openml" title="sklearn.datasets.fetch_openml" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">fetch_openml</span></a>
<span class="n">bike_sharing</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.fetch_openml.html#sklearn.datasets.fetch_openml" title="sklearn.datasets.fetch_openml" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">fetch_openml</span></a><span class="p">(</span><span class="s2">"Bike_Sharing_Demand"</span><span class="p">,</span> <span class="n">version</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">as_frame</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">df</span> <span class="o">=</span> <span class="n">bike_sharing</span><span class="o">.</span><span class="n">frame</span>
</pre></div>
</div>
<p>To get a quick understanding of the periodic patterns of the data, let us
have a look at the average demand per hour during a week.</p>
<p>Note that the week starts on a Sunday, during the weekend. We can clearly
distinguish the commute patterns in the morning and evenings of the work days
and the leisure use of the bikes on the weekends with a more spread peak
demand around the middle of the days:</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
<span class="n">average_week_demand</span> <span class="o">=</span> <span class="n">df</span><span class="o">.</span><span class="n">groupby</span><span class="p">([</span><span class="s2">"weekday"</span><span class="p">,</span> <span class="s2">"hour"</span><span class="p">])[</span><span class="s2">"count"</span><span class="p">]</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span>
<span class="n">average_week_demand</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">)</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">set</span><span class="p">(</span>
<span class="n">title</span><span class="o">=</span><span class="s2">"Average hourly bike demand during the week"</span><span class="p">,</span>
<span class="n">xticks</span><span class="o">=</span><span class="p">[</span><span class="n">i</span> <span class="o">*</span> <span class="mi">24</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">7</span><span class="p">)],</span>
<span class="n">xticklabels</span><span class="o">=</span><span class="p">[</span><span class="s2">"Sun"</span><span class="p">,</span> <span class="s2">"Mon"</span><span class="p">,</span> <span class="s2">"Tue"</span><span class="p">,</span> <span class="s2">"Wed"</span><span class="p">,</span> <span class="s2">"Thu"</span><span class="p">,</span> <span class="s2">"Fri"</span><span class="p">,</span> <span class="s2">"Sat"</span><span class="p">],</span>
<span class="n">xlabel</span><span class="o">=</span><span class="s2">"Time of the week"</span><span class="p">,</span>
<span class="n">ylabel</span><span class="o">=</span><span class="s2">"Number of bike rentals"</span><span class="p">,</span>
<span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_cyclical_feature_engineering_001.png" srcset="../../_images/sphx_glr_plot_cyclical_feature_engineering_001.png" alt="Average hourly bike demand during the week" class = "sphx-glr-single-img"/><p>The target of the prediction problem is the absolute count of bike rentals on
a hourly basis:</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">df</span><span class="p">[</span><span class="s2">"count"</span><span class="p">]</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
</pre></div>
</div>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>977
</pre></div>
</div>
<p>Let us rescale the target variable (number of hourly bike rentals) to predict
a relative demand so that the mean absolute error is more easily interpreted
as a fraction of the maximum demand.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>The fit method of the models used in this notebook all minimize the
mean squared error to estimate the conditional mean.
The absolute error, however, would estimate the conditional median.</p>
<p>Nevertheless, when reporting performance measures on the test set in
the discussion, we choose to focus on the mean absolute error instead
of the (root) mean squared error because it is more intuitive to
interpret. Note, however, that in this study the best models for one
metric are also the best ones in terms of the other metric.</p>
</div>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">y</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">"count"</span><span class="p">]</span> <span class="o">/</span> <span class="n">df</span><span class="p">[</span><span class="s2">"count"</span><span class="p">]</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
</pre></div>
</div>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
<span class="n">y</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">bins</span><span class="o">=</span><span class="mi">30</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">)</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">set</span><span class="p">(</span>
<span class="n">xlabel</span><span class="o">=</span><span class="s2">"Fraction of rented fleet demand"</span><span class="p">,</span>
<span class="n">ylabel</span><span class="o">=</span><span class="s2">"Number of hours"</span><span class="p">,</span>
<span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_cyclical_feature_engineering_002.png" srcset="../../_images/sphx_glr_plot_cyclical_feature_engineering_002.png" alt="plot cyclical feature engineering" class = "sphx-glr-single-img"/><p>The input feature data frame is a time annotated hourly log of variables
describing the weather conditions. It includes both numerical and categorical
variables. Note that the time information has already been expanded into
several complementary columns.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">X</span> <span class="o">=</span> <span class="n">df</span><span class="o">.</span><span class="n">drop</span><span class="p">(</span><span class="s2">"count"</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="s2">"columns"</span><span class="p">)</span>
<span class="n">X</span>
</pre></div>
</div>
<div class="output_subarea output_html rendered_html output_result">
<div>
<style scoped>
.dataframe tbody tr th:only-of-type {
vertical-align: middle;
}
.dataframe tbody tr th {
vertical-align: top;
}
.dataframe thead th {
text-align: right;
}
</style>
<table border="1" class="dataframe">
<thead>
<tr style="text-align: right;">
<th></th>
<th>season</th>
<th>year</th>
<th>month</th>
<th>hour</th>
<th>holiday</th>
<th>weekday</th>
<th>workingday</th>
<th>weather</th>
<th>temp</th>
<th>feel_temp</th>
<th>humidity</th>
<th>windspeed</th>
</tr>
</thead>
<tbody>
<tr>
<th>0</th>
<td>spring</td>
<td>0</td>
<td>1</td>
<td>0</td>
<td>False</td>
<td>6</td>
<td>False</td>
<td>clear</td>
<td>9.84</td>
<td>14.395</td>
<td>0.81</td>
<td>0.0000</td>
</tr>
<tr>
<th>1</th>
<td>spring</td>
<td>0</td>
<td>1</td>
<td>1</td>
<td>False</td>
<td>6</td>
<td>False</td>
<td>clear</td>
<td>9.02</td>
<td>13.635</td>
<td>0.80</td>
<td>0.0000</td>
</tr>
<tr>
<th>2</th>
<td>spring</td>
<td>0</td>
<td>1</td>
<td>2</td>
<td>False</td>
<td>6</td>
<td>False</td>
<td>clear</td>
<td>9.02</td>
<td>13.635</td>
<td>0.80</td>
<td>0.0000</td>
</tr>
<tr>
<th>3</th>
<td>spring</td>
<td>0</td>
<td>1</td>
<td>3</td>
<td>False</td>
<td>6</td>
<td>False</td>
<td>clear</td>
<td>9.84</td>
<td>14.395</td>
<td>0.75</td>
<td>0.0000</td>
</tr>
<tr>
<th>4</th>
<td>spring</td>
<td>0</td>
<td>1</td>
<td>4</td>
<td>False</td>
<td>6</td>
<td>False</td>
<td>clear</td>
<td>9.84</td>
<td>14.395</td>
<td>0.75</td>
<td>0.0000</td>
</tr>
<tr>
<th>...</th>
<td>...</td>
<td>...</td>
<td>...</td>
<td>...</td>
<td>...</td>
<td>...</td>
<td>...</td>
<td>...</td>
<td>...</td>
<td>...</td>
<td>...</td>
<td>...</td>
</tr>
<tr>
<th>17374</th>
<td>spring</td>
<td>1</td>
<td>12</td>
<td>19</td>
<td>False</td>
<td>1</td>
<td>True</td>
<td>misty</td>
<td>10.66</td>
<td>12.880</td>
<td>0.60</td>
<td>11.0014</td>
</tr>
<tr>
<th>17375</th>
<td>spring</td>
<td>1</td>
<td>12</td>
<td>20</td>
<td>False</td>
<td>1</td>
<td>True</td>
<td>misty</td>
<td>10.66</td>
<td>12.880</td>
<td>0.60</td>
<td>11.0014</td>
</tr>
<tr>
<th>17376</th>
<td>spring</td>
<td>1</td>
<td>12</td>
<td>21</td>
<td>False</td>
<td>1</td>
<td>True</td>
<td>clear</td>
<td>10.66</td>
<td>12.880</td>
<td>0.60</td>
<td>11.0014</td>
</tr>
<tr>
<th>17377</th>
<td>spring</td>
<td>1</td>
<td>12</td>
<td>22</td>
<td>False</td>
<td>1</td>
<td>True</td>
<td>clear</td>
<td>10.66</td>
<td>13.635</td>
<td>0.56</td>
<td>8.9981</td>
</tr>
<tr>
<th>17378</th>
<td>spring</td>
<td>1</td>
<td>12</td>
<td>23</td>
<td>False</td>
<td>1</td>
<td>True</td>
<td>clear</td>
<td>10.66</td>
<td>13.635</td>
<td>0.65</td>
<td>8.9981</td>
</tr>
</tbody>
</table>
<p>17379 rows × 12 columns</p>
</div>
</div>
<br />
<br /><div class="admonition note">
<p class="admonition-title">Note</p>
<p>If the time information was only present as a date or datetime column, we
could have expanded it into hour-in-the-day, day-in-the-week,
day-in-the-month, month-in-the-year using pandas:
<a class="reference external" href="https://pandas.pydata.org/pandas-docs/stable/user_guide/timeseries.html#time-date-components">https://pandas.pydata.org/pandas-docs/stable/user_guide/timeseries.html#time-date-components</a></p>
</div>
<p>We now introspect the distribution of the categorical variables, starting
with <code class="docutils literal notranslate"><span class="pre">"weather"</span></code>:</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">X</span><span class="p">[</span><span class="s2">"weather"</span><span class="p">]</span><span class="o">.</span><span class="n">value_counts</span><span class="p">()</span>
</pre></div>
</div>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>weather
clear 11413
misty 4544
rain 1419
heavy_rain 3
Name: count, dtype: int64
</pre></div>
</div>
<p>Since there are only 3 <code class="docutils literal notranslate"><span class="pre">"heavy_rain"</span></code> events, we cannot use this category to
train machine learning models with cross validation. Instead, we simplify the
representation by collapsing those into the <code class="docutils literal notranslate"><span class="pre">"rain"</span></code> category.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">X</span><span class="p">[</span><span class="s2">"weather"</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span>
<span class="n">X</span><span class="p">[</span><span class="s2">"weather"</span><span class="p">]</span>
<span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="nb">object</span><span class="p">)</span>
<span class="o">.</span><span class="n">replace</span><span class="p">(</span><span class="n">to_replace</span><span class="o">=</span><span class="s2">"heavy_rain"</span><span class="p">,</span> <span class="n">value</span><span class="o">=</span><span class="s2">"rain"</span><span class="p">)</span>
<span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="s2">"category"</span><span class="p">)</span>
<span class="p">)</span>
</pre></div>
</div>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">X</span><span class="p">[</span><span class="s2">"weather"</span><span class="p">]</span><span class="o">.</span><span class="n">value_counts</span><span class="p">()</span>
</pre></div>
</div>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>weather
clear 11413
misty 4544
rain 1422
Name: count, dtype: int64
</pre></div>
</div>
<p>As expected, the <code class="docutils literal notranslate"><span class="pre">"season"</span></code> variable is well balanced:</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">X</span><span class="p">[</span><span class="s2">"season"</span><span class="p">]</span><span class="o">.</span><span class="n">value_counts</span><span class="p">()</span>
</pre></div>
</div>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>season
fall 4496
summer 4409
spring 4242
winter 4232
Name: count, dtype: int64
</pre></div>
</div>
</section>
<section id="time-based-cross-validation">
<h2>Time-based cross-validation<a class="headerlink" href="#time-based-cross-validation" title="Link to this heading">¶</a></h2>
<p>Since the dataset is a time-ordered event log (hourly demand), we will use a
time-sensitive cross-validation splitter to evaluate our demand forecasting
model as realistically as possible. We use a gap of 2 days between the train
and test side of the splits. We also limit the training set size to make the
performance of the CV folds more stable.</p>
<p>1000 test datapoints should be enough to quantify the performance of the
model. This represents a bit less than a month and a half of contiguous test
data:</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.model_selection.TimeSeriesSplit.html#sklearn.model_selection.TimeSeriesSplit" title="sklearn.model_selection.TimeSeriesSplit" class="sphx-glr-backref-module-sklearn-model_selection sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">TimeSeriesSplit</span></a>
<span class="n">ts_cv</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.model_selection.TimeSeriesSplit.html#sklearn.model_selection.TimeSeriesSplit" title="sklearn.model_selection.TimeSeriesSplit" class="sphx-glr-backref-module-sklearn-model_selection sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">TimeSeriesSplit</span></a><span class="p">(</span>
<span class="n">n_splits</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span>
<span class="n">gap</span><span class="o">=</span><span class="mi">48</span><span class="p">,</span>
<span class="n">max_train_size</span><span class="o">=</span><span class="mi">10000</span><span class="p">,</span>
<span class="n">test_size</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span>
<span class="p">)</span>
</pre></div>
</div>
<p>Let us manually inspect the various splits to check that the
<code class="docutils literal notranslate"><span class="pre">TimeSeriesSplit</span></code> works as we expect, starting with the first split:</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">all_splits</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">ts_cv</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">))</span>
<span class="n">train_0</span><span class="p">,</span> <span class="n">test_0</span> <span class="o">=</span> <span class="n">all_splits</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
</pre></div>
</div>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">X</span><span class="o">.</span><span class="n">iloc</span><span class="p">[</span><span class="n">test_0</span><span class="p">]</span>
</pre></div>
</div>
<div class="output_subarea output_html rendered_html output_result">
<div>
<style scoped>
.dataframe tbody tr th:only-of-type {
vertical-align: middle;
}
.dataframe tbody tr th {
vertical-align: top;
}
.dataframe thead th {
text-align: right;
}
</style>
<table border="1" class="dataframe">
<thead>
<tr style="text-align: right;">
<th></th>
<th>season</th>
<th>year</th>
<th>month</th>
<th>hour</th>
<th>holiday</th>
<th>weekday</th>
<th>workingday</th>
<th>weather</th>
<th>temp</th>
<th>feel_temp</th>
<th>humidity</th>
<th>windspeed</th>
</tr>
</thead>
<tbody>
<tr>
<th>12379</th>
<td>summer</td>
<td>1</td>
<td>6</td>
<td>0</td>
<td>False</td>
<td>2</td>
<td>True</td>
<td>clear</td>
<td>22.14</td>
<td>25.760</td>
<td>0.68</td>
<td>27.9993</td>
</tr>
<tr>
<th>12380</th>
<td>summer</td>
<td>1</td>
<td>6</td>
<td>1</td>
<td>False</td>
<td>2</td>
<td>True</td>
<td>misty</td>
<td>21.32</td>
<td>25.000</td>
<td>0.77</td>
<td>22.0028</td>
</tr>
<tr>
<th>12381</th>
<td>summer</td>
<td>1</td>
<td>6</td>
<td>2</td>
<td>False</td>
<td>2</td>
<td>True</td>
<td>rain</td>
<td>21.32</td>
<td>25.000</td>
<td>0.72</td>
<td>19.9995</td>
</tr>
<tr>
<th>12382</th>
<td>summer</td>
<td>1</td>
<td>6</td>
<td>3</td>
<td>False</td>
<td>2</td>
<td>True</td>
<td>rain</td>
<td>20.50</td>
<td>24.240</td>
<td>0.82</td>
<td>12.9980</td>
</tr>
<tr>
<th>12383</th>
<td>summer</td>
<td>1</td>
<td>6</td>
<td>4</td>
<td>False</td>
<td>2</td>
<td>True</td>
<td>rain</td>
<td>20.50</td>
<td>24.240</td>
<td>0.82</td>
<td>12.9980</td>
</tr>
<tr>
<th>...</th>
<td>...</td>
<td>...</td>
<td>...</td>
<td>...</td>
<td>...</td>
<td>...</td>
<td>...</td>
<td>...</td>
<td>...</td>
<td>...</td>
<td>...</td>
<td>...</td>
</tr>
<tr>
<th>13374</th>
<td>fall</td>
<td>1</td>
<td>7</td>
<td>11</td>
<td>False</td>
<td>1</td>
<td>True</td>
<td>clear</td>
<td>34.44</td>
<td>40.150</td>
<td>0.53</td>
<td>15.0013</td>
</tr>
<tr>
<th>13375</th>
<td>fall</td>
<td>1</td>
<td>7</td>
<td>12</td>
<td>False</td>
<td>1</td>
<td>True</td>
<td>clear</td>
<td>34.44</td>
<td>39.395</td>
<td>0.49</td>
<td>8.9981</td>
</tr>
<tr>
<th>13376</th>
<td>fall</td>
<td>1</td>
<td>7</td>
<td>13</td>
<td>False</td>
<td>1</td>
<td>True</td>
<td>clear</td>
<td>34.44</td>
<td>39.395</td>
<td>0.49</td>
<td>19.0012</td>
</tr>
<tr>
<th>13377</th>
<td>fall</td>
<td>1</td>
<td>7</td>
<td>14</td>
<td>False</td>
<td>1</td>
<td>True</td>
<td>clear</td>
<td>36.08</td>
<td>40.910</td>
<td>0.42</td>
<td>7.0015</td>
</tr>
<tr>
<th>13378</th>
<td>fall</td>
<td>1</td>
<td>7</td>
<td>15</td>
<td>False</td>
<td>1</td>
<td>True</td>
<td>clear</td>
<td>35.26</td>
<td>40.150</td>
<td>0.47</td>
<td>16.9979</td>
</tr>
</tbody>
</table>
<p>1000 rows × 12 columns</p>
</div>
</div>
<br />
<br /><div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">X</span><span class="o">.</span><span class="n">iloc</span><span class="p">[</span><span class="n">train_0</span><span class="p">]</span>
</pre></div>
</div>
<div class="output_subarea output_html rendered_html output_result">
<div>
<style scoped>
.dataframe tbody tr th:only-of-type {
vertical-align: middle;
}
.dataframe tbody tr th {
vertical-align: top;
}
.dataframe thead th {
text-align: right;
}
</style>
<table border="1" class="dataframe">
<thead>
<tr style="text-align: right;">
<th></th>
<th>season</th>
<th>year</th>
<th>month</th>
<th>hour</th>
<th>holiday</th>
<th>weekday</th>
<th>workingday</th>
<th>weather</th>
<th>temp</th>
<th>feel_temp</th>
<th>humidity</th>
<th>windspeed</th>
</tr>
</thead>
<tbody>
<tr>
<th>2331</th>
<td>summer</td>
<td>0</td>
<td>4</td>
<td>1</td>
<td>False</td>
<td>2</td>
<td>True</td>
<td>misty</td>
<td>25.42</td>
<td>31.060</td>
<td>0.50</td>
<td>6.0032</td>
</tr>
<tr>
<th>2332</th>
<td>summer</td>
<td>0</td>
<td>4</td>
<td>2</td>
<td>False</td>
<td>2</td>
<td>True</td>
<td>misty</td>
<td>24.60</td>
<td>31.060</td>
<td>0.53</td>
<td>8.9981</td>
</tr>
<tr>
<th>2333</th>
<td>summer</td>
<td>0</td>
<td>4</td>
<td>3</td>
<td>False</td>
<td>2</td>
<td>True</td>
<td>misty</td>
<td>23.78</td>
<td>27.275</td>
<td>0.56</td>
<td>8.9981</td>
</tr>
<tr>
<th>2334</th>
<td>summer</td>
<td>0</td>
<td>4</td>
<td>4</td>
<td>False</td>
<td>2</td>
<td>True</td>
<td>misty</td>
<td>22.96</td>
<td>26.515</td>
<td>0.64</td>
<td>8.9981</td>
</tr>
<tr>
<th>2335</th>
<td>summer</td>
<td>0</td>
<td>4</td>
<td>5</td>
<td>False</td>
<td>2</td>
<td>True</td>
<td>misty</td>
<td>22.14</td>
<td>25.760</td>
<td>0.68</td>
<td>8.9981</td>
</tr>
<tr>
<th>...</th>
<td>...</td>
<td>...</td>
<td>...</td>
<td>...</td>
<td>...</td>
<td>...</td>
<td>...</td>
<td>...</td>
<td>...</td>
<td>...</td>
<td>...</td>
<td>...</td>
</tr>
<tr>
<th>12326</th>
<td>summer</td>
<td>1</td>
<td>6</td>
<td>19</td>
<td>False</td>
<td>6</td>
<td>False</td>
<td>clear</td>
<td>26.24</td>
<td>31.060</td>
<td>0.36</td>
<td>11.0014</td>
</tr>
<tr>
<th>12327</th>
<td>summer</td>
<td>1</td>
<td>6</td>
<td>20</td>
<td>False</td>
<td>6</td>
<td>False</td>
<td>clear</td>
<td>25.42</td>
<td>31.060</td>
<td>0.35</td>
<td>19.0012</td>
</tr>
<tr>
<th>12328</th>
<td>summer</td>
<td>1</td>
<td>6</td>
<td>21</td>
<td>False</td>
<td>6</td>
<td>False</td>
<td>clear</td>
<td>24.60</td>
<td>31.060</td>
<td>0.40</td>
<td>7.0015</td>
</tr>
<tr>
<th>12329</th>
<td>summer</td>
<td>1</td>
<td>6</td>
<td>22</td>
<td>False</td>
<td>6</td>
<td>False</td>
<td>clear</td>
<td>23.78</td>
<td>27.275</td>
<td>0.46</td>
<td>8.9981</td>
</tr>
<tr>
<th>12330</th>
<td>summer</td>
<td>1</td>
<td>6</td>
<td>23</td>
<td>False</td>
<td>6</td>
<td>False</td>
<td>clear</td>
<td>22.96</td>
<td>26.515</td>
<td>0.52</td>
<td>7.0015</td>
</tr>
</tbody>
</table>
<p>10000 rows × 12 columns</p>
</div>
</div>
<br />
<br /><p>We now inspect the last split:</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">train_4</span><span class="p">,</span> <span class="n">test_4</span> <span class="o">=</span> <span class="n">all_splits</span><span class="p">[</span><span class="mi">4</span><span class="p">]</span>
</pre></div>
</div>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">X</span><span class="o">.</span><span class="n">iloc</span><span class="p">[</span><span class="n">test_4</span><span class="p">]</span>
</pre></div>
</div>
<div class="output_subarea output_html rendered_html output_result">
<div>
<style scoped>
.dataframe tbody tr th:only-of-type {
vertical-align: middle;
}