This notebook illustrates how to use the hoggorm package to carry out principal component analysis (PCA) on spectroscopy data. Furthermore, we will learn how to visualise the results of the PCA using the hoggormPlot package.
First import hoggorm for analysis of the data and hoggormPlot for plotting of the analysis results. We'll also import pandas such that we can read the data into a data frame. numpy is needed for checking dimensions of the data.
In [1]:
import hoggorm as ho
import hoggormplot as hop
import pandas as pd
import numpy as np
Next, load the spectroscopy data that we are going to analyse using hoggorm. After the data has been loaded into the pandas data frame, we'll display it in the notebook.
In [6]:
# Load data
# Insert code for reading data from other folder in repository instead of directly from same repository.
data_df = pd.read_csv('gasoline_NIR.txt', header=None, sep='\s+')
Let's have a look at the dimensions of the data frame.
In [7]:
np.shape(data_df)
Out[7]:
(60, 401)
The nipalsPCA class in hoggorm accepts only numpy arrays with numerical values and not pandas data frames. Therefore, the pandas data frame holding the imported data needs to be "taken apart" into three parts:
The array with values will be used as input for the nipalsPCA class for analysis. The Python lists holding the variable and row names will be used later in the plotting function from the hoggormPlot package when visualising the results of the analysis. Below is the code needed to access both data, variable names and object names.
In [10]:
# Get the values from the data frame
data = data_df.values
Now, let's run PCA on the data using the nipalsPCA class. The documentation provides a description of the input parameters. Using input paramter arrX we define which numpy array we would like to analyse. By setting input parameter Xstand=False we make sure that the variables are only mean centered, not scaled to unit variance. This is the default setting and actually doesn't need to expressed explicitly. Setting paramter cvType=["loo"] we make sure that we compute the PCA model using full cross validation. "loo" means "Leave One Out". By setting paramter numpComp=4 we ask for four principal components (PC) to be computed.
In [12]:
model = ho.nipalsPCA(arrX=data, Xstand=False, cvType=["loo"], numComp=5)
loo
loo
That's it, the PCA model has been computed. Now we would like to inspect the results by visualising them. We can do this using the taylor-made plotting function for PCA from the separate hoggormPlot package. If we wish to plot the results for component 1 and component 2, we can do this by setting the input argument comp=[1, 2]. The input argument plots=[1, 6] lets the user define which plots are to be plotted. If this list for example contains value 1, the function will generate the scores plot for the model. If the list contains value 6, the function will generate a explained variance plot. The hoggormPlot documentation provides a description of input paramters.
In [15]:
hop.plot(model, comp=[1, 2],
plots=[1, 6])
It is also possible to generate the same plots one by one with specific plot functions as shown below.
In [19]:
hop.loadings(model, line=True)
Now that we have visualised the PCA results, we may also want to access the numerical results. Below are some examples. For a complete list of accessible results, please see this part of the documentation.
In [21]:
# Get scores and store in numpy array
scores = model.X_scores()
# Get scores and store in pandas dataframe with row and column names
scores_df = pd.DataFrame(model.X_scores())
#scores_df.index = data_objNames
scores_df.columns = ['PC{0}'.format(x+1) for x in range(model.X_scores().shape[1])]
scores_df
Out[21]:
PC1
PC2
PC3
PC4
PC5
0
0.020082
0.073100
0.096431
-0.037799
0.046846
1
0.542646
0.046265
0.045296
-0.002835
0.000012
2
0.449275
0.044604
-0.054206
0.084612
-0.001227
3
0.376704
0.051102
0.104006
-0.053364
-0.010051
4
-0.182992
0.115471
0.057602
0.065753
-0.038813
5
0.109397
0.104524
0.100058
-0.013542
-0.010737
6
-0.111562
0.060955
0.022934
0.076916
-0.027543
7
0.212391
0.025322
-0.043598
0.068100
-0.015676
8
-0.031795
0.041594
0.010894
0.081882
-0.027163
9
-0.128297
0.043146
0.034463
0.067407
-0.034408
10
-0.330325
0.062721
0.072876
0.041560
-0.050676
11
-0.150899
0.092627
0.054870
0.034622
0.023315
12
0.187740
0.057718
-0.021295
0.019425
0.025586
13
0.383453
-0.021562
-0.036986
0.083399
-0.003030
14
0.638147
-0.001555
-0.104313
0.108991
0.029752
15
-0.007105
0.117427
0.064642
-0.048103
0.013449
16
-0.088702
0.017913
0.026664
0.047621
-0.014257
17
-0.047416
-0.015238
-0.019832
0.048342
-0.034342
18
0.181089
-0.035604
-0.003778
-0.045163
-0.031364
19
0.178874
-0.019445
-0.077394
0.038980
-0.026786
20
-0.027648
-0.035444
-0.019790
-0.029763
0.005307
21
0.071045
0.091036
0.055278
0.052574
0.046931
22
0.077800
-0.043384
-0.032646
-0.011096
0.016625
23
0.031985
-0.031871
-0.046500
-0.003679
0.011674
24
0.041228
-0.024730
-0.033556
-0.021070
-0.009628
25
-0.060019
0.028806
-0.033591
0.038877
-0.030129
26
0.016830
-0.024295
0.010075
-0.019613
-0.034138
27
-0.038189
-0.002290
0.008420
-0.051550
-0.035685
28
0.023648
-0.022413
-0.013838
-0.036173
-0.029122
29
-0.105895
0.012047
-0.004296
-0.045851
-0.040868
30
-0.047441
0.000033
-0.008697
-0.042641
-0.032110
31
0.187534
-0.022869
0.013618
-0.092517
-0.024474
32
0.146407
-0.068205
-0.003919
-0.098227
-0.033467
33
0.195055
-0.024977
0.024834
-0.086974
-0.021873
34
0.159787
0.002144
0.018705
-0.099364
-0.022671
35
-0.081573
-0.017168
-0.027075
0.013575
0.015423
36
-0.015318
0.059270
0.044154
-0.072180
-0.021116
37
-0.106706
0.100428
-0.038002
-0.002219
0.026249
38
0.139389
0.065463
-0.095523
0.007187
0.031572
39
-0.055542
0.077330
-0.067287
-0.004627
0.023319
40
-0.446575
0.068214
0.044731
0.026488
0.007700
41
-0.227192
0.036635
0.025081
0.050707
0.001265
42
-0.092009
0.134978
0.019401
0.034867
0.025334
43
0.117264
0.081724
0.017791
-0.071819
0.027142
44
-0.237260
0.018575
-0.018433
0.017841
-0.032216
45
-0.223863
-0.017054
-0.133874
-0.050688
0.000184
46
-0.214449
0.060487
-0.128651
-0.063840
0.024707
47
-0.038774
-0.028185
-0.161677
-0.015499
0.026029
48
-0.246086
0.037270
-0.124576
-0.059362
0.022400
49
-0.299978
-0.020337
-0.138278
-0.058612
0.016963
50
-0.090237
-0.132572
0.033165
0.056402
0.019897
51
-0.258698
-0.035266
0.062520
0.004572
0.046272
52
-0.199072
-0.130261
0.052066
0.061786
0.018574
53
0.188517
-0.226176
0.078105
-0.018149
0.011294
54
0.001480
-0.121921
0.138903
-0.004198
0.045438
55
0.034911
0.024347
0.109181
-0.064924
0.066777
56
0.028317
-0.274534
-0.001543
0.039919
-0.002510
57
-0.143540
-0.135706
0.048483
0.000467
0.016535
58
-0.307520
-0.151975
-0.017598
0.051528
0.009738
59
-0.098318
-0.168236
0.015503
0.001042
-0.006231
In [22]:
help(ho.nipalsPCA.X_scores)
Help on function X_scores in module hoggorm.pca:
X_scores(self)
Returns array holding scores T. First column holds scores for
component 1, second column holds scores for component 2, etc.
In [23]:
# Dimension of the scores
np.shape(model.X_scores())
Out[23]:
(60, 5)
We see that the numpy array holds the scores for four components as required when computing the PCA model.
In [27]:
# Get loadings and store in numpy array
loadings = model.X_loadings()
# Get loadings and store in pandas dataframe with row and column names
loadings_df = pd.DataFrame(model.X_loadings())
#loadings_df.index = data_varNames
loadings_df.columns = ['PC{0}'.format(x+1) for x in range(model.X_loadings().shape[1])]
loadings_df
Out[27]:
PC1
PC2
PC3
PC4
PC5
0
0.010761
0.022410
0.033510
0.039027
0.041516
1
0.010313
0.021588
0.030888
0.040657
0.038927
2
0.011046
0.022215
0.029598
0.041633
0.035870
3
0.012475
0.024319
0.027347
0.045222
0.031199
4
0.013082
0.021474
0.025045
0.045259
0.035395
5
0.014159
0.022623
0.023366
0.045839
0.035860
6
0.013685
0.018651
0.022783
0.049866
0.043444
7
0.014221
0.022608
0.023914
0.044390
0.039649
8
0.013137
0.019569
0.029728
0.040631
0.033897
9
0.012153
0.020054
0.034402
0.030317
0.039549
10
0.011833
0.018964
0.038012
0.023652
0.033032
11
0.011517
0.018122
0.042049
0.020911
0.034410
12
0.011297
0.018341
0.043471
0.022028
0.036470
13
0.010584
0.017168
0.042978
0.022732
0.035776
14
0.010523
0.018850
0.041188
0.024057
0.033013
15
0.010191
0.020333
0.038235
0.021397
0.031560
16
0.009702
0.019763
0.038111
0.022951
0.031664
17
0.009874
0.019663
0.037252
0.024125
0.033766
18
0.009604
0.020898
0.036368
0.025869
0.029849
19
0.009308
0.020849
0.033899
0.027340
0.031473
20
0.009309
0.021116
0.033105
0.027756
0.032123
21
0.009072
0.021643
0.032641
0.029110
0.031637
22
0.008492
0.020763
0.032456
0.031100
0.030221
23
0.008263
0.022119
0.032671
0.031071
0.030439
24
0.008224
0.022728
0.033646
0.033244
0.028952
25
0.008109
0.022043
0.032851
0.032624
0.029149
26
0.007509
0.021407
0.031774
0.032708
0.032481
27
0.007734
0.023586
0.031442
0.030132
0.030561
28
0.007575
0.023376
0.031838
0.031354
0.027900
29
0.007508
0.023528
0.031659
0.033006
0.029653
...
...
...
...
...
...
371
-0.058063
0.030676
0.122583
-0.059704
-0.020427
372
-0.071378
0.032703
0.101851
-0.039050
-0.010061
373
-0.079272
0.036961
0.090956
-0.021982
-0.004134
374
-0.083489
0.040491
0.079749
-0.015572
-0.022317
375
-0.088267
0.042514
0.076098
-0.014075
-0.023332
376
-0.091112
0.040744
0.082183
-0.014404
-0.035643
377
-0.099531
0.043604
0.079853
-0.013647
-0.034683
378
-0.115351
0.044113
0.084350
-0.004084
-0.029785
379
-0.136418
0.040739
0.076814
-0.012732
-0.006682
380
-0.157427
0.034603
0.087621
0.010666
-0.031447
381
-0.181087
0.037014
0.090378
0.033724
-0.038384
382
-0.217112
0.033769
0.080569
0.047116
-0.018230
383
-0.239899
0.039866
0.053926
0.040353
0.025269
384
-0.255085
0.032248
0.066375
0.057970
0.047916
385
-0.259048
0.040755
0.026546
0.025177
0.030153
386
-0.244414
0.039376
0.070818
0.050437
-0.006634
387
-0.237757
0.033854
0.096441
0.055773
-0.043270
388
-0.214056
0.048676
0.037215
-0.014064
-0.016176
389
-0.184058
0.051850
0.063721
-0.012295
0.023153
390
-0.158723
0.071630
0.057600
-0.012336
0.081500
391
-0.126247
0.095758
0.043974
-0.013859
-0.117570
392
-0.109979
0.085793
-0.016974
-0.042322
0.178112
393
-0.097485
0.115826
-0.061785
-0.069528
0.149942
394
-0.061525
0.211030
-0.041989
-0.063295
0.034113
395
-0.023988
0.357850
-0.151683
-0.088816
-0.309900
396
0.004908
0.339741
-0.200986
-0.152534
-0.588274
397
-0.041207
0.276329
-0.281156
-0.198780
0.535838
398
-0.026630
0.231176
-0.241345
-0.202683
0.170423
399
-0.000669
0.277759
-0.075110
-0.144923
0.043571
400
-0.010330
0.276600
-0.167326
-0.150471
0.167772
401 rows × 5 columns
In [28]:
help(ho.nipalsPCA.X_loadings)
Help on function X_loadings in module hoggorm.pca:
X_loadings(self)
Returns array holding loadings P of array X. Rows represent variables
and columns represent components. First column holds loadings for
component 1, second column holds scores for component 2, etc.
In [29]:
np.shape(model.X_loadings())
Out[29]:
(401, 5)
In [30]:
# Get loadings and store in numpy array
loadings = model.X_corrLoadings()
# Get loadings and store in pandas dataframe with row and column names
loadings_df = pd.DataFrame(model.X_corrLoadings())
#loadings_df.index = data_varNames
loadings_df.columns = ['PC{0}'.format(x+1) for x in range(model.X_corrLoadings().shape[1])]
loadings_df
Out[30]:
PC1
PC2
PC3
PC4
PC5
0
0.502996
0.414017
0.484784
0.459178
0.253604
1
0.496101
0.410447
0.459857
0.492293
0.244697
2
0.523029
0.415747
0.433729
0.496223
0.221940
3
0.565736
0.435909
0.383789
0.516251
0.184878
4
0.597914
0.387894
0.354216
0.520687
0.211384
5
0.623573
0.393795
0.318431
0.508199
0.206368
6
0.604709
0.325726
0.311509
0.554671
0.250854
7
0.620098
0.389628
0.322674
0.487237
0.225915
8
0.606568
0.357106
0.424805
0.472232
0.204521
9
0.579231
0.377743
0.507474
0.363661
0.246333
10
0.576842
0.365359
0.573566
0.290162
0.210438
11
0.552626
0.343640
0.624518
0.252473
0.215777
12
0.535494
0.343593
0.637835
0.262740
0.225938
13
0.518008
0.332057
0.651067
0.279943
0.228825
14
0.518668
0.367171
0.628353
0.298380
0.212636
15
0.517930
0.408403
0.601468
0.273651
0.209600
16
0.500130
0.402618
0.608088
0.297722
0.213289
17
0.506369
0.398538
0.591331
0.311364
0.226290
18
0.493182
0.424145
0.578059
0.334334
0.200292
19
0.490109
0.433886
0.552472
0.362323
0.216554
20
0.490712
0.439904
0.540091
0.368217
0.221253
21
0.478438
0.451142
0.532813
0.386408
0.218022
22
0.456395
0.440996
0.539835
0.420670
0.212207
23
0.438455
0.463896
0.536575
0.414985
0.211049
24
0.428142
0.467638
0.542115
0.435602
0.196922
25
0.431751
0.463845
0.541333
0.437189
0.202773
26
0.410530
0.462567
0.537649
0.450087
0.232037
27
0.417684
0.503451
0.525544
0.409582
0.215652
28
0.409257
0.499140
0.532361
0.426353
0.196923
29
0.403647
0.499941
0.526789
0.446636
0.208295
...
...
...
...
...
...
371
-0.795561
0.166091
0.519969
-0.206051
-0.036569
372
-0.888902
0.160951
0.392666
-0.122511
-0.016377
373
-0.920237
0.169575
0.326862
-0.064308
-0.006285
374
-0.936794
0.179564
0.277001
-0.044038
-0.032744
375
-0.945323
0.179959
0.252285
-0.037996
-0.032672
376
-0.943833
0.166815
0.263540
-0.037608
-0.048271
377
-0.951827
0.164811
0.236390
-0.032897
-0.043360
378
-0.961086
0.145267
0.217549
-0.008602
-0.032449
379
-0.973893
0.114953
0.169754
-0.022915
-0.006242
380
-0.979956
0.085133
0.168836
0.016689
-0.025601
381
-0.981971
0.079331
0.151701
0.046017
-0.027225
382
-0.988198
0.060752
0.113509
0.053973
-0.010865
383
-0.992219
0.065178
0.069031
0.042005
0.013643
384
-0.990363
0.049491
0.079761
0.056646
0.024302
385
-0.994487
0.061851
0.031538
0.024327
0.015129
386
-0.988232
0.062932
0.088625
0.051328
-0.003503
387
-0.981587
0.055244
0.123242
0.057954
-0.023337
388
-0.983149
0.088376
0.052908
-0.016270
-0.009682
389
-0.972580
0.108297
0.104228
-0.016378
0.016043
390
-0.946047
0.168759
0.106265
-0.018539
0.063580
391
-0.907288
0.272021
0.097806
-0.025074
-0.110380
392
-0.889084
0.274163
-0.042494
-0.086160
0.188295
393
-0.820403
0.385326
-0.160980
-0.147310
0.165055
394
-0.496718
0.673463
-0.104993
-0.128639
0.036109
395
-0.141905
0.836769
-0.277835
-0.132183
-0.239548
396
0.027020
0.739548
-0.342668
-0.211353
-0.423593
397
-0.237065
0.628425
-0.500731
-0.287884
0.402993
398
-0.184102
0.631767
-0.516502
-0.352696
0.154094
399
-0.005140
0.841910
-0.178337
-0.279764
0.043640
400
-0.076794
0.812752
-0.385076
-0.281555
0.163119
401 rows × 5 columns
In [31]:
help(ho.nipalsPCA.X_corrLoadings)
Help on function X_corrLoadings in module hoggorm.pca:
X_corrLoadings(self)
Returns array holding correlation loadings of array X. First column
holds correlation loadings for component 1, second column holds
correlation loadings for component 2, etc.
In [32]:
# Get calibrated explained variance of each component
calExplVar = model.X_calExplVar()
# Get calibrated explained variance and store in pandas dataframe with row and column names
calExplVar_df = pd.DataFrame(model.X_calExplVar())
calExplVar_df.columns = ['calibrated explained variance']
calExplVar_df.index = ['PC{0}'.format(x+1) for x in range(model.X_loadings().shape[1])]
calExplVar_df
Out[32]:
calibrated explained variance
PC1
72.565138
PC2
11.338019
PC3
6.954257
PC4
4.599826
PC5
1.240297
In [33]:
help(ho.nipalsPCA.X_calExplVar)
Help on function X_calExplVar in module hoggorm.pca:
X_calExplVar(self)
Returns a list holding the calibrated explained variance for
each component. First number in list is for component 1, second number
for component 2, etc.
In [34]:
# Get cumulative calibrated explained variance
cumCalExplVar = model.X_cumCalExplVar()
# Get cumulative calibrated explained variance and store in pandas dataframe with row and column names
cumCalExplVar_df = pd.DataFrame(model.X_cumCalExplVar())
cumCalExplVar_df.columns = ['cumulative calibrated explained variance']
cumCalExplVar_df.index = ['PC{0}'.format(x) for x in range(model.X_loadings().shape[1] + 1)]
cumCalExplVar_df
Out[34]:
cumulative calibrated explained variance
PC0
0.000000
PC1
72.565138
PC2
83.903157
PC3
90.857413
PC4
95.457240
PC5
96.697537
In [35]:
help(ho.nipalsPCA.X_cumCalExplVar)
Help on function X_cumCalExplVar in module hoggorm.pca:
X_cumCalExplVar(self)
Returns a list holding the cumulative validated explained variance
for array X after each component. First number represents zero
components, second number represents component 1, etc.
In [37]:
# Get cumulative calibrated explained variance for each variable
cumCalExplVar_ind = model.X_cumCalExplVar_indVar()
# Get cumulative calibrated explained variance for each variable and store in pandas dataframe with row and column names
cumCalExplVar_ind_df = pd.DataFrame(model.X_cumCalExplVar_indVar())
#cumCalExplVar_ind_df.columns = data_varNames
cumCalExplVar_ind_df.index = ['PC{0}'.format(x) for x in range(model.X_loadings().shape[1] + 1)]
cumCalExplVar_ind_df
Out[37]:
0
1
2
3
4
5
6
7
8
9
...
391
392
393
394
395
396
397
398
399
400
PC0
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
...
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
PC1
25.300542
24.611602
27.355922
32.005666
35.750065
38.884360
36.567342
38.452109
36.792509
33.550817
...
82.317118
79.047055
67.306082
24.672910
2.013696
0.073010
5.619993
3.389344
0.002642
0.589727
PC2
42.441993
41.458724
44.640897
51.007847
50.796701
54.392295
47.177506
53.633605
49.545416
47.820232
...
89.716152
86.563084
82.153037
70.027533
72.031710
54.766212
45.111443
43.302068
70.883884
66.646222
PC3
65.948096
62.609792
63.457029
65.741002
63.346670
64.534962
56.883549
64.048268
67.594733
73.577576
...
90.673333
86.743400
84.743118
71.128313
79.745782
66.502726
70.177623
69.972282
74.060959
81.467589
PC4
87.040973
86.853587
88.088902
92.399968
90.465091
90.367660
87.656014
87.794167
89.902585
86.809442
...
90.736111
87.485897
86.914025
72.783629
81.494393
70.972463
78.470780
82.418617
81.889604
89.398996
PC5
93.476085
92.844979
93.018051
95.820907
94.936826
94.629706
93.953098
92.901335
94.088453
92.880195
...
91.954581
91.030901
89.637574
72.913872
87.233677
88.918380
94.707556
84.791428
82.079672
92.058344
6 rows × 401 columns
In [38]:
help(ho.nipalsPCA.X_cumCalExplVar_indVar)
Help on function X_cumCalExplVar_indVar in module hoggorm.pca:
X_cumCalExplVar_indVar(self)
Returns an array holding the cumulative calibrated explained variance
for each variable in X after each component. First row represents zero
components, second row represents one component, third row represents
two components, etc. Columns represent variables.
In [39]:
# Get calibrated predicted X for a given number of components
# Predicted X from calibration using 1 component
X_from_1_component = model.X_predCal()[1]
# Predicted X from calibration using 1 component stored in pandas data frame with row and columns names
X_from_1_component_df = pd.DataFrame(model.X_predCal()[1])
#X_from_1_component_df.index = data_objNames
#X_from_1_component_df.columns = data_varNames
X_from_1_component_df
Out[39]:
0
1
2
3
4
5
6
7
8
9
...
391
392
393
394
395
396
397
398
399
400
0
-0.052611
-0.047228
-0.043363
-0.038934
-0.034474
-0.032126
-0.030556
-0.033291
-0.036478
-0.039515
...
1.204451
1.215202
1.236595
1.252604
1.262773
1.264311
1.231643
1.225628
1.219023
1.201453
1
-0.046988
-0.041839
-0.037591
-0.032415
-0.027637
-0.024727
-0.023405
-0.025859
-0.029614
-0.033164
...
1.138479
1.157731
1.185653
1.220453
1.250238
1.266876
1.210109
1.211712
1.218673
1.196055
2
-0.047993
-0.042802
-0.038623
-0.033580
-0.028859
-0.026049
-0.024683
-0.027187
-0.030840
-0.034299
...
1.150267
1.168000
1.194755
1.226198
1.252478
1.266418
1.213957
1.214199
1.218736
1.197020
3
-0.048773
-0.043551
-0.039424
-0.034485
-0.029808
-0.027076
-0.025676
-0.028219
-0.031793
-0.035181
...
1.159429
1.175981
1.201830
1.230663
1.254219
1.266062
1.216947
1.216131
1.218784
1.197769
4
-0.054796
-0.049323
-0.045606
-0.041467
-0.037130
-0.035001
-0.033336
-0.036178
-0.039146
-0.041983
...
1.230089
1.237536
1.256392
1.265098
1.267644
1.263315
1.240011
1.231036
1.219159
1.203551
5
-0.051650
-0.046307
-0.042377
-0.037819
-0.033305
-0.030861
-0.029334
-0.032020
-0.035305
-0.038430
...
1.193176
1.205379
1.227888
1.247109
1.260631
1.264750
1.227962
1.223250
1.218963
1.200531
6
-0.054027
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-0.044817
-0.040576
-0.036196
-0.033990
-0.032358
-0.035163
-0.038208
-0.041115
...
1.221071
1.229680
1.249428
1.260703
1.265931
1.263665
1.237067
1.229134
1.219111
1.202813
7
-0.050542
-0.045245
-0.041239
-0.036535
-0.031958
-0.029403
-0.027925
-0.030556
-0.033952
-0.037178
...
1.180173
1.194052
1.217848
1.240772
1.258160
1.265255
1.223718
1.220507
1.218894
1.199467
8
-0.053169
-0.047763
-0.043936
-0.039581
-0.035152
-0.032860
-0.031266
-0.034028
-0.037160
-0.040146
...
1.211001
1.220908
1.241652
1.255795
1.264017
1.264057
1.233780
1.227010
1.219058
1.201989
9
-0.054208
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-0.045002
-0.040785
-0.036415
-0.034227
-0.032587
-0.035401
-0.038427
-0.041319
...
1.223184
1.231521
1.251060
1.261733
1.266332
1.263583
1.237757
1.229579
1.219122
1.202986
10
-0.056381
-0.050842
-0.047234
-0.043305
-0.039058
-0.037087
-0.035352
-0.038274
-0.041081
-0.043774
...
1.248689
1.253740
1.270755
1.274162
1.271178
1.262591
1.246082
1.234959
1.219258
1.205073
11
-0.054451
-0.048992
-0.045252
-0.041067
-0.036711
-0.034547
-0.032896
-0.035722
-0.038724
-0.041593
...
1.226037
1.234007
1.253263
1.263123
1.266874
1.263472
1.238688
1.230181
1.219138
1.203220
12
-0.050807
-0.045499
-0.041511
-0.036842
-0.032280
-0.029752
-0.028262
-0.030906
-0.034276
-0.037478
...
1.183285
1.196763
1.220251
1.242289
1.258751
1.265134
1.224734
1.221163
1.218911
1.199721
13
-0.048701
-0.043481
-0.039350
-0.034401
-0.029720
-0.026981
-0.025584
-0.028123
-0.031705
-0.035099
...
1.158577
1.175239
1.201172
1.230248
1.254057
1.266095
1.216669
1.215951
1.218780
1.197700
14
-0.045960
-0.040854
-0.036536
-0.031223
-0.026388
-0.023375
-0.022098
-0.024501
-0.028359
-0.032004
...
1.126423
1.147228
1.176343
1.214578
1.247947
1.267345
1.206174
1.209169
1.218610
1.195069
15
-0.052903
-0.047509
-0.043664
-0.039273
-0.034829
-0.032511
-0.030928
-0.033677
-0.036835
-0.039846
...
1.207884
1.218192
1.239245
1.254276
1.263425
1.264178
1.232763
1.226352
1.219041
1.201734
16
-0.053781
-0.048350
-0.044565
-0.040291
-0.035897
-0.033666
-0.032045
-0.034838
-0.037907
-0.040837
...
1.218185
1.227166
1.247200
1.259297
1.265383
1.263777
1.236125
1.228525
1.219096
1.202577
17
-0.053337
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-0.044109
-0.039776
-0.035357
-0.033081
-0.031480
-0.034250
-0.037365
-0.040336
...
1.212973
1.222626
1.243175
1.256757
1.264392
1.263980
1.234424
1.227426
1.219068
1.202151
18
-0.050878
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-0.028353
-0.031001
-0.034363
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...
1.184125
1.197495
1.220899
1.242698
1.258911
1.265102
1.225008
1.221340
1.218915
1.199790
19
-0.050902
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-0.036953
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-0.031032
-0.034392
-0.037585
...
1.184404
1.197739
1.221115
1.242834
1.258964
1.265091
1.225099
1.221399
1.218917
1.199813
20
-0.053124
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-0.033969
-0.037105
-0.040095
...
1.210477
1.220452
1.241248
1.255540
1.263918
1.264077
1.233609
1.226899
1.219055
1.201946
21
-0.052062
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...
1.198017
1.209597
1.231627
1.249468
1.261551
1.264561
1.229543
1.224271
1.218989
1.200927
22
-0.051990
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...
1.197165
1.208855
1.230968
1.249053
1.261389
1.264595
1.229264
1.224091
1.218985
1.200857
23
-0.052483
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...
1.202949
1.213893
1.235435
1.251871
1.262488
1.264370
1.231152
1.225311
1.219015
1.201330
24
-0.052383
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...
1.201782
1.212877
1.234534
1.251303
1.262266
1.264415
1.230771
1.225065
1.219009
1.201235
25
-0.053473
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...
1.214564
1.224012
1.244404
1.257532
1.264694
1.263918
1.234943
1.227761
1.219077
1.202281
26
-0.052646
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-0.039555
...
1.204862
1.215560
1.236912
1.252804
1.262851
1.264295
1.231777
1.225715
1.219025
1.201487
27
-0.053238
-0.047829
-0.044007
-0.039661
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-0.032951
-0.031354
-0.034119
-0.037244
-0.040223
...
1.211808
1.221611
1.242276
1.256189
1.264171
1.264025
1.234044
1.227180
1.219062
1.202055
28
-0.052573
-0.047192
-0.043324
-0.038889
-0.034427
-0.032075
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-0.033240
-0.036431
-0.039472
...
1.204001
1.214810
1.236248
1.252384
1.262688
1.264329
1.231496
1.225533
1.219021
1.201417
29
-0.053966
-0.048528
-0.044755
-0.040505
-0.036122
-0.033909
-0.032280
-0.035082
-0.038133
-0.041046
...
1.220355
1.229057
1.248876
1.260354
1.265795
1.263693
1.236834
1.228983
1.219107
1.202755
30
-0.053337
-0.047925
-0.044109
-0.039776
-0.035357
-0.033082
-0.031480
-0.034251
-0.037365
-0.040336
...
1.212976
1.222628
1.243178
1.256758
1.264393
1.263980
1.234425
1.227426
1.219068
1.202151
31
-0.050809
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-0.036845
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-0.029755
-0.028265
-0.030909
-0.034279
-0.037480
...
1.183311
1.196786
1.220271
1.242301
1.258756
1.265133
1.224742
1.221169
1.218911
1.199724
32
-0.051252
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-0.041968
-0.037358
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-0.030337
-0.028828
-0.031494
-0.034819
-0.037980
...
1.188503
1.201309
1.224280
1.244832
1.259743
1.264931
1.226437
1.222264
1.218939
1.200148
33
-0.050728
-0.045424
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-0.036751
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-0.029648
-0.028162
-0.030802
-0.034180
-0.037389
...
1.182361
1.195959
1.219538
1.241839
1.258576
1.265170
1.224432
1.220968
1.218906
1.199646
34
-0.051108
-0.045788
-0.041820
-0.037191
-0.032646
-0.030148
-0.028645
-0.031304
-0.034643
-0.037817
...
1.186814
1.199838
1.222976
1.244008
1.259422
1.264997
1.225886
1.221908
1.218930
1.200010
35
-0.053705
-0.048277
-0.044486
-0.040202
-0.035804
-0.033565
-0.031948
-0.034736
-0.037814
-0.040751
...
1.217285
1.226382
1.246505
1.258858
1.265212
1.263812
1.235831
1.228335
1.219091
1.202503
36
-0.052992
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-0.043754
-0.039375
-0.034937
-0.032627
-0.031041
-0.033794
-0.036943
-0.039945
...
1.208920
1.219096
1.240046
1.254782
1.263622
1.264138
1.233101
1.226571
1.219047
1.201819
37
-0.053975
-0.048536
-0.044764
-0.040515
-0.036132
-0.033921
-0.032292
-0.035094
-0.038144
-0.041056
...
1.220458
1.229146
1.248955
1.260404
1.265814
1.263689
1.236867
1.229004
1.219108
1.202763
38
-0.051327
-0.045998
-0.042045
-0.037445
-0.032913
-0.030436
-0.028924
-0.031594
-0.034911
-0.038065
...
1.189389
1.202081
1.224964
1.245263
1.259911
1.264897
1.226726
1.222451
1.218943
1.200221
39
-0.053425
-0.048008
-0.044199
-0.039877
-0.035463
-0.033196
-0.031591
-0.034366
-0.037472
-0.040434
...
1.213999
1.223519
1.243967
1.257257
1.264587
1.263940
1.234759
1.227642
1.219074
1.202235
40
-0.057632
-0.052041
-0.048518
-0.044755
-0.040579
-0.038733
-0.036943
-0.039927
-0.042609
-0.045187
...
1.263365
1.266525
1.282087
1.281315
1.273967
1.262021
1.250872
1.238055
1.219336
1.206274
41
-0.055272
-0.049778
-0.046095
-0.042018
-0.037709
-0.035627
-0.033940
-0.036807
-0.039727
-0.042520
...
1.235669
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60 rows × 401 columns
In [40]:
# Get predicted X for a given number of components
# Predicted X from calibration using 4 components
X_from_4_component = model.X_predCal()[4]
# Predicted X from calibration using 1 component stored in pandas data frame with row and columns names
X_from_4_component_df = pd.DataFrame(model.X_predCal()[4])
#X_from_4_component_df.index = data_objNames
#X_from_4_component_df.columns = data_varNames
X_from_4_component_df
Out[40]:
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9
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392
393
394
395
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398
399
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...
1.217538
1.226486
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1.270004
1.284545
1.286409
1.251413
1.244246
1.242654
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...
1.228434
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1.263089
1.283334
1.307714
1.305785
1.275744
1.261842
1.250179
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...
1.191358
1.209015
1.237949
1.262634
1.297188
1.305240
1.270244
1.259182
1.243259
1.233230
39
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...
1.218509
1.231492
1.257403
1.276694
1.302877
1.304442
1.275965
1.262696
1.246277
1.235579
40
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...
1.271497
1.270497
1.285383
1.292155
1.289240
1.272165
1.251880
1.237660
1.231084
1.213672
41
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...
1.239577
1.242969
1.259869
1.271286
1.273506
1.262768
1.234824
1.224351
1.220132
1.202314
42
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...
1.231898
1.237305
1.259533
1.284963
1.307724
1.300401
1.261174
1.248067
1.250079
1.231453
43
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-0.035992
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...
1.201786
1.214263
1.240481
1.267670
1.293367
1.299932
1.259495
1.252195
1.250730
1.230884
44
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-0.039318
-0.042364
...
1.237661
1.244656
1.263732
1.272001
1.276804
1.270342
1.249016
1.237608
1.223154
1.209649
45
-0.062082
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-0.041417
-0.039791
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-0.046056
-0.048964
...
1.228431
1.244986
1.270196
1.272843
1.287330
1.291958
1.284697
1.270765
1.231851
1.229284
46
-0.060582
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-0.044794
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...
1.235080
1.251071
1.278852
1.289241
1.315228
1.319305
1.306882
1.289845
1.254896
1.251740
47
-0.059898
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-0.050070
-0.045476
-0.040600
-0.038085
-0.036344
-0.039319
-0.043239
-0.046828
...
1.202288
1.222657
1.250135
1.258047
1.279999
1.289306
1.274817
1.262841
1.225624
1.223651
48
-0.061131
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-0.041847
-0.045361
-0.048088
...
1.236968
1.252300
1.278684
1.285833
1.306663
1.309760
1.299735
1.283430
1.247513
1.244289
49
-0.063432
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-0.049853
-0.045213
-0.043035
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-0.044210
-0.047573
-0.050347
...
1.237642
1.253485
1.278059
1.277520
1.289353
1.292563
1.289740
1.274702
1.232469
1.231091
50
-0.053456
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-0.044197
-0.040076
-0.035380
-0.033326
-0.030971
-0.034560
-0.037244
-0.040664
...
1.206360
1.213011
1.226024
1.226452
1.207938
1.203461
1.179019
1.178482
1.171609
1.151887
51
-0.054128
-0.048748
-0.045185
-0.041353
-0.037105
-0.035200
-0.033377
-0.036354
-0.038786
-0.041321
...
1.238955
1.241582
1.255507
1.259399
1.246951
1.237699
1.214899
1.208884
1.204056
1.183430
52
-0.053732
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-0.044564
-0.040617
-0.036038
-0.034127
-0.031718
-0.035364
-0.037848
-0.041127
...
1.221079
1.224631
1.235359
1.232501
1.208031
1.199092
1.177758
1.176262
1.170124
1.149678
53
-0.053958
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-0.044971
-0.041018
-0.035992
-0.033865
-0.031595
-0.034946
-0.037107
-0.039867
...
1.165215
1.176716
1.190414
1.192380
1.167561
1.175367
1.143851
1.153684
1.152852
1.126815
54
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-0.033176
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-0.037535
...
1.201291
1.204608
1.215997
1.222453
1.198893
1.195521
1.160500
1.165265
1.175346
1.145312
55
-0.050781
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-0.032800
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...
1.210611
1.216555
1.235738
1.256354
1.260335
1.260615
1.219968
1.217670
1.226984
1.199535
56
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...
1.176502
1.189080
1.201314
1.191700
1.161022
1.165302
1.147940
1.154224
1.137094
1.119684
57
-0.055770
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...
1.214239
1.220712
1.233800
1.231967
1.210740
1.207588
1.187161
1.186818
1.177730
1.157425
58
-0.058121
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...
1.229769
1.236311
1.248433
1.238165
1.214340
1.206748
1.197852
1.193022
1.170884
1.157992
59
-0.057095
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...
1.203956
1.213483
1.227621
1.223669
1.202966
1.203299
1.185467
1.185936
1.171058
1.153392
60 rows × 401 columns
In [41]:
help(ho.nipalsPCA.X_predCal)
Help on function X_predCal in module hoggorm.pca:
X_predCal(self)
Returns a dictionary holding the predicted arrays Xhat from
calibration after each computed component. Dictionary key represents
order of component.
In [42]:
# Get validated explained variance of each component
valExplVar = model.X_valExplVar()
# Get calibrated explained variance and store in pandas dataframe with row and column names
valExplVar_df = pd.DataFrame(model.X_valExplVar())
valExplVar_df.columns = ['validated explained variance']
valExplVar_df.index = ['PC{0}'.format(x+1) for x in range(model.X_loadings().shape[1])]
valExplVar_df
Out[42]:
validated explained variance
PC1
71.415215
PC2
10.672744
PC3
7.088484
PC4
5.448433
PC5
1.145096
In [43]:
help(ho.nipalsPCA.X_valExplVar)
Help on function X_valExplVar in module hoggorm.pca:
X_valExplVar(self)
Returns a list holding the validated explained variance for X after
each component. First number in list is for component 1, second number
for component 2, third number for component 3, etc.
In [44]:
# Get cumulative validated explained variance
cumValExplVar = model.X_cumValExplVar()
# Get cumulative validated explained variance and store in pandas dataframe with row and column names
cumValExplVar_df = pd.DataFrame(model.X_cumValExplVar())
cumValExplVar_df.columns = ['cumulative validated explained variance']
cumValExplVar_df.index = ['PC{0}'.format(x) for x in range(model.X_loadings().shape[1] + 1)]
cumValExplVar_df
Out[44]:
cumulative validated explained variance
PC0
0.000000
PC1
71.415215
PC2
82.087959
PC3
89.176443
PC4
94.624876
PC5
95.769973
In [45]:
help(ho.nipalsPCA.X_cumValExplVar)
Help on function X_cumValExplVar in module hoggorm.pca:
X_cumValExplVar(self)
Returns a list holding the cumulative validated explained variance
for array X after each component.
In [46]:
# Get cumulative validated explained variance for each variable
cumCalExplVar_ind = model.X_cumCalExplVar_indVar()
# Get cumulative validated explained variance for each variable and store in pandas dataframe with row and column names
cumValExplVar_ind_df = pd.DataFrame(model.X_cumValExplVar_indVar())
#cumValExplVar_ind_df.columns = data_varNames
cumValExplVar_ind_df.index = ['PC{0}'.format(x) for x in range(model.X_loadings().shape[1] + 1)]
cumValExplVar_ind_df
Out[46]:
0
1
2
3
4
5
6
7
8
9
...
391
392
393
394
395
396
397
398
399
400
PC0
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
...
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
PC1
22.710872
21.660941
24.633452
29.395892
32.929146
36.269480
33.410238
36.056511
34.476418
31.650333
...
81.508076
78.599717
66.107833
23.652124
-0.308331
-2.210922
2.928987
0.323311
-1.866828
-1.736965
PC2
37.041768
35.701940
39.251132
46.268708
45.824521
49.846358
41.555877
49.099234
44.884280
43.187382
...
88.428120
85.245979
79.717190
66.259572
69.632602
50.840185
40.400170
38.230413
67.908421
63.038326
PC3
59.549386
55.127538
55.861670
58.527133
55.416556
56.896679
47.825787
56.688266
61.150641
68.928297
...
88.968249
84.631048
82.184860
66.422820
77.869434
63.746844
65.688602
63.197396
69.828459
77.373464
PC4
84.409841
84.151860
85.759920
90.776563
88.410193
88.494435
85.189375
85.545819
87.891494
84.123411
...
88.700223
85.085762
84.491970
66.990241
78.535613
67.574335
74.788183
78.349408
78.462909
87.311900
PC5
91.611547
90.890894
91.184396
94.505493
93.312892
93.084239
92.169401
91.093997
92.373971
90.861056
...
89.548650
88.720966
86.525575
63.075198
84.344950
85.840815
93.573627
80.572202
76.758932
89.815669
6 rows × 401 columns
In [47]:
help(ho.nipalsPCA.X_cumValExplVar_indVar)
Help on function X_cumValExplVar_indVar in module hoggorm.pca:
X_cumValExplVar_indVar(self)
Returns an array holding the cumulative validated explained variance
for each variable in X after each component. First row represents
zero components, second row represents component 1, third row for
compnent 2, etc. Columns represent variables.
In [49]:
# Get validated predicted X for a given number of components
# Predicted X from validation using 1 component
X_from_1_component_val = model.X_predVal()[1]
# Predicted X from calibration using 1 component stored in pandas data frame with row and columns names
X_from_1_component_val_df = pd.DataFrame(model.X_predVal()[1])
#X_from_1_component_val_df.index = data_objNames
#X_from_1_component_val_df.columns = data_varNames
X_from_1_component_val_df
Out[49]:
0
1
2
3
4
5
6
7
8
9
...
391
392
393
394
395
396
397
398
399
400
0
-0.052654
-0.047253
-0.043385
-0.038966
-0.034495
-0.032144
-0.030568
-0.033327
-0.036519
-0.039577
...
1.204576
1.215067
1.236509
1.252646
1.263053
1.264538
1.231093
1.225307
1.218563
1.201118
1
-0.047475
-0.042245
-0.037951
-0.032718
-0.027856
-0.024933
-0.023602
-0.026006
-0.029788
-0.033307
...
1.140074
1.159301
1.185280
1.219966
1.249506
1.264172
1.209302
1.209640
1.216976
1.195430
2
-0.048160
-0.043013
-0.038847
-0.033862
-0.029165
-0.026398
-0.025090
-0.027483
-0.031057
-0.034387
...
1.150832
1.168292
1.194591
1.225073
1.251362
1.265056
1.213313
1.213155
1.217364
1.195619
3
-0.048993
-0.043709
-0.039550
-0.034547
-0.029842
-0.027097
-0.025709
-0.028282
-0.031926
-0.035339
...
1.159720
1.176811
1.202179
1.230568
1.253510
1.265437
1.217519
1.216286
1.217592
1.197049
4
-0.054901
-0.049436
-0.045730
-0.041604
-0.037243
-0.035085
-0.033372
-0.036204
-0.039167
-0.042003
...
1.229091
1.237254
1.256051
1.264647
1.266633
1.262159
1.240285
1.230951
1.218680
1.203491
5
-0.051742
-0.046399
-0.042469
-0.037919
-0.033391
-0.030948
-0.029415
-0.032108
-0.035405
-0.038539
...
1.192850
1.205387
1.227701
1.246833
1.260031
1.264153
1.227957
1.223175
1.218755
1.200373
6
-0.054114
-0.048671
-0.044907
-0.040678
-0.036286
-0.034081
-0.032450
-0.035264
-0.038304
-0.041197
...
1.220707
1.229692
1.249463
1.260550
1.265708
1.263024
1.237448
1.229354
1.219030
1.202849
7
-0.050596
-0.045307
-0.041314
-0.036630
-0.032055
-0.029521
-0.028038
-0.030657
-0.034040
-0.037225
...
1.179995
1.194176
1.217751
1.240628
1.258077
1.264336
1.223809
1.220514
1.218559
1.199847
8
-0.053225
-0.047823
-0.044000
-0.039660
-0.035221
-0.032936
-0.031338
-0.034103
-0.037231
-0.040201
...
1.210842
1.221006
1.241755
1.255860
1.263868
1.263652
1.234152
1.227244
1.219112
1.202090
9
-0.054279
-0.048829
-0.045078
-0.040876
-0.036489
-0.034311
-0.032660
-0.035482
-0.038508
-0.041383
...
1.223016
1.231621
1.251305
1.261676
1.266167
1.262965
1.238314
1.229963
1.219180
1.203228
10
-0.056608
-0.051037
-0.047434
-0.043545
-0.039261
-0.037275
-0.035505
-0.038459
-0.041296
-0.043968
...
1.248120
1.254471
1.271578
1.274293
1.269925
1.259988
1.247542
1.235868
1.219169
1.205495
11
-0.054549
-0.049090
-0.045344
-0.041185
-0.036812
-0.034641
-0.032996
-0.035814
-0.038825
-0.041716
...
1.225591
1.233629
1.252665
1.262470
1.265523
1.264272
1.238503
1.229731
1.219115
1.202677
12
-0.050908
-0.045569
-0.041593
-0.036948
-0.032373
-0.029853
-0.028361
-0.031005
-0.034369
-0.037559
...
1.182853
1.196213
1.219559
1.241581
1.257947
1.265327
1.224176
1.220392
1.218778
1.198834
13
-0.048885
-0.043686
-0.039564
-0.034683
-0.029987
-0.027266
-0.025915
-0.028403
-0.031930
-0.035245
...
1.159500
1.176465
1.201753
1.231145
1.254843
1.266980
1.218474
1.217215
1.219020
1.198370
14
-0.046766
-0.041815
-0.037483
-0.032258
-0.027576
-0.024561
-0.023485
-0.025645
-0.029256
-0.032611
...
1.131729
1.148309
1.177782
1.215363
1.249687
1.267777
1.199994
1.208301
1.217845
1.195189
15
-0.052977
-0.047570
-0.043724
-0.039334
-0.034881
-0.032562
-0.030977
-0.033729
-0.036901
-0.039918
...
1.207475
1.217680
1.238999
1.253922
1.262887
1.263568
1.232085
1.226166
1.218458
1.201334
16
-0.053816
-0.048388
-0.044600
-0.040340
-0.035940
-0.033709
-0.032084
-0.034877
-0.037952
-0.040866
...
1.218090
1.227185
1.247294
1.259450
1.265157
1.263902
1.236617
1.228605
1.219550
1.202496
17
-0.053305
-0.047895
-0.044080
-0.039759
-0.035344
-0.033066
-0.031463
-0.034231
-0.037348
-0.040303
...
1.213041
1.222856
1.243361
1.256781
1.264343
1.263839
1.234888
1.227866
1.219047
1.202331
18
-0.050754
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60 rows × 401 columns
In [50]:
# Get validated predicted X for a given number of components
# Predicted X from validation using 3 components
X_from_3_component_val = model.X_predVal()[3]
# Predicted X from calibration using 3 components stored in pandas data frame with row and columns names
X_from_3_component_val_df = pd.DataFrame(model.X_predVal()[3])
#X_from_3_component_val_df.index = data_objNames
#X_from_3_component_val_df.columns = data_varNames
X_from_3_component_val_df
Out[50]:
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2
3
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60 rows × 401 columns
In [51]:
help(ho.nipalsPCA.X_predVal)
Help on function X_predVal in module hoggorm.pca:
X_predVal(self)
Returns a dictionary holding the predicted arrays Xhat from
validation after each computed component. Dictionary key represents
order of component.
In [52]:
# Get predicted scores for new measurements (objects) of X
# First pretend that we acquired new X data by using part of the existing data and overlaying some noise
import numpy.random as npr
new_data = data[0:4, :] + npr.rand(4, np.shape(data)[1])
np.shape(new_data)
# Now insert the new data into the existing model and compute scores for two components (numComp=2)
pred_scores = model.X_scores_predict(new_data, numComp=2)
# Same as above, but results stored in a pandas dataframe with row names and column names
pred_scores_df = pd.DataFrame(model.X_scores_predict(new_data, numComp=2))
pred_scores_df.columns = ['PC{0}'.format(x) for x in range(2)]
pred_scores_df.index = ['new object {0}'.format(x) for x in range(np.shape(new_data)[0])]
pred_scores_df
Out[52]:
PC0
PC1
new object 0
2.143577
7.487844
new object 1
2.930911
6.962830
new object 2
1.878479
7.650605
new object 3
2.172548
7.371672
In [53]:
help(ho.nipalsPCA.X_scores_predict)
Help on function X_scores_predict in module hoggorm.pca:
X_scores_predict(self, Xnew, numComp=None)
Returns array of X scores from new X data using the exsisting model.
Rows represent objects and columns represent components.
In [ ]:
Content source: olivertomic/hoggorm
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