Originally, R was used to calculate PCA using both princomp and prcomp. However, rpy2 stopped was intorducing some issues on the galaxy server. I decided to switch the calculation over to a pure python solution. scikit-learn has a PCA package which we can used, but it only does SVD and matches the output of prcomp with its default values.
Here I am testing and figuing out how to output the different values.
In [147]:
import pandas as pd
import numpy as np
from sklearn.decomposition import PCA
In [210]:
dat = pd.read_table('../example_data/ST000015_log.tsv')
dat.set_index('Name', inplace=True)
In [211]:
dat[:3]
Out[211]:
a332577
a332581
a332585
a332589
a332593
a332597
a332601
a332469
a332477
a332481
...
a332337
a332341
a332345
a332349
a332217
a332221
a332225
a332229
a332233
a332237
Name
tyrosine
7.3923
7.4998
7.1898
9.0168
6.3038
6.5236
8.2288
7.5999
6.7549
8.9858
...
14.8625
7.5774
9.0688
14.4720
14.1080
11.2697
8.6366
11.4538
10.9766
14.1164
tryptophan
6.4594
7.1189
5.2095
7.0444
5.9542
7.3309
8.0056
4.0000
5.2095
3.0000
...
8.5507
7.2192
7.5314
8.0389
6.4757
9.2021
9.2503
8.5962
8.8202
10.9665
trehalose
8.9571
8.8361
9.5699
8.9129
8.0875
8.8234
9.0389
9.5565
8.8549
9.8074
...
10.2131
9.3061
9.1344
11.7385
11.0841
10.4949
11.3663
10.4737
10.6165
11.4949
3 rows × 125 columns
In [221]:
%%R -i dat
# First method uses princomp to calulate PCA using eigenvalues and eigenvectors
pr = princomp(dat)
#str(pr)
loadings = pr$loadings
scores = pr$scores
#summary(pr)
[1] 12.61808
In [223]:
%%R -i dat
pr = prcomp(dat)
#str(pr)
loadings = pr$rotation
scores = pr$x
sd = pr$sdev
#summary(pr)
scikit-learn has a PCA package that we will use. It uses the SVD method, so results match the prcomp from R.
http://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html
In [181]:
# Initiate PCA class
pca = PCA()
# Fit the model and transform data
scores = pca.fit_transform(dat)
# Get loadings
loadings = pca.components_
# R also outputs the following in their summaries
sd = loadings.std(axis=0)
propVar = pca.explained_variance_ratio_
cumPropVar = propVar.cumsum()
I compared these results with prcomp and they are identical, note that the python version formats the data in scientific notation.
At the top of each output file, the original R version includes the standard deviation and the proportion of variance explained. I want to first build this block.
In [148]:
# Labels used for the comment block
labels = np.array(['#Std. deviation', '#Proportion of variance explained', '#Cumulative proportion of variance explained'])
# Stack the data into a matrix
data = np.vstack([sd, propVar, cumPropVar])
# Add the labels to the first position in the matrix
block = np.column_stack([labels, data])
In [189]:
# Create header
header = np.array(['Comp{}'.format(x+1) for x in range(loadings.shape[1])])
compoundIndex = np.hstack([dat.index.name, dat.index])
sampleIndex = np.hstack(['sampleID', dat.columns])
# Create loadings output
loadHead = np.vstack([header, loadings])
loadIndex = np.column_stack([sampleIndex, loadHead])
loadOut = np.vstack([block, loadIndex])
# Create scores output
scoreHead = np.vstack([header, scores])
scoreIndex = np.column_stack([compoundIndex, scoreHead])
scoreOut = np.vstack([block, scoreIndex])
In [198]:
np.savetxt('/home/jfear/tmp/dan.tsv', loadOut, fmt="%s", delimiter='\t')
In [199]:
bob = pd.DataFrame(loadOut)
In [200]:
Out[200]:
0
1
2
3
4
5
6
7
8
9
...
116
117
118
119
120
121
122
123
124
125
0
#Std. deviation
0.0894106208128
0.0872859231919
0.0889353873848
0.0883950492616
0.0894074630293
0.089269416936
0.0889222157093
0.0894313538218
0.0878101808881
...
0.0894095300328
0.0889152037066
0.0889979196178
0.0893452895665
0.0893128108836
0.0871128038213
0.0893214244514
0.089437875108
0.0887774951295
0.0893028422611
1
#Proportion of variance explained
0.768408398347
0.0944852586284
0.0166584048729
0.0106266237539
0.00979897186803
0.00790398627099
0.00732960958491
0.00588902805794
0.00556921465521
...
2.03871235916e-05
1.77822280914e-05
1.60299095197e-05
1.57034683108e-05
1.4590216401e-05
1.39194117166e-05
1.10429619828e-05
1.0236398879e-05
9.40237128738e-06
7.5601070231e-06
2
#Cumulative proportion of variance explained
0.768408398347
0.862893656976
0.879552061849
0.890178685603
0.899977657471
0.907881643742
0.915211253327
0.921100281384
0.92666949604
...
0.999883732927
0.999901515155
0.999917545064
0.999933248533
0.999947838749
0.999961758161
0.999972801123
0.999983037522
0.999992439893
1.0
3
sampleID
Comp1
Comp2
Comp3
Comp4
Comp5
Comp6
Comp7
Comp8
Comp9
...
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Comp117
Comp118
Comp119
Comp120
Comp121
Comp122
Comp123
Comp124
Comp125
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