Visualize the correlation matrix by principal component analysis in Python
Premise
・ Mel frequency cepstrum analysis is performed by extracting the chorus of a certain song for 30 seconds. ・ Ask for KL divergence between two songs. ・ ↑ Visualize ・ Visualize what was analyzed for principal components ・ Success if it is a correlation matrix
data
Compare AKB48's Flying Get and Heavy Rotation.
The KL divergence sought is 16 x 16 dimensions
[[ 95.31099625 91.15557772 56.59372546 112.20285226 94.41219084
211.66976101 92.55439072 121.40280516 99.87466514 76.50081387
176.93201868 91.81223113 85.27707457 105.14295556 125.49246929
130.92378707]
[ 61.39054933 94.3470823 62.02704779 107.94425798 128.17543843
309.20131854 90.24173322 107.68055813 109.89023764 50.34427017
223.12270163 86.42437451 56.75452679 147.27774644 140.3949859
183.75894278]
[ 105.66621666 82.44161726 55.37485991 95.92704467 71.93089191
139.99784461 103.5305553 104.49783045 101.97799459 97.42010348
125.64532251 93.76049908 96.99409273 81.04788291 101.66325191
106.66200182]
[ 72.58173889 88.12377418 61.89530358 86.95335195 138.72571321
312.35785101 90.41438615 113.71909706 118.77928154 65.50818774
214.00175004 113.10626452 52.0092669 135.97299857 148.63792688
193.27541302]
[ 81.63626278 89.21027233 65.00120995 130.11972589 98.52470863
225.72264868 91.47807602 108.48086909 82.19549295 60.1953677
178.25090454 74.23288462 86.75234338 119.57743314 121.44196645
130.71085354]
[ 112.80955973 84.20293672 66.13356741 126.27130948 60.46044078
108.98487829 94.30643082 114.27767382 85.12283233 100.1694529
123.12525354 77.02509766 127.07893463 77.72584545 90.34136209
77.31272758]
[ 98.67181854 79.9882436 60.27699343 95.48883179 57.14726547
106.75881027 84.51898243 105.15391427 96.42217442 103.36893403
115.31304902 81.72145888 113.92827284 70.10342339 79.76864038
85.59532391]
[ 124.00540056 102.49330066 69.46940492 117.7972943 65.92281076
122.42686859 109.21028055 139.69386525 120.41384311 124.96030812
147.40336555 98.98037785 136.61224331 82.25578681 101.68799841
101.60176282]
[ 141.02536187 88.11442192 69.53316552 123.67378376 67.97351381
111.42573997 108.78252174 128.35881238 103.34373259 117.07395769
122.29312541 102.2082161 129.57301791 78.33587137 110.68395808
89.29850647]
[ 105.83495569 71.55826188 60.84049422 93.8003492 77.06177205
150.83061505 86.87908254 114.92215578 100.28873519 90.46477627
134.67789323 96.1906124 94.92596407 79.28705749 103.96680059
107.35708818]
[ 166.21174246 116.41752126 94.20800055 148.72009053 61.35802568
82.62043669 132.79504129 158.40382344 130.28234204 168.90800616
131.6410988 114.45081907 191.85294161 84.81226445 106.30195098
89.39215458]
[ 65.41033607 67.36512259 45.30766447 70.95585215 66.52775288
140.37168343 69.72982884 81.57225523 87.82282686 67.15724897
121.30574971 69.68125315 67.9074851 76.44269754 77.95359039
98.47073341]
[ 93.18094019 77.11815575 56.16982799 74.68534181 85.72265797
159.071974 86.2112096 110.31931314 105.62643628 95.54275032
131.41625514 110.34370673 79.29159169 78.66368263 104.24385502
122.82713447]
[ 151.91835442 95.8700754 78.95950183 106.69723914 66.8965109
83.65254447 116.18496042 145.24555922 122.32195846 154.69915632
107.94328396 128.95019683 145.70673878 67.11698712 105.83368936
95.34869169]
[ 77.74571566 68.14642544 49.52404341 90.78773066 80.01443641
181.90010793 78.31102815 87.9577934 82.56031457 62.65435512
139.59025763 74.27213077 71.97330552 91.39001379 99.40086861
112.40496471]
[ 80.29039282 80.71088572 58.43570222 109.4784385 67.87835361
153.32727136 84.13107423 99.60128605 93.34917358 74.31430677
147.10640919 65.51538298 99.68106666 93.5848086 87.98955945
99.60590161]]
Visualization
Draw with a heat map. Use a library called seaborn that can display graphs neatly.
- The title is garbled, so it needs to be translated into Japanese. Edit site-packages / seaborn / rcmod.py
def set(context="notebook", style="darkgrid", palette="deep", font="Hiragino Kaku Gothic Pro", font_scale=1, color_codes=False, rc=None):
You can change the font part to Japanese font.
Visualize KL divergence as it is
python
#16x16 dimensional data
KLD = [ 95.31099625 91.15557772 56.59372546 112.20285226 94.41219084
211.66976101 92.55439072 121.40280516 99.87466514 76.50081387
176.93201868 91.81223113 85.27707457 105.14295556 125.49246929
130.92378707]
[ 61.39054933 94.3470823 ...
import seaborn as sns
import matplotlib.pyplot as plt
#Character string to be displayed on the X-axis and Y-axis
feature_names = ['%d' % i for i in range(KLD.shape[1])]
#Visualization
sns.heatmap(KLD, annot=False, xticklabels=feature_names, yticklabels=feature_names)
plt.show()
There is no rule because the principal component analysis is not performed.
Try to output the value in each dimension.
python
#OK if annot is set to True
sns.heatmap(KLD, annot=True, xticklabels=feature_names, yticklabels=feature_names)
Visualize the correlation matrix by principal component analysis
Use a technique called PCA
python
from sklearn.decomposition import PCA
import numpy as np
# n_If components are not specified, the data will be analyzed as the number of dimensions.
pca = PCA()
pca.fit(KLD)
features = pca.fit_transform(KLD)
matrix = np.corrcoef(features.transpose())
sns.heatmap(matrix, annot=True, xticklabels=feature_names, yticklabels=feature_names)
plt.show()
The diagonal components are all 1! It satisfies the characteristics of the correlation matrix.
Dimensional compression, principal component analysis and visualization
The above was performed as it is in 16x16 dimensions, but the principal component analysis was performed. Since 16x16 is really a lot, I will drop the dimension to 5x5.
python
#n_components become the number of dimensions
pca = PCA(n_components=5)
Easy to see.
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