Scikit-learn: Perilaku tak terduga dari analisis korelasi kanonik (CCA)

Dibuat pada 23 Jun 2019 · 3Komentar · Sumber: scikit-learn/scikit-learn

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Keterangan

Diberikan dua matriks tampilan X dan Y , CCA harus mengembalikan n_components kombinasi linier elemen dalam X 's dan Y ' s vektor dengan korelasi terbesar, yaitu komponen pertama memiliki korelasi terbesar, yang kedua memiliki korelasi terbesar kedua dalam arah yang tidak berkorelasi dengan yang pertama, dll. Namun, dalam kode berikut, kolom kedua jelas kurang berkorelasi dari kolom ketiga:

Langkah/Kode untuk Mereproduksi

from sklearn.cross_decomposition import CCA
import numpy as np
from scipy import stats

X = [[0.006061109337620652, 0.0392466675239141, -0.04312459861840733], [-0.6652995467596429, 0.2076410843346226, -0.7817536882379651], [-1.4060868112838942, -0.055029478343267685, -1.006415484608637], [-2.170613455952169, -0.15770102997315535, -1.5223958036356375], [-2.895702070412092, -0.20498481413822175, -1.8232022285963847], [-3.687452614812402, -0.543003880524402, -2.2952030829468533], [-4.206168972149556, -0.3365693935548624, -2.841946351795423], [-5.231288268781064, -0.8024321344988571, -3.40532581256557], [-6.095805742721522, -0.9381144689340173, -3.593752186094848], [-6.297988264542059, -0.7231985020991631, -3.9435579269998406], [-7.10897027952524, -0.8639925998765747, -4.264992629284153], [-8.116238092376772, -1.0123970020855437, -4.96858178622968], [-8.969468878952105, -1.0235782019578692, -5.617282941713933], [-9.839359511108077, -1.2819621078971968, -5.8901943190245625], [-10.181936322525571, -0.9904671991812529, -6.240811384647836]]
Y = [[0.032927114749911154, 0.21320841666565743, -0.23427536580450153], [1.431742605643286, 0.23963850202268067, 0.8438745303679628], [2.908798834568648, 0.7357229001312737, 1.325345683629048], [4.438824821921929, 0.9473643810538429, 2.35038560647864], [5.887201894166226, 1.0302756424934638, 2.964806513433767], [7.409049064480012, 1.3070946380395154, 4.347473875547982], [8.51501831350366, 1.3380108570442941, 4.9533251686263275], [10.57244384646805, 2.31627294094068, 6.028949244604159], [12.22872203222364, 2.1165257564864675, 6.923464021607424], [12.664660419747504, 1.8911363532121173, 7.398432173930664], [14.29235367239137, 2.2098221962551343, 8.000538342827351], [16.327977920399373, 2.643183255720207, 9.257671785118596], [18.081288169620517, 2.968898443090926, 10.221747267811098], [19.754046559146662, 3.051682253577557, 11.244435627784393], [20.466418131910004, 2.644933083198568, 11.752014917896375]]

cca = CCA(n_components=3)
cca.fit(X, Y)
X_transformed, Y_transformed = cca.transform(X, Y)

print(X_transformed)

[[ 1.64277244  0.08237031  0.11724683]
 [ 1.41457457 -0.11600721  0.07162219]
 [ 1.18686358  0.00666119  0.08822118]
 [ 0.94070119 -0.02504267 -0.0112954 ]
 [ 0.71314666  0.02919558  0.25990473]
 [ 0.46246267  0.05607036 -0.16424275]
 [ 0.28625435 -0.09546609 -0.02850206]
 [-0.03644528 -0.03407977 -0.55790786]
 [-0.30127324  0.12266269 -0.12622283]
 [-0.37581414 -0.01941656 -0.0343278 ]
 [-0.62900674  0.05973748  0.13448604]
 [-0.95400947  0.0082079  -0.05487306]
 [-1.23214839 -0.07548718 -0.08864002]
 [-1.50031366  0.05776429  0.00665019]
 [-1.61776455 -0.0571703   0.38788062]]

print(Y_transformed)

[[ 1.64131294  0.01428169  0.11343087]
 [ 1.41330957 -0.06169376  0.06929115]
 [ 1.18580457  0.04946041  0.0853499 ]
 [ 0.9398609   0.01613582 -0.01092778]
 [ 0.71251056  0.06356946  0.25144578]
 [ 0.46205587 -0.05371303 -0.15889725]
 [ 0.28599564 -0.05298207 -0.02757442]
 [-0.03641563  0.02220818 -0.53975   ]
 [-0.30099795  0.01004611 -0.12211474]
 [-0.37547807 -0.063071   -0.03321056]
 [-0.62844374  0.02679924  0.13010901]
 [-0.95315959  0.0185694  -0.05308714]
 [-1.23105629  0.03726576 -0.08575511]
 [-1.49897395  0.01483407  0.00643375]
 [-1.61632484 -0.04171028  0.37525653]]

Hasil yang diharapkan

Korelasi antara kolom ketiga X_transfomed dan Y_transformed kira-kira 1, sedangkan korelasi antara kolom kedua hanya 0,389. Oleh karena itu, saya berharap kolom ketiga muncul di tempat kolom kedua.

Hasil nyata

Ketika saya menjalankan CCA dengan n_components=2 saya mendapatkan kolom pertama dan kedua, sedangkan saya seharusnya mendapatkan kolom pertama dan ketiga.