How do I get the components for LDA in scikit-lear

Question

When using PCA in sklearn, it's easy to get out the components:

from sklearn import decomposition
pca = decomposition.PCA(n_components=n_components)
pca_data = pca.fit(input_data)
pca_components = pca.components_

But I can't for the life of me figure out how to get the components out of LDA, as there is no components_ attribute. Is there a similar attribute in sklearn lda?

Answer 1

In the case of PCA, the documentation is clear. The pca.components_ are the eigenvectors.

In the case of LDA, we need the lda.scalings_ attribute.

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Visual example using iris data and sklearn:

import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets
import pandas as pd
from sklearn.preprocessing import StandardScaler
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis


iris = datasets.load_iris()
X = iris.data
y = iris.target
#In general it is a good idea to scale the data
scaler = StandardScaler()
scaler.fit(X)
X=scaler.transform(X)

lda = LinearDiscriminantAnalysis()
lda.fit(X,y)
x_new = lda.transform(X)   

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Verify that the lda.scalings_ are the eigenvectors:

print(lda.scalings_)
print(lda.transform(np.identity(4)))

[[-0.67614337  0.0271192 ]
 [-0.66890811  0.93115101]
 [ 3.84228173 -1.63586613]
 [ 2.17067434  2.13428251]]

[[-0.67614337  0.0271192 ]
 [-0.66890811  0.93115101]
 [ 3.84228173 -1.63586613]
 [ 2.17067434  2.13428251]]

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Additionally here is a useful function to plot the biplot and verify visually:

def myplot(score,coeff,labels=None):
    xs = score[:,0]
    ys = score[:,1]
    n = coeff.shape[0]

    plt.scatter(xs ,ys, c = y) #without scaling
    for i in range(n):
        plt.arrow(0, 0, coeff[i,0], coeff[i,1],color = 'r',alpha = 0.5)
        if labels is None:
            plt.text(coeff[i,0]* 1.15, coeff[i,1] * 1.15, "Var"+str(i+1), color = 'g', ha = 'center', va = 'center')
        else:
            plt.text(coeff[i,0]* 1.15, coeff[i,1] * 1.15, labels[i], color = 'g', ha = 'center', va = 'center')

plt.xlabel("LD{}".format(1))
plt.ylabel("LD{}".format(2))
plt.grid()

#Call the function. 
myplot(x_new[:,0:2], lda.scalings_) 
plt.show()

Results

Answer 2

My reading of the code is that the coef_ attribute is used to weight each of the components when scoring a sample's features against the different classes. scaling is the eigenvector and xbar_ is the mean. In the spirit of UTSL, here's the source for the decision function: https://github.com/scikit-learn/scikit-learn/blob/master/sklearn/lda.py#L188

Answer 3

In PCA, the transform operation uses self.components_.T (see the code):

    X_transformed = np.dot(X, self.components_.T)

In LDA, the transform operation uses self.scalings_ (see the code):

    X_new = np.dot(X, self.scalings_)

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Note the .T which transposes the array in the PCA, and not in LDA:

• PCA: components_ : array, shape (n_components, n_features)
• LDA: scalings_ : array, shape (n_features, n_classes - 1)