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Comparison of LDA and PCA 2D projection of Iris dataset in Scikit-learn

The Iris dataset represents 3 kind of Iris flowers (Setosa, Versicolour and Virginica) with 4 attributes: sepal length, sepal width, petal length and petal width.

Principal Component Analysis (PCA) applied to this data identifies the combination of attributes (principal components, or directions in the feature space) that account for the most variance in the data. Here we plot the different samples on the 2 first principal components.

Linear Discriminant Analysis (LDA) tries to identify attributes that account for the most variance between classes. In particular, LDA, in contrast to PCA, is a supervised method, using known class labels.

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Version¶

In [1]:
import sklearn
sklearn.__version__

Out[1]:
'0.18'

Imports¶

This tutorial imports PCA and LinearDiscriminantAnalysis.

In [2]:
import plotly.plotly as py
import plotly.graph_objs as go
from plotly import tools

from sklearn import datasets
from sklearn.decomposition import PCA
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis


Calculations¶

In [3]:
iris = datasets.load_iris()

X = iris.data
y = iris.target
target_names = iris.target_names

pca = PCA(n_components=2)
X_r = pca.fit(X).transform(X)

lda = LinearDiscriminantAnalysis(n_components=2)
X_r2 = lda.fit(X, y).transform(X)

# Percentage of variance explained for each components
print('explained variance ratio (first two components): %s'
% str(pca.explained_variance_ratio_))

colors = ['navy', 'turquoise', 'darkorange']

explained variance ratio (first two components): [ 0.92461621  0.05301557]


Plot Results¶

In [4]:
fig = tools.make_subplots(rows=1, cols=2,
subplot_titles=('PCA of IRIS dataset',
'LDA of IRIS dataset')
)

This is the format of your plot grid:
[ (1,1) x1,y1 ]  [ (1,2) x2,y2 ]


In [5]:
for color, i, target_name in zip(colors, [0, 1, 2], target_names):
pca = go.Scatter(x=X_r[y == i, 0],
y=X_r[y == i, 1],
mode='markers',
marker=dict(color=color),
name=target_name
)

fig.append_trace(pca, 1, 1)

for color, i, target_name in zip(colors, [0, 1, 2], target_names):
lda = go.Scatter(x=X_r2[y == i, 0],
y=X_r2[y == i, 1],
showlegend=False,
mode='markers',
marker=dict(color=color),
name=target_name
)

fig.append_trace(lda, 1, 2)

for i in map(str, range(1, 3)):
x = 'xaxis' + i
y = 'yaxis' + i

fig['layout'][x].update(zeroline=False, showgrid=False)
fig['layout'][y].update(zeroline=False, showgrid=False)

In [6]:
py.iplot(fig)

Out[6]:
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