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Normal and Shrinkage Linear Discriminant Analysis for classification in Scikit-learn

Shows how shrinkage improves classification.

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Version

In [1]:
import sklearn
sklearn.__version__
Out[1]:
'0.18'

Imports

This tutorial imports make_blobs and LinearDiscriminantAnalysis.

In [2]:
from __future__ import division

import plotly.plotly as py
import plotly.graph_objs as go

import numpy as np
import matplotlib.pyplot as plt

from sklearn.datasets import make_blobs
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis

Calculations

In [3]:
n_train = 20  # samples for training
n_test = 200  # samples for testing
n_averages = 50  # how often to repeat classification
n_features_max = 75  # maximum number of features
step = 4  # step size for the calculation


def generate_data(n_samples, n_features):
    """Generate random blob-ish data with noisy features.

    This returns an array of input data with shape `(n_samples, n_features)`
    and an array of `n_samples` target labels.

    Only one feature contains discriminative information, the other features
    contain only noise.
    """
    X, y = make_blobs(n_samples=n_samples, n_features=1, centers=[[-2], [2]])

    # add non-discriminative features
    if n_features > 1:
        X = np.hstack([X, np.random.randn(n_samples, n_features - 1)])
    return X, y

acc_clf1, acc_clf2 = [], []
n_features_range = range(1, n_features_max + 1, step)
for n_features in n_features_range:
    score_clf1, score_clf2 = 0, 0
    for _ in range(n_averages):
        X, y = generate_data(n_train, n_features)

        clf1 = LinearDiscriminantAnalysis(solver='lsqr', shrinkage='auto').fit(X, y)
        clf2 = LinearDiscriminantAnalysis(solver='lsqr', shrinkage=None).fit(X, y)

        X, y = generate_data(n_test, n_features)
        score_clf1 += clf1.score(X, y)
        score_clf2 += clf2.score(X, y)

    acc_clf1.append(score_clf1 / n_averages)
    acc_clf2.append(score_clf2 / n_averages)

features_samples_ratio = np.array(n_features_range) / n_train

Plots

In [4]:
lda_shrinkage = go.Scatter(x=features_samples_ratio, 
                           y=acc_clf1, mode= "lines",
                           name="Linear Discriminant Analysis with shrinkage", 
                           line=dict(color='navy', width=2))
lda_plot = go.Scatter(x=features_samples_ratio, y = acc_clf2,
                      mode="lines",
                      name="Linear Discriminant Analysis",
                      line=dict(color='gold'))

data = [lda_plot, lda_shrinkage]
layout = go.Layout(xaxis=dict(title="n_features/n_samples",
                               showgrid=False),
                   yaxis=dict(title= "Classification Accuracy",
                              showgrid=False))
fig = go.Figure(data=data, layout=layout)

py.iplot(fig)
Out[4]:
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