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sklearn框架

函数导图

1.2. Linear and Quadratic Discriminant Analysis

import numpy as np
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
X = np.array([[-1, -1], [-2, -1], [-3, -2], [1, 1], [2, 1], [3, 2]])
y = np.array([1, 1, 1, 2, 2, 2])
clf = LinearDiscriminantAnalysis()
clf.fit(X, y)
print(clf.predict([[-0.8, -1]]))

Normal and Shrinkage Linear Discriminant Analysis for classification

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import make_blobs

from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
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.
"""</span>
X<span class="token punctuation">,</span> y <span class="token operator">=</span> make_blobs<span class="token punctuation">(</span>n_samples<span class="token operator">=</span>n_samples<span class="token punctuation">,</span> n_features<span class="token operator">=</span><span class="token number">1</span><span class="token punctuation">,</span> centers<span class="token operator">=</span><span class="token punctuation">[</span><span class="token punctuation">[</span><span class="token operator">-</span><span class="token number">2</span><span class="token punctuation">]</span><span class="token punctuation">,</span> <span class="token punctuation">[</span><span class="token number">2</span><span class="token punctuation">]</span><span class="token punctuation">]</span><span class="token punctuation">)</span>

<span class="token comment"># add non-discriminative features</span>
<span class="token keyword">if</span> n_features <span class="token operator">&gt;</span> <span class="token number">1</span><span class="token punctuation">:</span>
    X <span class="token operator">=</span> np<span class="token punctuation">.</span>hstack<span class="token punctuation">(</span><span class="token punctuation">[</span>X<span class="token punctuation">,</span> np<span class="token punctuation">.</span>random<span class="token punctuation">.</span>randn<span class="token punctuation">(</span>n_samples<span class="token punctuation">,</span> n_features <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">]</span><span class="token punctuation">)</span>
<span class="token keyword">return</span> X<span class="token punctuation">,</span> 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 <span class="token operator">=</span> LinearDiscriminantAnalysis<span class="token punctuation">(</span>solver<span class="token operator">=</span><span class="token string">'lsqr'</span><span class="token punctuation">,</span> shrinkage<span class="token operator">=</span><span class="token string">'auto'</span><span class="token punctuation">)</span><span class="token punctuation">.</span>fit<span class="token punctuation">(</span>X<span class="token punctuation">,</span> y<span class="token punctuation">)</span>
    clf2 <span class="token operator">=</span> LinearDiscriminantAnalysis<span class="token punctuation">(</span>solver<span class="token operator">=</span><span class="token string">'lsqr'</span><span class="token punctuation">,</span> shrinkage<span class="token operator">=</span><span class="token boolean">None</span><span class="token punctuation">)</span><span class="token punctuation">.</span>fit<span class="token punctuation">(</span>X<span class="token punctuation">,</span> y<span class="token punctuation">)</span>

    X<span class="token punctuation">,</span> y <span class="token operator">=</span> generate_data<span class="token punctuation">(</span>n_test<span class="token punctuation">,</span> n_features<span class="token punctuation">)</span>
    score_clf1 <span class="token operator">+=</span> clf1<span class="token punctuation">.</span>score<span class="token punctuation">(</span>X<span class="token punctuation">,</span> y<span class="token punctuation">)</span>
    score_clf2 <span class="token operator">+=</span> clf2<span class="token punctuation">.</span>score<span class="token punctuation">(</span>X<span class="token punctuation">,</span> y<span class="token punctuation">)</span>

acc_clf1<span class="token punctuation">.</span>append<span class="token punctuation">(</span>score_clf1 <span class="token operator">/</span> n_averages<span class="token punctuation">)</span>
acc_clf2<span class="token punctuation">.</span>append<span class="token punctuation">(</span>score_clf2 <span class="token operator">/</span> n_averages<span class="token punctuation">)</span>

features_samples_ratio = np.array(n_features_range) / n_train
plt.plot(features_samples_ratio, acc_clf1, linewidth=2,

label="Linear Discriminant Analysis with shrinkage", color='navy')

plt.plot(features_samples_ratio, acc_clf2, linewidth=2,

label="Linear Discriminant Analysis", color='gold')
plt.xlabel('n_features / n_samples')

plt.ylabel('Classification accuracy')
plt.legend(loc=1, prop={'size': 12})

plt.suptitle('Linear Discriminant Analysis vs. 

shrinkage Linear Discriminant Analysis (1 discriminative feature)')

plt.show()

核心函数：

		X, y = generate_data(n_train, n_features)
    clf1 <span class="token operator">=</span> LinearDiscriminantAnalysis<span class="token punctuation">(</span>solver<span class="token operator">=</span><span class="token string">'lsqr'</span><span class="token punctuation">,</span> shrinkage<span class="token operator">=</span><span class="token string">'auto'</span><span class="token punctuation">)</span><span class="token punctuation">.</span>fit<span class="token punctuation">(</span>X<span class="token punctuation">,</span> y<span class="token punctuation">)</span>
    clf2 <span class="token operator">=</span> LinearDiscriminantAnalysis<span class="token punctuation">(</span>solver<span class="token operator">=</span><span class="token string">'lsqr'</span><span class="token punctuation">,</span> shrinkage<span class="token operator">=</span><span class="token boolean">None</span><span class="token punctuation">)</span><span class="token punctuation">.</span>fit<span class="token punctuation">(</span>X<span class="token punctuation">,</span> y<span class="token punctuation">)</span>

    X<span class="token punctuation">,</span> y <span class="token operator">=</span> generate_data<span class="token punctuation">(</span>n_test<span class="token punctuation">,</span> n_features<span class="token punctuation">)</span>
    score_clf1 <span class="token operator">+=</span> clf1<span class="token punctuation">.</span>score<span class="token punctuation">(</span>X<span class="token punctuation">,</span> y<span class="token punctuation">)</span>
    score_clf2 <span class="token operator">+=</span> clf2<span class="token punctuation">.</span>score<span class="token punctuation">(</span>X<span class="token punctuation">,</span> y<span class="token punctuation">)</span>