《統計學習方法》第 2 章 感知機

源碼地址：pypi.org/project/slm…

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import make_classification
%matplotlib inline
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生成數據

# X 爲樣本特徵，y 爲樣本類別輸出，共 30 個樣本，每一個樣本 2 個特
# 輸出有 2 個類別，沒有冗餘特徵，每一個類別一個簇，隨機狀態爲小武小久
X, y = make_classification(n_samples=40,
                           n_features=2,
                           n_informative=2,
                           n_redundant=0,
                           n_classes=2,
                           n_clusters_per_class=1,
                           random_state=59)
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處理 y 值，取值爲範圍 {-1, 1}

y = np.array([1 if i == 1 else -1 for i in y])
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X
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array([[ 1.26654361,  1.20833252],
       [ 2.06535223, -2.13177734],
       [ 0.11811139,  0.76083319],
       [ 0.90184139, -0.93177662],
       [ 0.96240122, -0.99933393],
       [ 0.32421018, -0.79732491],
       [ 0.16465073, -0.67426018],
       [-0.8393532 ,  0.02946355],
       [ 1.50737475, -1.62701845],
       [ 1.81169336, -1.46844229],
       [ 2.63399788,  0.97604937],
       [ 1.59518059, -1.52110826],
       [ 1.74505037,  1.46262955],
       [ 1.86201667,  0.93060442],
       [ 0.11905276, -0.52595242],
       [ 1.48508147, -0.97794231],
       [-0.92705557,  0.39367018],
       [ 3.42983834, -2.72193889],
       [ 1.99481682,  1.60244273],
       [ 2.59197055,  1.29968242],
       [ 1.60598522, -1.13518763],
       [ 1.52118196,  1.12174498],
       [ 0.13097699, -0.58481754],
       [ 0.84318571,  0.65777867],
       [ 1.0940501 , -0.02064728],
       [ 0.36579428,  1.32704784],
       [ 1.46113021,  1.11893705],
       [ 0.42126239, -0.25448586],
       [ 0.97213672,  0.63569881],
       [ 0.81731191,  0.7569019 ],
       [ 1.85348049, -1.36379487],
       [ 0.81830809,  0.89762419],
       [ 0.9559071 , -1.13200362],
       [ 1.19788365,  0.24486292],
       [ 0.43394253,  1.2190042 ],
       [ 0.75245696, -1.00391468],
       [ 0.26120942, -0.49444024],
       [ 0.23915671,  1.72744475],
       [ 1.33104015,  1.73132756],
       [ 2.37528241,  1.47588251]])
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y
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array([ 1, -1,  1, -1, -1, -1, -1, -1, -1, -1,  1, -1,  1,  1, -1, -1, -1,
       -1,  1,  1, -1,  1, -1,  1,  1,  1,  1, -1,  1,  1, -1,  1, -1,  1,
        1, -1, -1,  1,  1,  1])
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plt.scatter(X[:, 0], X[:, 1], c=y, s=40, marker='o')
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<matplotlib.collections.PathCollection at 0x129908d68>
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sklearn 裏面的 Perceptron

from sklearn.linear_model import Perceptron
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clf = Perceptron(fit_intercept=True, max_iter=1000, shuffle=False)
clf.fit(X, y)
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Perceptron(alpha=0.0001, class_weight=None, early_stopping=False, eta0=1.0,
           fit_intercept=True, max_iter=1000, n_iter_no_change=5, n_jobs=None,
           penalty=None, random_state=0, shuffle=False, tol=0.001,
           validation_fraction=0.1, verbose=0, warm_start=False)
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# Weights 權重（值）
print(clf.coef_)
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[[2.06165026 2.89632885]]
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# bias 截距
print(clf.intercept_)
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[-1.]
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plt.scatter(X[:, 0], X[:, 1], c=y, s=40, marker='o')

minX = np.min(X[:, 0])
maxX = np.max(X[:, 0])
x_points = np.array([minX, maxX])

sklearn_y = -(clf.coef_[0][0] * x_points + clf.intercept_) / clf.coef_[0][1]
plt.plot(x_points, sklearn_y, 'b-.', label='sklearn', linewidth=0.3)
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[<matplotlib.lines.Line2D at 0x12bdbe320>]
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原始感知機

from slmethod.perceptron import Perceptron
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origin_clf = Perceptron(dual=False)
origin_clf.fit(X, y)
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print(origin_clf.w)
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[0.20616503 0.28963289]
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print(origin_clf.b)
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-0.1
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對偶形式

dual_clf = Perceptron(dual=True)
dual_clf.fit(X, y)
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print(dual_clf.w)
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[0.20616503 0.28963289]
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print(dual_clf.b)
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-0.1
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繪圖

plt.scatter(X[:, 0], X[:, 1], c=y, s=40, marker='o')
sklearn_y = -(clf.coef_[0][0] * x_points + clf.intercept_) / clf.coef_[0][1]
origin_y = -(origin_clf.w[0] * x_points + origin_clf.b) / origin_clf.w[1]
dual_y = -(dual_clf.w[0] * x_points + dual_clf.b) / dual_clf.w[1]
plt.plot(x_points, sklearn_y, 'b*', label='sklearn')
plt.plot(x_points, origin_y, 'r.-', label='origin')
plt.plot(x_points, dual_y, 'g-.', label='dual')
plt.legend()
plt.show()
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從上圖能夠看到 sklearn，原始類型和對偶形式的線幾乎重合了。