机器学习系列4：进阶算法-SVM

import plotly.plotly as py              # for sending things to plotly
import plotly.tools as tls              # for mpl, config, etc.
from plotly.graph_objs import *         # __all__ is safely defined
import plotly.graph_objs as go
import cufflinks as cf
import pandas as pd
from pandas import Series,DataFrame
import numpy as np
import datetime

py.sign_in('DemoAccount','2qdyfjyr7o')

def get_y1(x):
    return (25-x**2)**0.5
def get_y2(x):
    return (100-x**2)**0.5

symbol = np.random.random(100)

symbol[symbol>0.5] = 1
symbol[symbol<=0.5] = -1
# 添加一点小噪音也没多大的意思
x1 = np.linspace(-5, 5, 100)
x2 = np.linspace(-10, 10, 100)
y1 = []
y2 = []
for x in x1:
    y1.append(get_y1(x))
for x in x2:
    y2.append(get_y2(x))
y1 = np.array(y1)*symbol
y2 = np.array(y2)*symbol

trace0 = go.Scatter(
    x = x1,
    y = y1,
    name = '类别1',
    mode='markers',
    marker=dict(
        size=12,
        line=dict(
            color='rgba(217, 217, 217, 0.14)',
            width=0.5
        ),
        opacity=0.8
    )
)

trace1 = go.Scatter(
    x = x2,
    y = y2,
    name = '类别2',
    mode='markers',
    marker=dict(
        color='rgb(127, 127, 127)',
        size=12,
        symbol='circle',
        line=dict(
            color='rgb(204, 204, 204)',
            width=1
        ),
        opacity=0.9
    )
)

data = [trace0, trace1]

layout = dict(title = '原数据',
              yaxis = dict(zeroline = False),
              xaxis = dict(zeroline = False)
             )

fig = dict(data=data, layout=layout)
py.iplot(fig, filename='原数据集')

# 进行核变换
a1 = x1**2
a2 = y1**2
a3 = y1
b1 = x2**2
b2 = y2**2
b3 = y2

import plotly.plotly as py
import plotly.graph_objs as go
trace1 = go.Scatter3d(
    x=a1,
    y=a2,
    z=a3,
    name = '类别1',
    mode='markers',
    marker=dict(
        size=12,
        line=dict(
            color='rgba(217, 217, 217, 0.14)',
            width=0.5
        ),
        opacity=0.8
    )
)


trace2 = go.Scatter3d(
    x=b1,
    y=b2,
    z=b3,
    name = '类别2',
    mode='markers',
    marker=dict(
        color='rgb(127, 127, 127)',
        size=12,
        symbol='circle',
        line=dict(
            color='rgb(204, 204, 204)',
            width=1
        ),
        opacity=0.9
    )
)
data = [trace1, trace2]
layout = go.Layout(
    margin=dict(
        l=0,
        r=0,
        b=0,
        t=0
    )
)
fig = go.Figure(data=data, layout=layout)
py.iplot(fig, filename='映射后的数据集')

import numpy as np
X = np.array([[-1, -1], [-2, -1], [1, 0], [2, 1]])
y = np.array([1, 1, 0, 2])
from sklearn.svm import SVC
clf = SVC()
clf.fit(X, y) 
print(clf.predict([[-2, -1]]))
print(clf.predict([[1, 0]]))
print(clf.predict([[2, 1]]))

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.colors import ListedColormap
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.datasets import make_moons, make_circles, make_classification
from sklearn.neural_network import MLPClassifier
from sklearn.neighbors import KNeighborsClassifier
from sklearn.svm import SVC
from sklearn.gaussian_process import GaussianProcessClassifier
from sklearn.gaussian_process.kernels import RBF
from sklearn.tree import DecisionTreeClassifier
from sklearn.ensemble import RandomForestClassifier, AdaBoostClassifier
from sklearn.naive_bayes import GaussianNB
from sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis

h = .02  # step size in the mesh

names = ["Nearest Neighbors", "Linear SVM", "RBF SVM"]

classifiers = [
    KNeighborsClassifier(3),
    SVC(kernel="linear", C=0.025),
    SVC(gamma=2, C=1)]

X, y = make_classification(n_features=2, n_redundant=0, n_informative=2,
                           random_state=1, n_clusters_per_class=1)
rng = np.random.RandomState(2)
X += 2 * rng.uniform(size=X.shape)
linearly_separable = (X, y)

datasets = [make_moons(noise=0.3, random_state=0),
            make_circles(noise=0.2, factor=0.5, random_state=1),
            linearly_separable
            ]

figure = plt.figure(figsize=(27, 9))
i = 1
# iterate over datasets
for ds_cnt, ds in enumerate(datasets):
    # preprocess dataset, split into training and test part
    X, y = ds
    X = StandardScaler().fit_transform(X)
    X_train, X_test, y_train, y_test = \
        train_test_split(X, y, test_size=.4, random_state=42)

    x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5
    y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5
    xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
                         np.arange(y_min, y_max, h))

    # just plot the dataset first
    cm = plt.cm.RdBu
    cm_bright = ListedColormap(['#FF0000', '#0000FF'])
    ax = plt.subplot(len(datasets), len(classifiers) + 1, i)
    if ds_cnt == 0:
        ax.set_title("Input data")
    # Plot the training points
    ax.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap=cm_bright)
    # and testing points
    ax.scatter(X_test[:, 0], X_test[:, 1], c=y_test, cmap=cm_bright, alpha=0.6)
    ax.set_xlim(xx.min(), xx.max())
    ax.set_ylim(yy.min(), yy.max())
    ax.set_xticks(())
    ax.set_yticks(())
    i += 1

    # iterate over classifiers
    for name, clf in zip(names, classifiers):
        ax = plt.subplot(len(datasets), len(classifiers) + 1, i)
        clf.fit(X_train, y_train)
        score = clf.score(X_test, y_test)

        # Plot the decision boundary. For that, we will assign a color to each
        # point in the mesh [x_min, x_max]x[y_min, y_max].
        if hasattr(clf, "decision_function"):
            Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()])
        else:
            Z = clf.predict_proba(np.c_[xx.ravel(), yy.ravel()])[:, 1]

        # Put the result into a color plot
        Z = Z.reshape(xx.shape)
        ax.contourf(xx, yy, Z, cmap=cm, alpha=.8)

        # Plot also the training points
        ax.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap=cm_bright)
        # and testing points
        ax.scatter(X_test[:, 0], X_test[:, 1], c=y_test, cmap=cm_bright,
                   alpha=0.6)

        ax.set_xlim(xx.min(), xx.max())
        ax.set_ylim(yy.min(), yy.max())
        ax.set_xticks(())
        ax.set_yticks(())
        if ds_cnt == 0:
            ax.set_title(name)
        ax.text(xx.max() - .3, yy.min() + .3, ('%.2f' % score).lstrip('0'),
                size=15, horizontalalignment='right')
        i += 1

plt.tight_layout()
plt.show()

from itertools import product

import numpy as np
import matplotlib.pyplot as plt

from sklearn import datasets
from sklearn.tree import DecisionTreeClassifier
from sklearn.neighbors import KNeighborsClassifier
from sklearn.svm import SVC
from sklearn.ensemble import VotingClassifier

# Loading some example data
iris = datasets.load_iris()
X = iris.data[:, [0, 2]]
y = iris.target

# Training classifiers
clf1 = DecisionTreeClassifier(max_depth=4)
clf2 = KNeighborsClassifier(n_neighbors=7)
clf3 = SVC(kernel='rbf', probability=True)
eclf = VotingClassifier(estimators=[('dt', clf1), ('knn', clf2),
                                    ('svc', clf3)],
                        voting='soft', weights=[2, 1, 2])

clf1.fit(X, y)
clf2.fit(X, y)
clf3.fit(X, y)
eclf.fit(X, y)

# Plotting decision regions
x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
xx, yy = np.meshgrid(np.arange(x_min, x_max, 0.1),
                     np.arange(y_min, y_max, 0.1))

f, axarr = plt.subplots(2, 2, sharex='col', sharey='row', figsize=(10, 8))

for idx, clf, tt in zip(product([0, 1], [0, 1]),
                        [clf1, clf2, clf3, eclf],
                        ['Decision Tree (depth=4)', 'KNN (k=7)',
                         'Kernel SVM', 'Soft Voting']):

    Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
    Z = Z.reshape(xx.shape)

    axarr[idx[0], idx[1]].contourf(xx, yy, Z, alpha=0.4)
    axarr[idx[0], idx[1]].scatter(X[:, 0], X[:, 1], c=y, alpha=0.8)
    axarr[idx[0], idx[1]].set_title(tt)

plt.show()

import numpy as np
from sklearn.svm import SVR
import matplotlib.pyplot as plt

X = np.sort(5 * np.random.rand(40, 1), axis=0)
y = np.sin(X).ravel()

y[::5] += 3 * (0.5 - np.random.rand(8))

svr_rbf = SVR(kernel='rbf', C=1e3, gamma=0.1)
svr_lin = SVR(kernel='linear', C=1e3)
svr_poly = SVR(kernel='poly', C=1e3, degree=2)
y_rbf = svr_rbf.fit(X, y).predict(X)
y_lin = svr_lin.fit(X, y).predict(X)
y_poly = svr_poly.fit(X, y).predict(X)

lw = 2
plt.scatter(X, y, color='darkorange', label='data')
plt.hold('on')
plt.plot(X, y_rbf, color='navy', lw=lw, label='RBF model')
plt.plot(X, y_lin, color='c', lw=lw, label='Linear model')
plt.plot(X, y_poly, color='cornflowerblue', lw=lw, label='Polynomial model')
plt.xlabel('data')
plt.ylabel('target')
plt.title('Support Vector Regression')
plt.legend()
plt.show()