machine-learning
  • 機器學習:使用Python
    • 簡介Scikit-learn 機器學習
  • 分類法 Classification
    • Ex 1: Recognizing hand-written digits
    • EX 2: Normal and Shrinkage Linear Discriminant Analysis for classification
    • EX 3: Plot classification probability
    • EX 4: Classifier Comparison
    • EX 5: Linear and Quadratic Discriminant Analysis with confidence ellipsoid
  • 特徵選擇 Feature Selection
    • Ex 1: Pipeline Anova SVM
    • Ex 2: Recursive Feature Elimination
    • Ex 3: Recursive Feature Elimination with Cross-Validation
    • Ex 4: Feature Selection using SelectFromModel
    • Ex 5: Test with permutations the significance of a classification score
    • Ex 6: Univariate Feature Selection
    • Ex 7: Comparison of F-test and mutual information
  • 互分解 Cross Decomposition
  • 通用範例 General Examples
    • Ex 1: Plotting Cross-Validated Predictions
    • Ex 2: Concatenating multiple feature extraction methods
    • Ex 3: Isotonic Regression
    • Ex 4: Imputing missing values before building an estimator
    • Ex 5: ROC Curve with Visualization API
    • Ex 7: Face completion with a multi-output estimators
  • 群聚法 Clustering
    • EX 1: Feature_agglomeration.md
    • EX 2: Mean-shift 群聚法.md
    • EX 6: 以群聚法切割錢幣影像.md
    • EX 10:_K-means群聚法
    • EX 12: Spectral clustering for image segmentation
    • Plot Hierarchical Clustering Dendrogram
  • 支持向量機
    • EX 1:Non_linear_SVM.md
    • [EX 4: SVM_with _custom _kernel.md](SVM/EX4_SVM_with _custom _kernel.md)
  • 機器學習資料集 Datasets
    • Ex 1: The digits 手寫數字辨識
    • Ex 2: Plot randomly generated classification dataset 分類數據集
    • Ex 3: The iris 鳶尾花資料集
    • Ex 4: Plot randomly generated multilabel dataset 多標籤數據集
  • 應用範例 Application
    • 用特徵臉及SVM進行人臉辨識實例
    • 維基百科主要的特徵向量
    • 波士頓房地產雲端評估(一)
    • 波士頓房地產雲端評估(二)
  • 類神經網路 Neural_Networks
    • Ex 1: Visualization of MLP weights on MNIST
    • Ex 2: Restricted Boltzmann Machine features for digit classification
    • Ex 3: Compare Stochastic learning strategies for MLPClassifier
    • Ex 4: Varying regularization in Multi-layer Perceptron
  • 決策樹 Decision_trees
    • Ex 1: Decision Tree Regression
    • Ex 2: Multi-output Decision Tree Regression
    • Ex 3: Plot the decision surface of a decision tree on the iris dataset
    • Ex 4: Understanding the decision tree structure
  • 機器學習:使用 NVIDIA JetsonTX2
    • 從零開始
    • 讓 TX2 動起來
    • 安裝OpenCV
    • 安裝TensorFlow
  • 廣義線性模型 Generalized Linear Models
    • Ex 3: SGD: Maximum margin separating hyperplane
  • 模型選擇 Model Selection
    • Ex 3: Plotting Validation Curves
    • Ex 4: Underfitting vs. Overfitting
  • 半監督式分類法 Semi-Supervised Classification
    • Ex 3: Label Propagation digits: Demonstrating performance
    • Ex 4: Label Propagation digits active learning
    • Decision boundary of label propagation versus SVM on the Iris dataset
  • Ensemble_methods
    • IsolationForest example
  • Miscellaneous_examples
    • Multilabel classification
  • Nearest_Neighbors
    • Nearest Neighbors Classification
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  • (一)引入函式庫
  • (二)SVM Model
  • (三)完整程式碼

支持向量機

PreviousPlot Hierarchical Clustering DendrogramNext[EX 4: SVM_with _custom _kernel.md](SVM/EX4_SVM_with _custom _kernel.md)

Last updated 6 years ago

此範例是展示如何使用 RBF Kernel 之非線性 SVC 去做二元分類,去預測出 XOR 的輸入分佈並用 Color Map 去繪製出分類的決策邊界及區域。

(一)引入函式庫

引入函式如下:

  1. numpy : 產生陣列數值

  2. matplotlib.pyplot : 用來繪製影像

  3. sklearn.svm : SVM 支持向量機之演算法物件

import numpy as np
import matplotlib.pyplot as plt
from sklearn import svm
xx, yy = np.meshgrid(np.linspace(-3, 3, 500),
                     np.linspace(-3, 3, 500))
np.random.seed(0)
X = np.random.randn(300, 2)
Y = np.logical_xor(X[:, 0] > 0, X[:, 1] > 0)

利用np.meshgrid生成網格採樣點,再利用np.random.randn()產生隨機的資料點X,接著利用np.logical_xor對隨機生成之資料點做 xor 的分類產生Y。

(二)SVM Model

# fit the model
clf = svm.NuSVC()
clf.fit(X, Y)

svm.NuSVC: 與 svm.SVC 類似,但是多了可以控制支持向量(Support Vector)個數之參數

# plot the decision function for each datapoint on the grid
Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)

plt.imshow(Z, interpolation='nearest',
           extent=(xx.min(), xx.max(), yy.min(), yy.max()), aspect='auto',
           origin='lower', cmap=plt.cm.PuOr_r)
contours = plt.contour(xx, yy, Z, levels=[0], linewidths=2,
                       linetypes='--')
plt.scatter(X[:, 0], X[:, 1], s=30, c=Y, cmap=plt.cm.Paired,
            edgecolors='k')
plt.xticks(())
plt.yticks(())
plt.axis([-3, 3, -3, 3])
plt.show()

最後繪製出非線性之決策邊界及資料點分布位置,繪圖方式可參考 EX7: SVM-Kernels 之解說。

下方為非線性分割之結果圖 :

(三)完整程式碼

Python source code: plot_svm_nonlinear.py

iPython source code: plot_svm_nonlinear.ipynb

"""
==============
Non-linear SVM
==============

Perform binary classification using non-linear SVC
with RBF kernel. The target to predict is a XOR of the
inputs.

The color map illustrates the decision function learned by the SVC.
"""
print(__doc__)

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

xx, yy = np.meshgrid(np.linspace(-3, 3, 500),
                     np.linspace(-3, 3, 500))
np.random.seed(0)
X = np.random.randn(300, 2)
Y = np.logical_xor(X[:, 0] > 0, X[:, 1] > 0)

# fit the model
clf = svm.NuSVC()
clf.fit(X, Y)

# plot the decision function for each datapoint on the grid
Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)

plt.imshow(Z, interpolation='nearest',
           extent=(xx.min(), xx.max(), yy.min(), yy.max()), aspect='auto',
           origin='lower', cmap=plt.cm.PuOr_r)
contours = plt.contour(xx, yy, Z, levels=[0], linewidths=2,
                       linetypes='--')
plt.scatter(X[:, 0], X[:, 1], s=30, c=Y, cmap=plt.cm.Paired,
            edgecolors='k')
plt.xticks(())
plt.yticks(())
plt.axis([-3, 3, -3, 3])
plt.show()

https://scikit-learn.org/stable/auto_examples/svm/plot_svm_nonlinear.html#sphx-glr-auto-examples-svm-plot-svm-nonlinear-py
https://scikit-learn.org/stable/_downloads/plot_svm_nonlinear.py
https://scikit-learn.org/stable/_downloads/plot_svm_nonlinear.ipynb
Non-linear