昨天介紹完Linear Regression，今天要來繼續介紹高斯函數在Linear-Regression的應用。高斯函數本身不是SKlearn中的模組，因此，需要自己編寫一個自訂的高斯函式：

1. 匯入sklearn.base中的估算器BaseEstimator、轉換器TransformerMixin，
2. 自定義GaussianFeatures函數。
   sklearn.base.BaseEstimator詳細可以參考(官方文件)：http://scikit-learn.org/stable/modules/generated/sklearn.base.BaseEstimator.html

from sklearn.base import BaseEstimator, TransformerMixin
from sklearn.linear_model import LinearRegression
from sklearn.pipeline import make_pipeline

class GaussianFeatures(BaseEstimator, TransformerMixin):
    """Uniformly spaced Gaussian features for one-dimensional input"""
    
    def __init__(self, N, width_factor=1.0):
        self.N = N
        self.width_factor = width_factor
    
    @staticmethod
    def _gauss_basis(x, y, width, axis=None):
        arg = (x - y) / width
        return np.exp(-0.5 * np.sum(arg ** 2, axis))
        
    def fit(self, X, y=None):
        # create N centers spread along the data range
        self.centers_ = np.linspace(X.min(), X.max(), self.N)
        self.width_ = self.width_factor * (self.centers_[1] - self.centers_[0])
        return self
        
    def transform(self, X):
        return self._gauss_basis(X[:, :, np.newaxis], self.centers_,
                                 self.width_, axis=1)
    
gauss_model = make_pipeline(GaussianFeatures(20),
                            LinearRegression())
gauss_model.fit(x[:, np.newaxis], y)
yfit = gauss_model.predict(xfit[:, np.newaxis])

plt.scatter(x, y)
plt.plot(xfit, yfit)
plt.xlim(0, 10);

• Lasso regression
  第二種正規化方式，是把第一種方式的回歸係數原本用平方和處理轉換為取絕對值的和，其公式如下：
  ![](https://chart.googleapis.com/chart?cht=tx&chl=P%20%3D%20%5Calpha%5Csum_%7Bn%3D1%7D%5EN%20%7C%5Ctheta_n%7C
  from sklearn.linear_model import Lasso)

model = make_pipeline(GaussianFeatures(25), Lasso(alpha=0.001))
basis_plot(model, title='Lasso Regression')