RBF network

1.radial basis function

RBF表示某种距离，$\mu_m$为中心点，相当于将点$x$到中心点的某种距离作为特征转换

Output方法可以根据需求任意选取（比如使用SVM，logistic regression等）

关键在于：中心点选取，距离函数选择

2.使用kmean选取中心点，后使用logistic regression

import numpy as np
from sklearn.cluster import KMeans
from sklearn.linear_model import LogisticRegression
from matplotlib import pyplot as plt
from sklearn import cross_validation
from sklearn.base import BaseEstimator

class KMeansRBF:
    def __init__(self,n_clusters,beta,C):
        self.n_clusters=n_clusters
        self.beta=beta
        self.C=C

    def fit(self,X,y):
        km = KMeans(n_clusters=self.n_clusters);
        km.fit(X)
        ct = km.cluster_centers_
        self.ct = ct
        G = self._nFeature(ct, X)
        lg=LogisticRegression(C=self.C)
        lg.fit(G,y)
        self.lg=lg

    def predict(self,X):
        G = self._nFeature(self.ct, X)
        return self.lg.predict(G)

    def _nFeature(self,cts,X):
        G = np.zeros((X.shape[0],cts.shape[0]))
        for xi,x in enumerate(X):
            for ci,c in enumerate(cts):
                G[xi,ci] = self._kernal(x, c)
        return G

    def _kernal(self,x1,x2):
        x = x1-x2;
        return np.exp(-self.beta*np.dot(np.transpose(x),x))

    def predict_proba(self,X):
        G = self._nFeature(self.ct, X)
        return self.lg.predict_proba(G)

    def get_params(self, deep=True):
        return {'n_clusters':self.n_clusters,'beta':self.beta,'C':self.C}

    def set_params(self, **parameters):
        for parameter, value in parameters.items():
            setattr(self, parameter, value)

    def plot(self,X,y):
        pos = np.where(y==1)
        neg = np.where(y==-1)

        x1 = X[pos[0],:]
        x2 = X[neg[0],:]

        plt.figure()
        plt.plot(x1[:,0],x1[:,1],'o')
        plt.plot(x2[:,0],x2[:,1],'o')
        plt.plot(self.ct[0,0],self.ct[0,1],'ro')
        plt.plot(self.ct[1,0],self.ct[1,1],'ro')

        xmax = np.max(X[:,0])+5
        xmin = np.min(X[:,0])-5
        ymax = np.max(X[:,1])+5
        ymin = np.min(X[:,1])-5

        numx = int((xmax-xmin)*10)
        numy = int((ymax-ymin)*10)
        total = numx*numy;
        lx = np.linspace(xmin,xmax,numx)
        ly = np.linspace(ymin,ymax,numy)
        mgrid = np.meshgrid(lx,ly)
        px = np.hstack((mgrid[0].reshape(total,1),mgrid[1].reshape(total,1)))
        pre=self.predict_proba(px)
        ind = np.where(abs(pre[:,1]-pre[:,0])<0.01)

        px=px[ind]
        plt.plot(px[:,0],px[:,1],'yo')
        plt.show()
if __name__ == '__main__':
    x1=np.random.normal(10, 6.0, (80,2))
    x2=np.random.normal(-10, 6.0, (80,2))

    X = np.vstack((x1,x2))
    y = np.zeros((160,1))
    y[range(0,80),0]=y[range(0,80),0]+1
    y[range(80,160),0]=y[range(80,160),0]-1
    y=np.ravel(y)

    betas = np.linspace(0.001,0.1,100)
    k = range(100)
    score = np.zeros((100,1),'float')

    bestbeta = 0.001;
    maxscore = -1;
    for i,beta  in enumerate(betas):
        krbf = KMeansRBF(2,beta,1)
        scores =cross_validation.cross_val_score(krbf,X,y,scoring="accuracy",cv=5)
        score[i,0]=scores.mean()
        if score[i,0]>maxscore:
            maxscore=score[i,0]
            bestbeta = beta

    plt.figure()
    plt.plot(k,score,'b-')
    plt.show()
    print bestbeta;
    krbf = KMeansRBF(2,bestbeta,1)
    krbf.fit(X, y)
    krbf.plot(X,y)

3.结果

    gussian中beta的値设置非常关键

由于指数函数增加得很快，所以大的beta値，意味着只有和中心点很近的点才能被判定和中心点为同一类

beta = 1	beta = 0.001