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   源码介绍

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支持向量机（support vector machine，简称SVM）于1964年由Vapnik和Chervonenkis建立，在上世纪90年代获得快速发展并衍生出一系列改进和扩展算法，在人像识别、文本分类、手写字识别及生物信息学等领域获得广泛应用。

class SMO(object):
    def __init__(self, C = 100, toler = 0.001, maxIter = 10000):
        self.C = C
        self.tol = toler
        self.maxIter = maxIter
            
    def fit(self, X, y):
        self.X, self.y = X, y
        self.n_samples = len(X)
        self.alphas = np.zeros(self.n_samples, dtype = float)
        self.b = 0.
        self.Error = np.zeros_like(self.alphas)
        self.iterNum = 0
        iterNum = 0
        examineAll = True
        alphaChanged = 0
        while iterNum < self.maxIter and (alphaChanged > 0 or examineAll == True):
            alphaChanged = 0
            if examineAll:
                for i in range(len(self.X)): alphaChanged  = self._innerLoop(i)
                iterNum  = 1
                examineAll = False
            else:
                nonBoundInd = np.nonzero((self.alphas > 0) * (self.alphas < self.C))[0]
                for i in nonBoundInd: alphaChanged  = self._innerLoop(i)
                iterNum  = 1
                if alphaChanged == 0: examineAll = True
        self.iterNum = iterNum
        return self

    def _innerLoop(self, i):
        Ei = self.updateError(i)
        if (((Ei * self.y[i] < -self.tol) and (self.alphas[i] < self.C)) or 
            ((Ei * self.y[i] > self.tol) and (self.alphas[i] > 0))):
            j = self.selectJ(i)
            Ej = self.Error[j]
            alphaIold, alphaJold = self.alphas[i], self.alphas[j]
            if self.y[i] != self.y[j]:
                L = max(0, alphaIold - alphaJold)
                H = min(self.C, self.C   alphaIold - alphaJold)
            else:
                L = max(0, alphaJold   alphaIold -self.C)
                H = min(self.C, alphaJold   alphaIold)
            if H == L: return 0
            Kii, Kij, Kjj = (self.K(self.X[i], self.X[i]), self.K(self.X[i], self.X[j]), 
                             self.K(self.X[j], self.X[j]))
            eta = Kii   Kjj - 2 * Kij
            if eta <= 0: return 0
            self.alphas[i]  = self.y[i] * (Ej - Ei)/eta
            if self.alphas[i] <= L: 
                self.alphas[i] = L
            elif self.alphas[i] >= H: 
                self.alphas[i] = H
            if np.abs(self.alphas[i] - alphaIold) < 1.e-10: return 0
            self.alphas[j]  = self.y[j] * self.y[i] * (alphaIold - self.alphas[i])
            b0 = (self.b - Ej - self.y[j] * Kjj * (self.alphas[j] - alphaJold) - 
                  self.y[i] * Kij * (self.alphas[i] - alphaIold))
            b1 = (self.b - Ei - self.y[j] * Kij * (self.alphas[j] - alphaJold) - 
                  self.y[i] * Kii * (self.alphas[i] - alphaIold))
            if 0 < self.alphas[j] < self.C: self.b = b0
            elif 0 < self.alphas[i] < self.C: self.b = b1
            else: self.b = (b0   b1) / 2
            return 1
        else: return 0
            
    def selectJ(self, i):
        j = 0
        maxDeltaE = -1.
        priorIndices = np.nonzero(self.Error)[0]
        if len(priorIndices) > 1:
            for k in priorIndices:
                if k == i: continue
                Ek = self.updateError(k)
                deltaE = np.abs(Ek - self.Error[i])
                if deltaE > maxDeltaE: j, maxDeltaE = k, deltaE
            return j
        else:
            j = np.random.choice([k for k in range(self.n_samples) if k != i])
            self.updateError(j)
            return j
        
    def updateError(self, i):
        fxi = np.sum(self.alphas * self.y * np.array([self.K(self.X[i], self.X[j]) for
                     j in range(self.n_samples)]))   self.b
        self.Error[i] = fxi - self.y[i]
        return self.Error[i]

    def K(self, Xi, Xj):
        return np.sum(Xi * Xj)
    
    def predict(self, testX):
        num = len(testX)
        y_pred = np.ones(num, dtype = int)
        for i in range(num):
            fxi = np.sum(self.alphas * self.y * np.array([self.K(testX[i], self.X[j]) for 
                         j in range(self.n_samples)]))   self.b
            if fxi < 0: y_pred[i] = -1
        return y_pred