第二章

1.MED分类器

  • 均值是对类中所有训练样本代表误差最小的一种表达方式

  • MED分类器采用欧式距离作为距离度量，没有考虑特征变化的不同及特征之间的相关性

    1.对角线元素不相等：每维特征的变化不同

    2.非对角元素不为0：特征之间存在相关性

  • 代码

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    def MED(dataset, is_2d=None):
    #     实现MED分类器
        train = dataset['train']
        test = dataset['test']
        target = dataset['target']
        
        train_pos_mean_2d = None
        train_neg_mean_2d = None
    #     画2d图
        if is_2d == True:
            scaler = pre.StandardScaler()
            pca = PCA(n_components=2)
            
            train_2d = copy.deepcopy(train)
            label = train_2d[:, -1]
            
            train_2d = scaler.fit_transform(train_2d[:, :4])
            train_2d = pca.fit_transform(train_2d)
            train_2d = np.c_[train_2d, label]
            
            train_pos = np.array(train_2d[train[:, -1] == target[0]])
            train_neg = np.array(train_2d[train[:, -1] ==  target[1]])
        
            train_pos_mean_2d = np.mean(train_pos[:, :2], axis=0)
            train_neg_mean_2d = np.mean(train_neg[:, :2], axis=0)  
    #     target[0]为正样本，target[1]为负样本
        train_pos = np.array(train[train[:, -1] == target[0]])
        train_neg = np.array(train[train[:, -1] ==  target[1]])
        
        print('positive num:', train_pos.shape)
        print('negative num:', train_neg.shape)
    #     分别取平均
        train_pos_mean = np.mean(train_pos[:, :4], axis=0)
        train_neg_mean = np.mean(train_neg[:, :4], axis=0)    
        
        x_test = test[:, :4]
        y_test = test[:, -1].flatten()
        
        y_pre = np.array([])
        
        for i in range(x_test.shape[0]):
    #         欧氏距离
            dis_pos = (x_test[i] - train_pos_mean).T @ (x_test[i] - train_pos_mean)
            dis_neg = (x_test[i] - train_neg_mean).T @ (x_test[i] - train_neg_mean)
    #         预测
            if dis_pos < dis_neg:
                y_pre = np.append(y_pre, target[0])
            else:
                y_pre = np.append(y_pre, target[1])
    #     准确率  
        acc = (y_pre == y_test.astype(int)).sum() / y_test.shape[0]
        print(acc)
        
        if is_2d == True:
            return train_pos_mean_2d, train_neg_mean_2d
        else:
            return y_test, y_pre

2.特征白化

  • 目的

    image-20210430202044962

  • 步骤

    1.解耦，去除特征之间相关性，即使对角元素为0，矩阵对角化

    2.白化，对特征进行尺度变化，使所有特征具有相同的方差

  • 原始特征投影到协方差矩阵对应的特征向量上，其中每一个特征向量构成一个坐标轴

  • 转换前后欧氏距离保持一致，W1只起到旋转作用

  • 代码

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    def whitening(dataset):
    #     进行特征白化
        data = dataset.data
        print('data shape:', data.shape)
    #     计算协方差矩阵
        cov = np.cov(data, rowvar=False)
        print('cov shape:', cov.shape)
    #     特征值，特征向量
        w, v = np.linalg.eig(cov)
        print('w shape:', w.shape)
        print('v shape:', v.shape)
    #     单位化特征向量
        sum_list = []
        for i in range(v.shape[0]):
            sum = 0.
            for j in range(v.shape[1]):
                sum += v[i][j] * v[i][j]
            sum_list.append(math.sqrt(sum))
        
        for i in range(v.shape[0]):
            for j in range(v.shape[1]):
                v[i][j] /= sum_list[i]
    #     计算W
        W1 = v.T
        print('W1 shape:', W1.shape)
        W2 = np.diag(w ** (-0.5)) 
        print('W2 shape:', W2.shape)
        W = W2 @ W1
        print('W shape:', W.shape)
        data = data @ W
        print('data shape', data.shape)
        
        return data

3.MICD分类器

  • image-20210430204137366

  • 代码有空再补