【one vs one】基于svm的二分类器实现多分类

你的名字 2023-01-21 15:23 299阅读 0赞

### 文章目录 ###

*  一、教案版本代码解析
 *   *  1、整体代码
     *  2、逐段分析
     *   *  （1）输入可视化
         *  （2） train\_OvO分段解析
         *  （3）test\_OvO 分段解析
         *  （4）score\_svm函数解析
 *  二、20-21题，加入score\_svm后的分类
 *   *  1、整体代码
     *  2、逐段解析
     *   *  （1）test\_OvO分析
         *  （2）对我作出的更改进行测试

# 一、教案版本代码解析 #

## 1、整体代码 ##

import numpy as np
    from sklearn.svm import LinearSVC
    from sklearn.datasets import load_digits
    from sklearn.model_selection import train_test_split
    from sklearn.metrics import confusion_matrix
    import matplotlib.pyplot as plt
    import numpy as np
    import scipy as sp
    import warnings
    
    warnings.filterwarnings('ignore')
    
    
    # unit test utilities: you can ignore these function
    def is_approximately_equal(test, target, eps=1e-2):
        return np.mean(np.fabs(np.array(test) - np.array(target))) < eps
    
    
    def assert_test_equality(test, target):
        assert is_approximately_equal(test, target), 'Expected:\n %s \nbut got:\n %s' % (target, test)
    
    
    def train_svm(X_train, y_train, param):
        est = LinearSVC(C=param).fit(X_train, y_train)
        return est
    
    
    def test_svm(X_test, est):
        return est.predict(X_test)
    
    
    def score_svm(X_test, est):
        return est.decision_function(X_test)
    
    
    def train_OvO(X_train, y_train, train_func, param):
        classes = sorted(set(y_train))
        print("classes:", classes)
        estimators = dict()
        for i, ci in enumerate(classes):
            print('-' * 20)
            print("i, ci:", i, ci)
            for j, cj in enumerate(classes):
                print('-' * 7)
                print("j, cj:", j, cj)
                if j > i:
                    X = X_train.copy()
                    X = X[np.logical_or(y_train == ci, y_train == cj)]
                    print("np.logical_or(y_train == ci, y_train == cj):", np.logical_or(y_train == ci, y_train == cj))
                    print("X:", X)
                    y = y_train.copy()
                    y = y[np.logical_or(y_train == ci, y_train == cj)]
                    print("y:", y)
                    yp = y.copy()
                    yp[y == ci] = 1
                    yp[y == cj] = -1
                    print("yp:", yp)
                    est = train_func(X, yp, param)
                    estimators[(i, j)] = est
        return estimators
    
    
    def test_OvO(X_test, test_func, estimators):
        print("len(estimators):", len(estimators))
        all_scores = np.zeros((X_test.shape[0], len(estimators)))
        print("all_scores.shape:", all_scores.shape)
        for i, j in estimators:
            est = estimators[(i, j)]
            preds = test_func(X_test, est)
            print("preds:", preds)
            print("i:", i)
            print("preds == 1:", preds == 1)
            print('all_scores:', all_scores)
            all_scores[:, i][preds == 1] += 1
            print('all_scores:', all_scores)
            print('j:', j)
            print('preds == -1:', preds == -1)
            all_scores[:, j][preds == -1] += 1
            print('all_scores:', all_scores)
        # 为什么这里是以横轴判断类别。说明每一样代表一个X_test。
        preds = np.argmax(all_scores, axis=1)
        return preds
    
    
    # This cell is reserved for the unit tests. Do not consider this cell.
    ### BEGIN TESTS
    X_train = np.array([[10, 10], [8, 10], [-5, 5.5], [-5.4, 5.5], [-20, -20], [-15, -20]])
    y_train = np.array([0, 0, 1, 1, 2, 2])
    X_test = np.array([[11, 11], [-5, 5], [-15, -15]])
    y_test = np.array([0, 1, 2])
    # plt.scatter(X_train[:, 0], X_train[:, 1])
    # plt.show()
    est = train_OvO(X_train, y_train, train_svm, param=1)
    # print(est)
    print('=' * 40)
    preds = test_OvO(X_test, test_svm, est)
    print("preds:", preds)
    test_cm = confusion_matrix(y_test, preds)
    # print(test_cm)
    target_cm = np.eye(3)
    assert_test_equality(target_cm, test_cm)
    ### END TESTS
    
    print('-' * 50)
    for i, j in est:
        print(score_svm(X_test, est[(i, j)]))

*  控制台输出

classes: [0, 1, 2]
    --------------------
    i, ci: 0 0
    -------
    j, cj: 0 0
    -------
    j, cj: 1 1
    np.logical_or(y_train == ci, y_train == cj): [ True  True  True  True False False]
    X: [[10.  10. ]
     [ 8.  10. ]
     [-5.   5.5]
     [-5.4  5.5]]
    y: [0 0 1 1]
    yp: [ 1  1 -1 -1]
    -------
    j, cj: 2 2
    np.logical_or(y_train == ci, y_train == cj): [ True  True False False  True  True]
    X: [[ 10.  10.]
     [  8.  10.]
     [-20. -20.]
     [-15. -20.]]
    y: [0 0 2 2]
    yp: [ 1  1 -1 -1]
    --------------------
    i, ci: 1 1
    -------
    j, cj: 0 0
    -------
    j, cj: 1 1
    -------
    j, cj: 2 2
    np.logical_or(y_train == ci, y_train == cj): [False False  True  True  True  True]
    X: [[ -5.    5.5]
     [ -5.4   5.5]
     [-20.  -20. ]
     [-15.  -20. ]]
    y: [1 1 2 2]
    yp: [ 1  1 -1 -1]
    --------------------
    i, ci: 2 2
    -------
    j, cj: 0 0
    -------
    j, cj: 1 1
    -------
    j, cj: 2 2
    ========================================
    len(estimators): 3
    all_scores.shape: (3, 3)
    preds: [ 1 -1 -1]
    i: 0
    preds == 1: [ True False False]
    all_scores: [[0. 0. 0.]
     [0. 0. 0.]
     [0. 0. 0.]]
    all_scores: [[1. 0. 0.]
     [0. 0. 0.]
     [0. 0. 0.]]
    j: 1
    preds == -1: [False  True  True]
    all_scores: [[1. 0. 0.]
     [0. 1. 0.]
     [0. 1. 0.]]
    preds: [ 1  1 -1]
    i: 0
    preds == 1: [ True  True False]
    all_scores: [[1. 0. 0.]
     [0. 1. 0.]
     [0. 1. 0.]]
    all_scores: [[2. 0. 0.]
     [1. 1. 0.]
     [0. 1. 0.]]
    j: 2
    preds == -1: [False False  True]
    all_scores: [[2. 0. 0.]
     [1. 1. 0.]
     [0. 1. 1.]]
    preds: [ 1  1 -1]
    i: 1
    preds == 1: [ True  True False]
    all_scores: [[2. 0. 0.]
     [1. 1. 0.]
     [0. 1. 1.]]
    all_scores: [[2. 1. 0.]
     [1. 2. 0.]
     [0. 1. 1.]]
    j: 2
    preds == -1: [False False  True]
    all_scores: [[2. 1. 0.]
     [1. 2. 0.]
     [0. 1. 2.]]
    preds: [0 1 2]
    --------------------------------------------------
    [ 1.45548543 -0.97524791 -2.01288786]
    [ 1.20241692  0.06646526 -1.62537764]
    [ 0.57513497  0.93275666 -0.74550495]
    
    Process finished with exit code 0

## 2、逐段分析 ##

### （1）输入可视化 ###

# This cell is reserved for the unit tests. Do not consider this cell.
    ### BEGIN TESTS
    X_train = np.array([[10, 10], [8, 10], [-5, 5.5], [-5.4, 5.5], [-20, -20], [-15, -20]])
    y_train = np.array([0, 0, 1, 1, 2, 2])
    X_test = np.array([[11, 11], [-5, 5], [-15, -15]])
    y_test = np.array([0, 1, 2])
    plt.scatter(X_train[:, 0], X_train[:, 1], color="r")
    plt.scatter(X_test[:, 0], X_test[:, 1], color="b")
    plt.show()

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L21pcmFjbGVvYQ_size_16_color_FFFFFF_t_70]  
\- 从输入可以看出训练集和测试集不同标签分得很开，能够很好分类

### （2） train\_OvO分段解析 ###

def train_OvO(X_train, y_train, train_func, param):
        classes = sorted(set(y_train))
        print("classes:", classes)
        estimators = dict()
        for i, ci in enumerate(classes):
            print('-' * 20)
            print("i, ci:", i, ci)
            for j, cj in enumerate(classes):
                print('-' * 7)
                print("j, cj:", j, cj)
                if j > i:
                    X = X_train.copy()
                    X = X[np.logical_or(y_train == ci, y_train == cj)]
                    print("np.logical_or(y_train == ci, y_train == cj):", np.logical_or(y_train == ci, y_train == cj))
                    print("X:", X)
                    y = y_train.copy()
                    y = y[np.logical_or(y_train == ci, y_train == cj)]
                    print("y:", y)
                    yp = y.copy()
                    yp[y == ci] = 1
                    yp[y == cj] = -1
                    print("yp:", yp)
                    est = train_func(X, yp, param)
                    estimators[(i, j)] = est
        return estimators
    
    
    est = train_OvO(X_train, y_train, train_svm, param=1)

*  输出

可以看出遍历了i，j的所有情况，每一个i和j都代表了一种类别，对i和j进行分类的过程就是一个二分类的过程。这样每一对（i，j）都产生了一个分类器 C i C\_i Ci。返回值estimators就是一个key为（i，j），value为 C i C\_i Ci的字典。

### （3）test\_OvO 分段解析 ###

def test_OvO(X_test, test_func, estimators):
        print("len(estimators):", len(estimators))
        all_scores = np.zeros((X_test.shape[0], len(estimators)))
        print("all_scores.shape:", all_scores.shape)
        for i, j in estimators:
            est = estimators[(i, j)]
            preds = test_func(X_test, est)
            print("preds:", preds)
            print("i:", i)
            print("preds == 1:", preds == 1)
            print('all_scores:', all_scores)
            all_scores[:, i][preds == 1] += 1
            print('all_scores:', all_scores)
            print('j:', j)
            print('preds == -1:', preds == -1)
            all_scores[:, j][preds == -1] += 1
            print('all_scores:', all_scores)
        # 为什么这里是以横轴判断类别。说明每一样代表一个X_test。
        preds = np.argmax(all_scores, axis=1)
        return preds
    
    
    preds = test_OvO(X_test, test_svm, est)

*  输出

len(estimators): 3
    all_scores.shape: (3, 3)
    preds: [ 1 -1 -1]
    i: 0
    preds == 1: [ True False False]
    all_scores: [[0. 0. 0.]
     [0. 0. 0.]
     [0. 0. 0.]]
    all_scores: [[1. 0. 0.]
     [0. 0. 0.]
     [0. 0. 0.]]
    j: 1
    preds == -1: [False  True  True]
    all_scores: [[1. 0. 0.]
     [0. 1. 0.]
     [0. 1. 0.]]
    preds: [ 1  1 -1]
    i: 0
    preds == 1: [ True  True False]
    all_scores: [[1. 0. 0.]
     [0. 1. 0.]
     [0. 1. 0.]]
    all_scores: [[2. 0. 0.]
     [1. 1. 0.]
     [0. 1. 0.]]
    j: 2
    preds == -1: [False False  True]
    all_scores: [[2. 0. 0.]
     [1. 1. 0.]
     [0. 1. 1.]]
    preds: [ 1  1 -1]
    i: 1
    preds == 1: [ True  True False]
    all_scores: [[2. 0. 0.]
     [1. 1. 0.]
     [0. 1. 1.]]
    all_scores: [[2. 1. 0.]
     [1. 2. 0.]
     [0. 1. 1.]]
    j: 2
    preds == -1: [False False  True]
    all_scores: [[2. 1. 0.]
     [1. 2. 0.]
     [0. 1. 2.]]
    preds: [0 1 2]
    --------------------------------------------------
    [ 1.45548543 -0.97524791 -2.01288786]
    [ 1.20241692  0.06646526 -1.62537764]
    [ 0.57513497  0.93275666 -0.74550495]
    
    Process finished with exit code 0

这一段解释了test\_OvO是如何工作的，首先构造了all\_scores为一个行数为输入测试集的个数，列数为分类器字典中，分类器的总数。这意味着，每一个分类器都会对每一个输入进行一次分类，对分类结果累加，最后得到一个分类矩阵。最后对分类矩阵按行求最大值的下标，就得到了每个输入的预测分类。

### （4）score\_svm函数解析 ###

print('-' * 50)
    for i, j in est:
        print(score_svm(X_test, est[(i, j)]))

*  输出

[ 1.45548543 -0.97524791 -2.01288786]
    [ 1.20241692  0.06646526 -1.62537764]
    [ 0.57513497  0.93275666 -0.74550495]

此处score\_svm的输出为（i，j）之间的距离，对于三种分类器

# 二、20-21题，加入score\_svm后的分类 #

![在这里插入图片描述][2021051710001425.png]  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L21pcmFjbGVvYQ_size_16_color_FFFFFF_t_70 1]  
根据上面老师的解释，这一题的关键是要解决在使用test\_svm函数得到得结果矩阵如果在一行中，出现了两个一样大得最大数值后，要使用score\_svm来区分谁最优。这里就构造一个一样维度的结果矩阵

## 1、整体代码 ##

import numpy as np
    from sklearn.svm import LinearSVC
    from sklearn.datasets import load_digits
    from sklearn.model_selection import train_test_split
    from sklearn.metrics import confusion_matrix
    import matplotlib.pyplot as plt
    import numpy as np
    import scipy as sp
    import warnings
    
    warnings.filterwarnings('ignore')
    
    
    # unit test utilities: you can ignore these function
    def is_approximately_equal(test, target, eps=1e-2):
        return np.mean(np.fabs(np.array(test) - np.array(target))) < eps
    
    
    def assert_test_equality(test, target):
        assert is_approximately_equal(test, target), 'Expected:\n %s \nbut got:\n %s' % (target, test)
    
    
    def train_svm(X_train, y_train, param):
        est = LinearSVC(C=param).fit(X_train, y_train)
        return est
    
    
    def test_svm(X_test, est):
        return est.predict(X_test)
    
    
    def score_svm(X_test, est):
        return est.decision_function(X_test)
    
    
    def train_OvO(X_train, y_train, train_func, param):
        classes = sorted(set(y_train))
        estimators = dict()
        for i, ci in enumerate(classes):
            for j, cj in enumerate(classes):
                if j > i:
                    X = X_train.copy()
                    X = X[np.logical_or(y_train == ci, y_train == cj)]
                    y = y_train.copy()
                    y = y[np.logical_or(y_train == ci, y_train == cj)]
                    yp = y.copy()
                    yp[y == ci] = 1
                    yp[y == cj] = -1
                    est = train_func(X, yp, param)
                    estimators[(i, j)] = est
        return estimators
    
    
    def test_OvO(X_test, test_func, score_func, estimators):
        all_scores = np.zeros((X_test.shape[0], len(estimators)))
        score_m = np.zeros((X_test.shape[0], len(estimators)))
        for i, j in estimators:
            est = estimators[(i, j)]
            preds = test_func(X_test, est)
            # the result of score_func
            preds_s = score_func(X_test, est)
    
            all_scores[:, i][preds == 1] += 1
            score_m[:, i][preds > 0] += preds_s[preds_s > 0]
            all_scores[:, j][preds == -1] += 1
            score_m[:, j][preds < 0] += preds_s[preds_s < 0]
        print("all_scores:\n", all_scores)
        print("score_m:\n",score_m)
    
        print("preds:\n", preds)
        # When two or more classifiers end in a tie, use score_func to break the tie
        preds = np.argmax(all_scores, axis=1)
        # judge whether two or more classifiers end in a tie
        for i in range(len(preds)):
            all_scores_sort = sorted(all_scores[i])
            # use score_func to break the tie
            if all_scores_sort[-1] == all_scores_sort[-2]:
                preds[i] = np.argmax(score_m, axis=1)[i]
        print("preds:\n", preds)
    
        return preds
    
    
    # This cell is reserved for the unit tests. Do not consider this cell.
    ### BEGIN TESTS
    X_train = np.array([[10, 10], [8, 10], [-5, 5.5], [-5.4, 5.5], [-20, -20], [-15, -20]])
    y_train = np.array([0, 0, 1, 1, 2, 2])
    X_test = np.array([[11, 11], [-5, 5], [-15, -15]])
    y_test = np.array([0, 1, 2])
    est = train_OvO(X_train, y_train, train_svm, param=1)
    preds = test_OvO(X_test, test_svm, score_svm, est)
    test_cm = confusion_matrix(y_test, preds)
    target_cm = np.eye(3)
    assert_test_equality(target_cm, test_cm)
    ### END TESTS

*  输出

all_scores:
     [[2. 1. 0.]
     [1. 2. 0.]
     [0. 1. 2.]]
    score_m:
     [[ 2.65790263  0.57513497  0.        ]
     [ 0.06646526 -0.04249243  0.        ]
     [ 0.         -2.0128883  -2.3708826 ]]
    preds:
     [ 1  1 -1]
    preds:
     [0 1 2]
    
    Process finished with exit code 0

## 2、逐段解析 ##

### （1）test\_OvO分析 ###

def test_OvO(X_test, test_func, score_func, estimators):
        all_scores = np.zeros((X_test.shape[0], len(estimators)))
        score_m = np.zeros((X_test.shape[0], len(estimators)))
        for i, j in estimators:
            est = estimators[(i, j)]
            preds = test_func(X_test, est)
            # the result of score_func
            preds_s = score_func(X_test, est)
    
            all_scores[:, i][preds == 1] += 1
            score_m[:, i][preds > 0] += preds_s[preds_s > 0]
            all_scores[:, j][preds == -1] += 1
            score_m[:, j][preds < 0] += preds_s[preds_s < 0]
        print("all_scores:\n", all_scores)
        print("score_m:\n",score_m)
    
        print("preds:\n", preds)
        # When two or more classifiers end in a tie, use score_func to break the tie
        preds = np.argmax(all_scores, axis=1)
        # judge whether two or more classifiers end in a tie
        for i in range(len(preds)):
            all_scores_sort = sorted(all_scores[i])
            # use score_func to break the tie
            if all_scores_sort[-1] == all_scores_sort[-2]:
                preds[i] = np.argmax(score_m, axis=1)[i]
        print("preds:\n", preds)
    
        return preds
    
    
    preds = test_OvO(X_test, test_svm, score_svm, est)

*  输出

all_scores:
     [[2. 1. 0.]
     [1. 2. 0.]
     [0. 1. 2.]]
    score_m:
     [[ 2.65790263  0.57513497  0.        ]
     [ 0.06646526 -0.04249243  0.        ]
     [ 0.         -2.0128883  -2.3708826 ]]
    preds:
     [ 1  1 -1]
    preds:
     [0 1 2]

由于train\_OvO没有改变故而这里不讲。接着本节开始的分析，对test\_func, score\_func分别构造了矩阵 all\_scores，score\_m用于存取分类器的结果。代码中`score_m[:, i][preds > 0] += preds_s[preds_s > 0]`意思是取出score\_func输出的结果大于零的部分相加。矩阵 all\_scores，score\_m的构造过程相同。得到的结果如上面输出所示，可以发现score\_m其实就是更加精细化输出的all\_scores。代码的最后部分，判断了all\_scores每一行中，最大的两个数是否相同，如果相同，就使用score\_m矩阵得最优解。

### （2）对我作出的更改进行测试 ###

import numpy as np
    
    all_scores = np.array([
        [0, 2, 1],
        [1, 1, 0],
        [2, 0, 2]
    ])
    
    score_m = np.array([
        [0, 2.1, 1.2],
        [1.6, 1.3, 0],
        [2.1, 0, 2.9]
    ])
    
    preds = np.argmax(all_scores, axis=1)
    print('preds:', preds)
    
    for i in range(len(preds)):
        print('all_scores[i]:', all_scores[i])
        all_scores_sort = sorted(all_scores[i])
        print('all_scores_sort:', all_scores_sort)
        if all_scores_sort[-1] == all_scores_sort[-2]:
            preds[i] = np.argmax(score_m, axis=1)[i]
    
    print('preds:', preds)

*  输出

preds: [1 0 0]
    all_scores[i]: [0 2 1]
    all_scores_sort: [0, 1, 2]
    all_scores[i]: [1 1 0]
    all_scores_sort: [0, 1, 1]
    all_scores[i]: [2 0 2]
    all_scores_sort: [0, 2, 2]
    preds: [1 0 2]

分析我给出的矩阵 all\_scores，score\_m，all\_scores中第二行和第三行有相同的值，得到的预测是`preds: [1 0 0]`，再判断all\_scores中每一行，最大的两个数是否相同，如果相同，就使用score\_m矩阵得最优解。最后矫正之后的预测为`preds: [1 0 2]`，可见，算法可行。

[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L21pcmFjbGVvYQ_size_16_color_FFFFFF_t_70]: /images/20221020/242ac9e521ed4e9095edfaa1a40b76d3.png
[2021051710001425.png]: /images/20221020/f15e78ff3484402f8745743fe7eb8454.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L21pcmFjbGVvYQ_size_16_color_FFFFFF_t_70 1]: /images/20221020/870c8cea01d644fe8b057bbaa45224aa.png