4.4编程实现CART

# -*- coding: utf-8 -*

'''''
@author: PY131
'''''
import os
os.environ["PATH"] += os.pathsep + 'D:/python(ruanjian)/Graphviz/bin/'

class Node(object):
    '''
    definition of decision node class

    attr: attribution as parent for a new branching
    attr_down: dict: {key, value}
            key:   categoric:  categoric attr_value
                   continuous: '<= div_value' for small part
                               '> div_value' for big part
            value: children (Node class)
    label： class label (the majority of current sample labels)
    '''

    def __init__(self, attr_init=None, label_init=None, attr_down_init={}):
        self.attr = attr_init
        self.label = label_init
        self.attr_down = attr_down_init


def TreeGenerate(df):
    '''
    Branching for decision tree using recursion

    @param df: the pandas dataframe of the data_set
    @return root: Node, the root node of decision tree
    '''
    # generating a new root node
    new_node = Node(None, None, {})
    label_arr = df[df.columns[-1]]

    label_count = NodeLabel(label_arr)
    if label_count:  # assert the label_count isn's empty
        new_node.label = max(label_count, key=label_count.get)

        # end if there is only 1 class in current node data
        # end if attribution array is empty
        if len(label_count) == 1 or len(label_arr) == 0:
            return new_node

        # get the optimal attribution for a new branching
        new_node.attr, div_value = OptAttr_Gini(df)  # via Gini index

        # recursion
        if div_value == 0:  # categoric variable
            value_count = ValueCount(df[new_node.attr])
            for value in value_count:
                df_v = df[df[new_node.attr].isin([value])]  # get sub set
                # delete current attribution
                df_v = df_v.drop(new_node.attr, 1)
                new_node.attr_down[value] = TreeGenerate(df_v)

        else:  # continuous variable # left and right child
            value_l = "<=%.3f" % div_value
            value_r = ">%.3f" % div_value
            df_v_l = df[df[new_node.attr] <= div_value]  # get sub set
            df_v_r = df[df[new_node.attr] > div_value]

            new_node.attr_down[value_l] = TreeGenerate(df_v_l)
            new_node.attr_down[value_r] = TreeGenerate(df_v_r)

    return new_node


def Predict(root, df_sample):
    '''
    make a predict based on root

    @param root: Node, root Node of the decision tree
    @param df_sample: dataframe, a sample line
    '''
    try:
        import re  # using Regular Expression to get the number in string
    except ImportError:
        print("module re not found")

    while root.attr != None:
        # continuous variable
        if df_sample[root.attr].dtype == float:
            # get the div_value from root.attr_down
            for key in list(root.attr_down):
                num = re.findall(r"\d+\.?\d*", key)
                div_value = float(num[0])
                break
            if df_sample[root.attr].values[0] <= div_value:
                key = "<=%.3f" % div_value
                root = root.attr_down[key]
            else:
                key = ">%.3f" % div_value
                root = root.attr_down[key]

        # categoric variable
        else:
            key = df_sample[root.attr].values[0]
            # check whether the attr_value in the child branch
            if key in root.attr_down:
                root = root.attr_down[key]
            else:
                break

    return root.label


def PredictAccuracy(root, df_test):
    '''
    calculating accuracy of prediction on test set

    @param root: Node, root Node of the decision tree
    @param df_test: dataframe, test data set
    @return accuracy, float,
    '''
    if len(df_test.index) == 0: return 0
    pred_true = 0
    for i in df_test.index:
        label = Predict(root, df_test[df_test.index == i])
        if label == df_test[df_test.columns[-1]][i]:
            pred_true += 1
    return pred_true / len(df_test.index)


def PrePurn(df_train, df_test):
    '''
    pre-purning to generating a decision tree

    @param df_train: dataframe, the training set to generating a tree
    @param df_test: dataframe, the testing set for purning decision
    @return root: Node, root of the tree using purning
    '''
    # generating a new root node
    new_node = Node(None, None, {})
    label_arr = df_train[df_train.columns[-1]]

    label_count = NodeLabel(label_arr)
    if label_count:  # assert the label_count isn's empty
        new_node.label = max(label_count, key=label_count.get)

        # end if there is only 1 class in current node data
        # end if attribution array is empty
        if len(label_count) == 1 or len(label_arr) == 0:
            return new_node

        # calculating the test accuracy up to current node
        a0 = PredictAccuracy(new_node, df_test)

        # get the optimal attribution for a new branching
        new_node.attr, div_value = OptAttr_Gini(df_train)  # via Gini index

        # get the new branch
        if div_value == 0:  # categoric variable
            value_count = ValueCount(df_train[new_node.attr])
            for value in value_count:
                df_v = df_train[df_train[new_node.attr].isin([value])]  # get sub set
                df_v = df_v.drop(new_node.attr, 1)
                # for child node
                new_node_child = Node(None, None, {})
                label_arr_child = df_train[df_v.columns[-1]]
                label_count_child = NodeLabel(label_arr_child)
                new_node_child.label = max(label_count_child, key=label_count_child.get)
                new_node.attr_down[value] = new_node_child

            # calculating to check whether need further branching
            a1 = PredictAccuracy(new_node, df_test)
            if a1 > a0:  # need branching
                for value in value_count:
                    df_v = df_train[df_train[new_node.attr].isin([value])]  # get sub set
                    df_v = df_v.drop(new_node.attr, 1)
                    new_node.attr_down[value] = TreeGenerate(df_v)
            else:
                new_node.attr = None
                new_node.attr_down = {}

        else:  # continuous variable # left and right child
            value_l = "<=%.3f" % div_value
            value_r = ">%.3f" % div_value
            df_v_l = df_train[df_train[new_node.attr] <= div_value]  # get sub set
            df_v_r = df_train[df_train[new_node.attr] > div_value]

            # for child node
            new_node_l = Node(None, None, {})
            new_node_r = Node(None, None, {})
            label_count_l = NodeLabel(df_v_l[df_v_r.columns[-1]])
            label_count_r = NodeLabel(df_v_r[df_v_r.columns[-1]])
            new_node_l.label = max(label_count_l, key=label_count_l.get)
            new_node_r.label = max(label_count_r, key=label_count_r.get)
            new_node.attr_down[value_l] = new_node_l
            new_node.attr_down[value_r] = new_node_r

            # calculating to check whether need further branching
            a1 = PredictAccuracy(new_node, df_test)
            if a1 > a0:  # need branching
                new_node.attr_down[value_l] = TreeGenerate(df_v_l)
                new_node.attr_down[value_r] = TreeGenerate(df_v_r)
            else:
                new_node.attr = None
                new_node.attr_down = {}

    return new_node


def PostPurn(root, df_test):
    '''
    pre-purning to generating a decision tree

    @param root: Node, root of the tree
    @param df_test: dataframe, the testing set for purning decision
    @return accuracy score through traversal the tree
    '''
    # leaf node
    if root.attr == None:
        return PredictAccuracy(root, df_test)

    # calculating the test accuracy on children node
    a1 = 0
    value_count = ValueCount(df_test[root.attr])
    for value in list(value_count):
        df_test_v = df_test[df_test[root.attr].isin([value])]  # get sub set
        if value in root.attr_down:  # root has the value
            a1_v = PostPurn(root.attr_down[value], df_test_v)
        else:  # root doesn't have value
            a1_v = PredictAccuracy(root, df_test_v)
        if a1_v == -1:  # -1 means no pruning back from this child
            return -1
        else:
            a1 += a1_v * len(df_test_v.index) / len(df_test.index)

    # calculating the test accuracy on this node
    node = Node(None, root.label, {})
    a0 = PredictAccuracy(node, df_test)

    # check if need pruning
    if a0 >= a1:
        root.attr = None
        root.attr_down = {}
        return a0
    else:
        return -1


def NodeLabel(label_arr):
    '''
    calculating the appeared label and it's counts

    @param label_arr: data array for class labels
    @return label_count: dict, the appeared label and it's counts
    '''
    label_count = {}  # store count of label

    for label in label_arr:
        if label in label_count:
            label_count[label] += 1
        else:
            label_count[label] = 1

    return label_count


def ValueCount(data_arr):
    '''
    calculating the appeared value for categoric attribute and it's counts

    @param data_arr: data array for an attribute
    @return value_count: dict, the appeared value and it's counts
    '''
    value_count = {}  # store count of value

    for label in data_arr:
        if label in value_count:
            value_count[label] += 1
        else:
            value_count[label] = 1

    return value_count


'''
optimal attribution selection in CART algorithm based on gini index
'''


def OptAttr_Gini(df):
    '''
    find the optimal attributes of current data_set based on gini index

    @param df: the pandas dataframe of the data_set
    @return opt_attr:  the optimal attribution for branch
    @return div_value: for discrete variable value = 0
                       for continuous variable value = t for bisection divide value
    '''
    gini_index = float('Inf')
    for attr_id in df.columns[1:-1]:
        gini_index_tmp, div_value_tmp = InfoGain(df, attr_id)
        if gini_index_tmp < gini_index:
            gini_index = gini_index_tmp
            opt_attr = attr_id
            div_value = div_value_tmp

    return opt_attr, div_value


def GiniIndex(df, attr_id):
    '''
    calculating the gini index of an attribution

    @param df:      dataframe, the pandas dataframe of the data_set
    @param attr_id: the target attribution in df
    @return gini_index: the gini index of current attribution
    @return div_value: for discrete variable, value = 0
                   for continuous variable, value = t (the division value)
    '''
    gini_index = 0  # info_gain for the whole label
    div_value = 0  # div_value for continuous attribute

    n = len(df[attr_id])  # the number of sample

    # 1.for continuous variable using method of bisection
    if df[attr_id].dtype == float:
        sub_gini = {}  # store the div_value (div) and it's subset gini value

        df = df.sort_values([attr_id], ascending=1)  # sorting via column
        df = df.reset_index(drop=True)

        data_arr = df[attr_id]
        label_arr = df[df.columns[-1]]

        for i in range(n - 1):
            div = (data_arr[i] + data_arr[i + 1]) / 2
            sub_gini[div] = ((i + 1) * Gini(label_arr[0:i + 1]) / n) \
                            + ((n - i - 1) * Gini(label_arr[i + 1:-1]) / n)
        # our goal is to get the min subset entropy sum and it's divide value
        div_value, gini_index = min(sub_gini.items(), key=lambda x: x[1])

    # 2.for discrete variable (categoric variable)
    else:
        data_arr = df[attr_id]
        label_arr = df[df.columns[-1]]
        value_count = ValueCount(data_arr)

        for key in value_count:
            key_label_arr = label_arr[data_arr == key]
            gini_index += value_count[key] * Gini(key_label_arr) / n

    return gini_index, div_value


def Gini(label_arr):
    '''
    calculating the gini value of an attribution

    @param label_arr: ndarray, class label array of data_arr
    @return gini: the information entropy of current attribution
    '''
    gini = 1

    n = len(label_arr)
    label_count = NodeLabel(label_arr)
    for key in label_count:
        gini -= (label_count[key] / n) * (label_count[key] / n)

    return gini


'''
optimal attribution selection in ID3 algorithm based on information entropy
'''


def OptAttr_Ent(df):
    '''
    find the optimal attributes of current data_set based on info entropy

    @param df: the pandas dataframe of the data_set
    @return opt_attr:  the optimal attribution for branch
    @return div_value: for discrete variable value = 0
                       for continuous variable value = t for bisection divide value
    '''
    info_gain = 0

    for attr_id in df.columns[1:-1]:
        info_gian_tmp, div_value_tmp = InfoGain(df, attr_id)
        if info_gian_tmp > info_gain:
            info_gain = info_gian_tmp
            opt_attr = attr_id
            div_value = div_value_tmp

    return opt_attr, div_value


def InfoGain(df, attr_id):
    '''
    calculating the information gain of an attribution

    @param df:      dataframe, the pandas dataframe of the data_set
    @param attr_id: the target attribution in df
    @return info_gain: the information gain of current attribution
    @return div_value: for discrete variable, value = 0
                   for continuous variable, value = t (the division value)
    '''
    info_gain = InfoEnt(df.values[:, -1])  # info_gain for the whole label
    div_value = 0  # div_value for continuous attribute

    n = len(df[attr_id])  # the number of sample
    # 1.for continuous variable using method of bisection
    if df[attr_id].dtype == float:
        sub_info_ent = {}  # store the div_value (div) and it's subset entropy

        df = df.sort([attr_id], ascending=1)  # sorting via column
        df = df.reset_index(drop=True)

        data_arr = df[attr_id]
        label_arr = df[df.columns[-1]]

        for i in range(n - 1):
            div = (data_arr[i] + data_arr[i + 1]) / 2
            sub_info_ent[div] = ((i + 1) * InfoEnt(label_arr[0:i + 1]) / n) \
                                + ((n - i - 1) * InfoEnt(label_arr[i + 1:-1]) / n)
        # our goal is to get the min subset entropy sum and it's divide value
        div_value, sub_info_ent_max = min(sub_info_ent.items(), key=lambda x: x[1])
        info_gain -= sub_info_ent_max

    # 2.for discrete variable (categoric variable)
    else:
        data_arr = df[attr_id]
        label_arr = df[df.columns[-1]]
        value_count = ValueCount(data_arr)

        for key in value_count:
            key_label_arr = label_arr[data_arr == key]
            info_gain -= value_count[key] * InfoEnt(key_label_arr) / n

    return info_gain, div_value


def InfoEnt(label_arr):
    '''
    calculating the information entropy of an attribution

    @param label_arr: ndarray, class label array of data_arr
    @return ent: the information entropy of current attribution
    '''
    try:
        from math import log2
    except ImportError:
        print("module math.log2 not found")

    ent = 0
    n = len(label_arr)
    label_count = NodeLabel(label_arr)

    for key in label_count:
        ent -= (label_count[key] / n) * log2(label_count[key] / n)

    return ent


def DrawPNG(root, out_file):
    '''
    visualization of decision tree from root.
    @param root: Node, the root node for tree.
    @param out_file: str, name and path of output file
    '''
    try:
        from pydotplus import graphviz
    except ImportError:
        print("module pydotplus.graphviz not found")

    g = graphviz.Dot()  # generation of new dot

    TreeToGraph(0, g, root)
    g2 = graphviz.graph_from_dot_data(g.to_string())

    g2.write_png(out_file)


def TreeToGraph(i, g, root):
    '''
    build a graph from root on
    @param i: node number in this tree
    @param g: pydotplus.graphviz.Dot() object
    @param root: the root node

    @return i: node number after modified
#     @return g: pydotplus.graphviz.Dot() object after modified
    @return g_node: the current root node in graphviz
    '''
    try:
        from pydotplus import graphviz
    except ImportError:
        print("module pydotplus.graphviz not found")

    if root.attr == None:
        g_node_label = "Node:%d\n好瓜:%s" % (i, root.label)
    else:
        g_node_label = "Node:%d\n好瓜:%s\n属性:%s" % (i, root.label, root.attr)
    g_node = i
    g.add_node(graphviz.Node(g_node, label=g_node_label, fontname="FangSong"))

    for value in list(root.attr_down):
        i, g_child = TreeToGraph(i + 1, g, root.attr_down[value])
        g.add_edge(graphviz.Edge(g_node, g_child, label=value, fontname="FangSong"))

    return i, g_node

# -*- coding: utf-8 -*

'''''
create on 2017/3/24, the day after our national football team beat south korea
@author: PY131
'''''

'''
import data and pre-analysis through data visualization
'''
# using pandas dataframe for .csv read which contains chinese char.
import pandas as pd

data_file_encode = "gb18030"
with open("../data/watermelon_2.csv", mode='r', encoding=data_file_encode) as data_file:
    df = pd.read_csv(data_file)

'''
implementation of CART rely on decision_tree.py
'''
import Chapter4.decision_tree4_4 as decision_tree

# dicision tree visualization using pydotplus.graphviz
index_train = [0, 1, 2, 5, 6, 9, 13, 14, 15, 16]

df_train = df.iloc[index_train]
df_test = df.drop(index_train)

# generate a full tree
root = decision_tree.TreeGenerate(df_train)
decision_tree.DrawPNG(root, "decision_tree_full.png")
print("accuracy of full tree: %.3f" % decision_tree.PredictAccuracy(root, df_test))

# pre-purning
root = decision_tree.PrePurn(df_train, df_test)
decision_tree.DrawPNG(root, "decision_tree_pre.png")
print("accuracy of pre-purning tree: %.3f" % decision_tree.PredictAccuracy(root, df_test))

# # post-puring
root = decision_tree.TreeGenerate(df_train)
decision_tree.PostPurn(root, df_test)
decision_tree.DrawPNG(root, "decision_tree_post.png")
print("accuracy of post-purning tree: %.3f" % decision_tree.PredictAccuracy(root, df_test))

# print the accuracy
# k-folds cross prediction
accuracy_scores = []
n = len(df.index)
k = 5
for i in range(k):
    m = int(n / k)
    test = []
    for j in range(i * m, i * m + m):
        test.append(j)

    df_train = df.drop(test)
    df_test = df.iloc[test]
    root = decision_tree.TreeGenerate(df_train)  # generate the tree
    decision_tree.PostPurn(root, df_test)  # post-purning

    # test the accuracy
    pred_true = 0
    for i in df_test.index:
        label = decision_tree.Predict(root, df[df.index == i])
        if label == df_test[df_test.columns[-1]][i]:
            pred_true += 1

    accuracy = pred_true / len(df_test.index)
    accuracy_scores.append(accuracy)

# print the prediction accuracy result
accuracy_sum = 0
print("accuracy: ", end="")
for i in range(k):
    print("%.3f  " % accuracy_scores[i], end="")
    accuracy_sum += accuracy_scores[i]
print("\naverage accuracy: %.3f" % (accuracy_sum / k))

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参考网址：

https://blog.csdn.net/snoopy_yuan/article/details/69223240