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206 lines
5.8 KiB
206 lines
5.8 KiB
"""
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:Author: james
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:Date: 21/10/2019
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:License: MIT
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:name: DecisionTree.py
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Basic implementation of a binary decision tree algorithm, with one
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discriminant per node.
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"""
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import numpy as np
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from sklearn import datasets
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def proportion_k(ym):
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"""
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Get the proportions of each class in the current set of values.
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:param ym: y values (class) of the data at a given node.
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:return:
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"""
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counts = list(np.unique(ym, return_counts=True))
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counts[1] = counts[1]/(ym.shape[0])
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return counts
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def gini(k_proportions):
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"""
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Gini impurity function.
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:param k_proportions:
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:return:
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"""
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return (k_proportions*(1-k_proportions)).sum()
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def node_impurity(ym):
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"""
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Calculate the impurity of data at a given node of the tree.
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:param ym:
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:return:
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"""
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if ym.shape[0] == 0:
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return {"impurity": 0, "max_group": 0}
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k_prop = proportion_k(ym)
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return {"impurity": gini(k_prop[1]), "max_group": k_prop[0][np.argmax(k_prop[1])]}
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def disc_val_impurity(yleft, yright):
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"""
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Calculate the level of impurity left in the given data split.
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:param yleft:
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:param yright:
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:return:
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"""
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nleft = yleft.shape[0]
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nright = yright.shape[0]
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ntot = nleft + nright
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left_imp = node_impurity(yleft)
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right_imp = node_impurity(yright)
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return {
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"impurity": ((nleft/ntot)*left_imp["impurity"])+((nright/ntot)*right_imp["impurity"]),
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"lmax_group": left_imp["max_group"],
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"rmax_group": right_imp["max_group"]
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}
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def niave_min_impurity(xm, ym):
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minxs = xm.min(axis=0)
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maxxs = xm.max(axis=0)
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# discriminator with the smallest impurity.
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cur_min_disc = None
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for x_idx, (dmin, dmax) in enumerate(zip(minxs, maxxs)):
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disc_vals = np.linspace(dmin, dmax, 10)
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for disc_val in disc_vals:
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selection = xm[:, x_idx] < disc_val
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yleft = ym[selection]
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yright = ym[selection==False]
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imp = disc_val_impurity(yleft, yright)
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try:
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if cur_min_disc["impurity"] > imp["impurity"]:
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imp["discriminator"] = x_idx
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imp["val"] = disc_val
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cur_min_disc = imp
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except TypeError:
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imp["discriminator"] = x_idx
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imp["val"] = disc_val
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cur_min_disc = imp
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return cur_min_disc
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class BinaryTreeClassifier:
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def __init__(self, max_depth=4, min_data=5):
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tree = dict()
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self.depth = max_depth
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self.min_data = min_data
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def _node_mask(X, node):
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return X[:, node["discriminator"]] < node["val"]
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def _apply_disc(X, y, node):
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left_cond = BinaryTreeClassifier._node_mask(X, node)
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right_cond = left_cond == False
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left_X, left_y = X[left_cond], y[left_cond]
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right_X, right_y = X[right_cond], y[right_cond]
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return left_X, left_y, right_X, right_y
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def _tree_node(X, y, max_depth, min_data):
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node = niave_min_impurity(X, y)
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left_X, left_y, right_X, right_y = BinaryTreeClassifier._apply_disc(X, y, node)
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if max_depth > 0:
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if left_X.shape[0] >= min_data:
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node["left"] = BinaryTreeClassifier._tree_node(left_X, left_y, max_depth-1, min_data)
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if right_X.shape[0] >= min_data:
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node["right"] = BinaryTreeClassifier._tree_node(right_X, right_y, max_depth-1, min_data)
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return node
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def _run_tree(X, node):
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y = np.zeros(X.shape[0])
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left_cond = BinaryTreeClassifier._node_mask(X, node)
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right_cond = left_cond == False
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try:
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y[left_cond] = BinaryTreeClassifier._run_tree(X[left_cond], node["left"])
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except KeyError:
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y[left_cond] = node["lmax_group"]
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try:
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y[right_cond] = BinaryTreeClassifier._run_tree(X[right_cond], node["right"])
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except KeyError:
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y[right_cond] = node["rmax_group"]
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return y
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def _node_dict(node, idx=0):
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nodes = {}
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node_data = {"lmax_group": node["lmax_group"],
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"rmax_group": node["rmax_group"],
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"discriminator": node["discriminator"],
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"val": node["val"]}
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nodes[idx] = node_data
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try:
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left_idx = 2 * idx + 1
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nodes.update(BinaryTreeClassifier._node_dict(node["left"], left_idx))
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except KeyError:
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pass
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try:
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right_idx = 2 * idx + 2
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nodes.update(BinaryTreeClassifier._node_dict(node["right"], right_idx))
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except KeyError:
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pass
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return nodes
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def build_tree(self, X, y):
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self.tree = BinaryTreeClassifier._tree_node(X, y, self.depth, self.min_data)
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def classify(self, X):
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return BinaryTreeClassifier._run_tree(X, self.tree)
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def tree_to_heap_array(self):
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tree_dict = BinaryTreeClassifier._node_dict(self.tree)
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return [tree_dict[key] for key in sorted(tree_dict.keys())]
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def shuffle_split(x, y, frac=0.6):
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"""
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Shuffle and split X and y data.
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:param x:
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:param y:
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:param frac:
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:return:
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"""
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data_idx = np.arange(x.shape[0])
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sample1 = data_idx < (data_idx.max()*frac)
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np.random.shuffle(data_idx)
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np.random.shuffle(sample1)
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sample2 = sample1 == False
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x1, y1 = x[data_idx[sample1]], y[data_idx[sample1]]
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x2, y2 = x[data_idx[sample2]], y[data_idx[sample2]]
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return x1, y1, x2, y2
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if __name__ == "__main__":
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np.random.seed(10)
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iris_data = datasets.load_iris()
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X = iris_data["data"]
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y = iris_data["target"]
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X_train, y_train, X_test, y_test = shuffle_split(X, y)
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classifier = BinaryTreeClassifier()
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classifier.build_tree(X_train, y_train)
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result = classifier.classify(X_test)
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print("accuracy:", (result == y_test).sum()/(result.shape[0]))
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tree_arr = classifier.tree_to_heap_array()
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pass
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