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""" |
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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 |