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342 lines
12 KiB
342 lines
12 KiB
"""
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:Author: James Sherratt
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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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Useful links:
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https://scikit-learn.org/stable/modules/tree.html
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https://en.wikipedia.org/wiki/Decision_tree
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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: list containing the classes and the fraction of those classes present.
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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. This is used to determine the impurity of a given
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set of data, given the proportions of the classes in the dataset.
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This is equivalent to:
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H = ∑ pk(1-pk) for all k classes.
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k_proportions, in this case, is an array of pk's
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:param k_proportions: array containing proportions of different classes. Proportions sum to 1.
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:return: the impurity of the dataset.
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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 on one side of node after split.
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:param ym: Actual y data for the selected dataset.
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:return: dict containing the impurity value of the side and the most common class on that side.
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"""
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if ym.shape[0] == 0:
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return {"impurity": 0, "max_class": 0}
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k_prop = proportion_k(ym)
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return {"impurity": gini(k_prop[1]), "max_class": 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 after splitting. This returns
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a dict which contains:
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- The impurity of the data after being split.
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- The class of the largest proportion on the left and right side of the split.
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The aim is to find a split which minimises impurity.
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The impurity calculated is:
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G = (nleft/ntot)*Hleft + (nright/ntot)*Hright
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This gives the impurity of the split data.
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:param yleft: Real/ training y values for the data on the left.
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:param yright: Real/ training y values for the data on the right.
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:return: Dict containing the data impurity after split and the most common class on the left and right of the split.
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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_class": left_imp["max_class"],
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"rmax_class": right_imp["max_class"]
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}
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def niave_min_impurity(xm, ym):
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"""
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Find a discriminator which minimises the impurity of the data. The discriminator
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is used to split data at a node.
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This works by:
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1. Selecting a data column as a discriminator.
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2. Splitting the possible values of the discriminator into 1000 even spaced values
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(between the minimum and maximum value in the dataset).
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3. Selecting the discriminator column + value which minimises the impurity.
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:param xm: Data on the left.
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:param ym: Data on the right.
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:return: dict containing the current niave minimum impurity.
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"""
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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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# Choose a column to discriminate by.
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for x_idx, (dmin, dmax) in enumerate(zip(minxs, maxxs)):
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# Create a set of possibly values to use as the discriminator for that column.
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disc_vals = np.linspace(dmin, dmax, 1000)
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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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# Calculate impurity.
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imp = disc_val_impurity(yleft, yright)
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# Choose a column with the smallest impurity.
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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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"""
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Initialise the binary decision tree classifier. This classifier works by:
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- Splitting the data into 2 sets at every node.
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- These 2 sets are then split into 2 more sets at their nodes etc. until they reach a leaf.
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- At the leaves, the data is classified into whatever class was "most common" in that leaf during training.
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:param max_depth: The maximum depth the binary tree classifier goes to.
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:param min_data: The minimum sample size of the training data before the tree stops splitting.
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"""
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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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"""
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Get the discriminator mask for the node. This splits the data into left and right components.
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:param X: dataset input data.
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:param node: the current node of the tree, with its discriminator value.
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:return: truth array, which splits data left and right.
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"""
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return X[:, node["discriminator"]] < node["val"]
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def _apply_disc(X, y, node):
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"""
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Apply the discriminator to the data at a given node.
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:param X: dataset input.
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:param y: dataset (observed) output.
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:param node: The node to split data by.
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:return: The x and y data, split left and right.
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"""
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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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"""
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Create a tree node. This also creates child nodes of this node recursively.
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:param X: input data for the dataset at a node.
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:param y: output (observed) data for the dataset at a node.
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:param max_depth: The maximum depth of the tree from this node.
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:param min_data: The minimum amount of data which can be discriminated.
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:return: The node + its children, as a dict.
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"""
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# Get the new node, as a dict.
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node = niave_min_impurity(X, y)
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# Split the data using the discriminator.
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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 > 1:
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if left_X.shape[0] >= min_data:
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# Create a new node on the left (recursively) if max depth
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# and min data have not been reached.
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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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# Create a new node on the right (recursively) if max depth
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# and min data have not been reached.
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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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"""
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Run a node of the classifier, recurisively.
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:param node: The node to run on the data.
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:return: The classified y (expected) data.
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"""
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# Setup y array.
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y = np.zeros(X.shape[0])
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# Get the discriminator left conditional.
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left_cond = BinaryTreeClassifier._node_mask(X, node)
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# Right conditional
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right_cond = left_cond == False
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try:
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# Try to split the data further on the left side.
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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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# If we cannot split any further, get the class of the data on the left (as this is a leaf).
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y[left_cond] = node["lmax_class"]
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try:
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# Try to split the data further on the right side.
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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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# If we cannot split any further, get the class of the data on the right (as this is a leaf).
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y[right_cond] = node["rmax_class"]
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return y
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def _node_dict(node, idx=0):
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"""
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Get a dict of all the nodes, recursively. The keys are the index of an array,
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as if the array is a heap.
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:param node: The current node to add to the dict and to get children of recursively.
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:param idx: current index (key) of the node.
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:return: dict containing all the nodes retrieved.
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"""
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# Current nodes.
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nodes = {}
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node_data = {"lmax_class": node["lmax_class"],
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"rmax_class": node["rmax_class"],
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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 to get the left nodes.
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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 to get the right nodes.
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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 the dict of nodes retrieved.
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return nodes
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def build_tree(self, X, y):
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"""
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Build (train) the decision tree classifier.
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:param X: input training data.
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:param y: output training (observed) data.
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:return: None
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"""
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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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"""
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Classify some data using the tree.
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:param X: Input data.
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:return: output (expected) classes of the data, or y values, for the given input.
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"""
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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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"""
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Convert the tree to a binary heap, stored in an array with standard indexing.
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i.e. a node at index i has children at 2i*1 and 2i+2 and a parent at (i-1)//2.
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:return: list containing the tree nodes.
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"""
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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. "frac" is the ratio of the split.
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e.g. 0.6 means 60% of the data goes into the left fraction, 40% into the right.
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Note X and y are shuffled the same, so row i in X data is still matched with row i in y after shuffle.
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:param x: X values of the data (predictor).
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:param y: y values of the data (observation).
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:param frac: fraction to split data by.
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:return: x1, y1, x2, y2 data where x1, y1 is the left fraction and x2, y2 is the right.
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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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# Set the seed for expected test results.
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np.random.seed(10)
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# Test decision tree with iris data.
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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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# Split iris data into test and train.
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X_train, y_train, X_test, y_test = shuffle_split(X, y)
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# create the decision tree classifier.
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classifier = BinaryTreeClassifier()
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# Train the classifier.
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classifier.build_tree(X_train, y_train)
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# Get the result when the classifier is applied to to the test data.
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result = classifier.classify(X_test)
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# Get the accuracy of the classifier.
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# accuracy = (number of correct results)/(total number of results)
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print("accuracy:", (result == y_test).sum()/(result.shape[0]))
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# convert the tree into a heap array.
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tree_arr = classifier.tree_to_heap_array()
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print("heap:")
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for i, node in enumerate(tree_arr):
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print(i, node)
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