Merge pull request #32 from Jammyjamjamman/decisiontree_py

Python simple decision tree classifier

ML Cookbook/DecisionTree.py

@@ -0,0 +1,342 @@
+"""
+:Author: James Sherratt
+:Date: 21/10/2019
+:License: MIT
+
+:name: DecisionTree.py
+
+Basic implementation of a binary decision tree algorithm, with one
+discriminant per node.
+
+Useful links:
+https://scikit-learn.org/stable/modules/tree.html
+https://en.wikipedia.org/wiki/Decision_tree
+"""
+
+import numpy as np
+from sklearn import datasets
+
+
+def proportion_k(ym):
+    """
+    Get the proportions of each class in the current set of values.
+
+    :param ym: y values (class) of the data at a given node.
+    :return: list containing the classes and the fraction of those classes present.
+    """
+    counts = list(np.unique(ym, return_counts=True))
+    counts[1] = counts[1]/(ym.shape[0])
+    return counts
+
+
+def gini(k_proportions):
+    """
+    Gini impurity function. This is used to determine the impurity of a given
+    set of data, given the proportions of the classes in the dataset.
+
+    This is equivalent to:
+    H = ∑ pk(1-pk) for all k classes.
+
+    k_proportions, in this case, is an array of pk's
+
+    :param k_proportions: array containing proportions of different classes. Proportions sum to 1.
+    :return: the impurity of the dataset.
+    """
+    return (k_proportions*(1-k_proportions)).sum()
+
+
+def node_impurity(ym):
+    """
+    Calculate the impurity of data on one side of node after split.
+
+    :param ym: Actual y data for the selected dataset.
+    :return: dict containing the impurity value of the side and the most common class on that side.
+    """
+    if ym.shape[0] == 0:
+        return {"impurity": 0, "max_class": 0}
+    k_prop = proportion_k(ym)
+    return {"impurity": gini(k_prop[1]), "max_class": k_prop[0][np.argmax(k_prop[1])]}
+
+
+def disc_val_impurity(yleft, yright):
+    """
+    Calculate the level of impurity left in the given data after splitting. This returns
+    a dict which contains:
+
+    - The impurity of the data after being split.
+    - The class of the largest proportion on the left and right side of the split.
+
+    The aim is to find a split which minimises impurity.
+
+    The impurity calculated is:
+    G = (nleft/ntot)*Hleft + (nright/ntot)*Hright
+
+    This gives the impurity of the split data.
+
+    :param yleft: Real/ training y values for the data on the left.
+    :param yright: Real/ training y values for the data on the right.
+    :return: Dict containing the data impurity after split and the most common class on the left and right of the split.
+    """
+    nleft = yleft.shape[0]
+    nright = yright.shape[0]
+    ntot = nleft + nright
+    left_imp = node_impurity(yleft)
+    right_imp = node_impurity(yright)
+
+    return {
+        "impurity": ((nleft/ntot)*left_imp["impurity"])+((nright/ntot)*right_imp["impurity"]),
+        "lmax_class": left_imp["max_class"],
+        "rmax_class": right_imp["max_class"]
+    }
+
+
+def niave_min_impurity(xm, ym):
+    """
+    Find a discriminator which minimises the impurity of the data. The discriminator
+    is used to split data at a node.
+
+    This works by:
+    1. Selecting a data column as a discriminator.
+    2. Splitting the possible values of the discriminator into 1000 even spaced values
+    (between the minimum and maximum value in the dataset).
+    3. Selecting the discriminator column + value which minimises the impurity.
+
+    :param xm: Data on the left.
+    :param ym: Data on the right.
+    :return: dict containing the current niave minimum impurity.
+    """
+    minxs = xm.min(axis=0)
+    maxxs = xm.max(axis=0)
+
+    # discriminator with the smallest impurity.
+    cur_min_disc = None
+
+    # Choose a column to discriminate by.
+    for x_idx, (dmin, dmax) in enumerate(zip(minxs, maxxs)):
+        # Create a set of possibly values to use as the discriminator for that column.
+        disc_vals = np.linspace(dmin, dmax, 1000)
+        for disc_val in disc_vals:
+            selection = xm[:, x_idx] < disc_val
+            yleft = ym[selection]
+            yright = ym[selection==False]
+            # Calculate impurity.
+            imp = disc_val_impurity(yleft, yright)
+            # Choose a column with the smallest impurity.
+            try:
+                if cur_min_disc["impurity"] > imp["impurity"]:
+                    imp["discriminator"] = x_idx
+                    imp["val"] = disc_val
+                    cur_min_disc = imp
+            except TypeError:
+                imp["discriminator"] = x_idx
+                imp["val"] = disc_val
+                cur_min_disc = imp
+
+    return cur_min_disc
+
+
+class BinaryTreeClassifier:
+
+    def __init__(self, max_depth=4, min_data=5):
+        """
+        Initialise the binary decision tree classifier. This classifier works by:
+        - Splitting the data into 2 sets at every node.
+        - These 2 sets are then split into 2 more sets at their nodes etc. until they reach a leaf.
+        - At the leaves, the data is classified into whatever class was "most common" in that leaf during training.
+
+        :param max_depth: The maximum depth the binary tree classifier goes to.
+        :param min_data: The minimum sample size of the training data before the tree stops splitting.
+        """
+        tree = dict()
+        self.depth = max_depth
+        self.min_data = min_data
+
+    def _node_mask(X, node):
+        """
+        Get the discriminator mask for the node. This splits the data into left and right components.
+
+        :param X: dataset input data.
+        :param node: the current node of the tree, with its discriminator value.
+        :return: truth array, which splits data left and right.
+        """
+        return X[:, node["discriminator"]] < node["val"]
+
+    def _apply_disc(X, y, node):
+        """
+        Apply the discriminator to the data at a given node.
+
+        :param X: dataset input.
+        :param y: dataset (observed) output.
+        :param node: The node to split data by.
+        :return: The x and y data, split left and right.
+        """
+        left_cond = BinaryTreeClassifier._node_mask(X, node)
+        right_cond = left_cond == False
+        left_X, left_y = X[left_cond], y[left_cond]
+        right_X, right_y = X[right_cond], y[right_cond]
+
+        return left_X, left_y, right_X, right_y
+
+    def _tree_node(X, y, max_depth, min_data):
+        """
+        Create a tree node. This also creates child nodes of this node recursively.
+
+        :param X: input data for the dataset at a node.
+        :param y: output (observed) data for the dataset at a node.
+        :param max_depth: The maximum depth of the tree from this node.
+        :param min_data: The minimum amount of data which can be discriminated.
+        :return: The node + its children, as a dict.
+        """
+        # Get the new node, as a dict.
+        node = niave_min_impurity(X, y)
+        # Split the data using the discriminator.
+        left_X, left_y, right_X, right_y = BinaryTreeClassifier._apply_disc(X, y, node)
+
+        if max_depth > 1:
+            if left_X.shape[0] >= min_data:
+                # Create a new node on the left (recursively) if max depth
+                # and min data have not been reached.
+                node["left"] = BinaryTreeClassifier._tree_node(left_X, left_y, max_depth-1, min_data)
+            if right_X.shape[0] >= min_data:
+                # Create a new node on the right (recursively) if max depth
+                # and min data have not been reached.
+                node["right"] = BinaryTreeClassifier._tree_node(right_X, right_y, max_depth-1, min_data)
+
+        return node
+
+    def _run_tree(X, node):
+        """
+        Run a node of the classifier, recurisively.
+
+        :param node: The node to run on the data.
+        :return: The classified y (expected) data.
+        """
+        # Setup y array.
+        y = np.zeros(X.shape[0])
+        # Get the discriminator left conditional.
+        left_cond = BinaryTreeClassifier._node_mask(X, node)
+        # Right conditional
+        right_cond = left_cond == False
+        try:
+            # Try to split the data further on the left side.
+            y[left_cond] = BinaryTreeClassifier._run_tree(X[left_cond], node["left"])
+        except KeyError:
+            # If we cannot split any further, get the class of the data on the left (as this is a leaf).
+            y[left_cond] = node["lmax_class"]
+        try:
+            # Try to split the data further on the right side.
+            y[right_cond] = BinaryTreeClassifier._run_tree(X[right_cond], node["right"])
+        except KeyError:
+            # If we cannot split any further, get the class of the data on the right (as this is a leaf).
+            y[right_cond] = node["rmax_class"]
+
+        return y
+
+    def _node_dict(node, idx=0):
+        """
+        Get a dict of all the nodes, recursively. The keys are the index of an array,
+        as if the array is a heap.
+
+        :param node: The current node to add to the dict and to get children of recursively.
+        :param idx: current index (key) of the node.
+        :return: dict containing all the nodes retrieved.
+        """
+        # Current nodes.
+        nodes = {}
+        node_data = {"lmax_class": node["lmax_class"],
+                     "rmax_class": node["rmax_class"],
+                     "discriminator": node["discriminator"],
+                     "val": node["val"]}
+        nodes[idx] = node_data
+
+        # Try to get the left nodes.
+        try:
+            left_idx = 2 * idx + 1
+            nodes.update(BinaryTreeClassifier._node_dict(node["left"], left_idx))
+        except KeyError:
+            pass
+
+        # Try to get the right nodes.
+        try:
+            right_idx = 2 * idx + 2
+            nodes.update(BinaryTreeClassifier._node_dict(node["right"], right_idx))
+        except KeyError:
+            pass
+
+        # return the dict of nodes retrieved.
+        return nodes
+
+    def build_tree(self, X, y):
+        """
+        Build (train) the decision tree classifier.
+
+        :param X: input training data.
+        :param y: output training (observed) data.
+        :return: None
+        """
+        self.tree = BinaryTreeClassifier._tree_node(X, y, self.depth, self.min_data)
+
+    def classify(self, X):
+        """
+        Classify some data using the tree.
+
+        :param X: Input data.
+        :return: output (expected) classes of the data, or y values, for the given input.
+        """
+        return BinaryTreeClassifier._run_tree(X, self.tree)
+
+    def tree_to_heap_array(self):
+        """
+        Convert the tree to a binary heap, stored in an array with standard indexing.
+        i.e. a node at index i has children at 2i*1 and 2i+2 and a parent at (i-1)//2.
+
+        :return: list containing the tree nodes.
+        """
+        tree_dict = BinaryTreeClassifier._node_dict(self.tree)
+        return [tree_dict[key] for key in sorted(tree_dict.keys())]
+
+
+def shuffle_split(x, y, frac=0.6):
+    """
+    Shuffle and split X and y data. "frac" is the ratio of the split.
+    e.g. 0.6 means 60% of the data goes into the left fraction, 40% into the right.
+    Note X and y are shuffled the same, so row i in X data is still matched with row i in y after shuffle.
+
+    :param x: X values of the data (predictor).
+    :param y: y values of the data (observation).
+    :param frac: fraction to split data by.
+    :return: x1, y1, x2, y2 data where x1, y1 is the left fraction and x2, y2 is the right.
+    """
+    data_idx = np.arange(x.shape[0])
+    sample1 = data_idx < (data_idx.max()*frac)
+    np.random.shuffle(data_idx)
+    np.random.shuffle(sample1)
+    sample2 = sample1 == False
+    x1, y1 = x[data_idx[sample1]], y[data_idx[sample1]]
+    x2, y2 = x[data_idx[sample2]], y[data_idx[sample2]]
+    return x1, y1, x2, y2
+
+
+if __name__ == "__main__":
+    # Set the seed for expected test results.
+    np.random.seed(10)
+    # Test decision tree with iris data.
+    iris_data = datasets.load_iris()
+    X = iris_data["data"]
+    y = iris_data["target"]
+    # Split iris data into test and train.
+    X_train, y_train, X_test, y_test = shuffle_split(X, y)
+    # create the decision tree classifier.
+    classifier = BinaryTreeClassifier()
+    # Train the classifier.
+    classifier.build_tree(X_train, y_train)
+    # Get the result when the classifier is applied to to the test data.
+    result = classifier.classify(X_test)
+    # Get the accuracy of the classifier.
+    # accuracy = (number of correct results)/(total number of results)
+    print("accuracy:", (result == y_test).sum()/(result.shape[0]))
+    # convert the tree into a heap array.
+    tree_arr = classifier.tree_to_heap_array()
+    print("heap:")
+    for i, node in enumerate(tree_arr):
+        print(i, node)