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mdlp.py
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mdlp.py
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import math
import numpy as np
from collections import Counter
from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split
class Decision:
def __init__(self, pos, val):
self.pos = pos
self.val = val
def is_continuous(self):
return isinstance(self.val, int) or isinstance(self.val, float)
def decide(self, feature):
if not feature[self.pos]:
return False
if self.is_continuous():
return feature[self.pos] < self.val
else:
return feature[self.pos] == self.val
def __repr__(self):
if self.is_continuous():
return '{} < {}'.format(self.pos, self.val)
else:
return '{} == {}'.format(self.pos, self.val)
class Node:
def __init__(self, decision, left, right, tree):
self.tree = tree
self.decision = decision
self.left = left
self.right = right
def __repr__(self):
return repr(self.decision)
class Leaf:
def __init__(self, tree, elements):
self.tree = tree
self.elements = elements
self.counts = Counter()
for e in elements:
self.counts[e[-1]] += 1
self.class_ = max(self.counts, key=lambda x: self.counts[x])
def __repr__(self):
return repr(self.counts)
class Tree:
def __init__(self, train, test=None):
self.features = train
self.features_test = test
self.classes = set([f[-1] for f in self.features])
self.attributes = [[] for _ in self.features[0][:-1]]
for feature in self.features:
for i, e in enumerate(feature[:-1]):
if e is None:
continue
self.attributes[i].append(e)
for i, attr in enumerate(self.attributes):
self.attributes[i] = list(sorted(set(attr)))
self.root = self._build_tree(Leaf(self, self.features))
self._prune_tree(self.root)
def classify(self, feature):
cur = self.root
while isinstance(cur, Node):
if cur.decision.decide(feature):
cur = cur.right
else:
cur = cur.left
return cur.class_
def _build_tree(self, leaf: Leaf):
mdlp, decision = self._best_split(leaf)
if not decision:
return leaf
left, right = self._split(leaf.elements, decision)
return Node(decision, self._build_tree(Leaf(self, left)), self._build_tree(Leaf(self, right)), self)
def _prune_tree(self, root):
if root is None:
return
s1 = []
s2 = []
s1.append(root)
while s1:
node = s1.pop()
if isinstance(node, Node):
s2.append(node)
node.left.parent = node
node.left.branch = 'L'
node.right.parent = node
node.right.branch = 'R'
s1.append(node.left)
s1.append(node.right)
while s2:
node = s2.pop()
if isinstance(node.left, Leaf) and isinstance(node.right, Leaf):
cur_mdl = 3 + self._mdlp_attribute(node.decision) + (2 * math.log2(len(self.classes))) \
+ self._mdlp_exceptions([l[-1] for l in node.left.elements]) \
+ self._mdlp_exceptions([r[-1] for r in node.right.elements])
new_mdl = 1 + self._mdlp_exceptions([e[-1] for e in node.left.elements + node.right.elements])
if cur_mdl >= new_mdl:
if node.branch == 'L':
node.parent.left = Leaf(node.tree, node.left.elements + node.right.elements)
elif node.branch == 'R':
node.parent.right = Leaf(node.tree, node.left.elements + node.right.elements)
def _best_split(self, cur_leaf: Leaf):
features = cur_leaf.elements
best = (math.inf, None)
for i, attr in enumerate(self.attributes):
if len(attr) == 0:
continue
if not isinstance(attr[0], str):
sq = math.sqrt(len(attr))
attr = [attr[i] for i in range(0, len(attr), math.floor(sq))]
for val in attr:
decision = Decision(i, val)
left, right = self._split(features, decision)
if not left or not right:
continue
# 2 new nodes, 1 new default class, 1 new attribute, 2 exception costs, subtract previous exception cost
mdlp = 2 + math.log2(len(self.classes)) + self._mdlp_attribute(decision) \
+ self._mdlp_exceptions([l[-1] for l in left]) \
+ self._mdlp_exceptions([r[-1] for r in right]) \
- self._mdlp_exceptions([e[-1] for e in cur_leaf.elements])
if mdlp < best[0]:
best = (mdlp, decision)
return best
def _split(self, features, decision):
left, right = [], []
for feature in features:
if decision.decide(feature):
right.append(feature)
else:
left.append(feature)
return left, right
def _calc_l(self, n, k, b):
n_choose_k = math.log2(math.factorial(n) // (math.factorial(n - k) * math.factorial(k)))
return n_choose_k + math.log2(b + 1)
def _mdlp_exceptions(self, labels, counts=None):
if not counts:
counts = {}
for l in labels:
if l not in counts:
counts[l] = 1
else:
counts[l] += 1
default = max(counts, key=lambda x: counts[x])
n = len(labels)
k = counts[default]
b = (len(labels) - 1) // 2
del counts[default]
result = self._calc_l(n, k, b)
return 8 * result if len(counts) <= 1 else 8 * (result + self._mdlp_exceptions([l for l in labels if l != default],
counts))
def _count_nodes(self, node, counts=np.array([0, 0, 0])):
if isinstance(node, Leaf):
return counts + [1, 1, 0]
else:
return counts + [1, 0, self._mdlp_attribute(node.decision)] + self._count_nodes(
node.left) + self._count_nodes(node.right)
def _mdlp_tree(self, root):
n, k, a = self._count_nodes(root)
return n + (math.log2(len(self.classes)) * k) + a
def _mdlp_attribute(self, decision):
attr = self.attributes[decision.pos]
if isinstance(attr, str):
return math.log2(len(self.attributes)) + math.log2(len(attr))
else:
return math.log2(len(self.attributes)) + math.log2(math.sqrt(len(attr)))
if __name__ == '__main__':
X, y = load_iris(return_X_y=True)
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, random_state=42)
train = []
for i in range(len(X_train)):
train.append(np.append(X_train[i], y_train[i]))
test = []
for i in range(len(X_test)):
test.append(np.append(X_test[i], y_test[i]))
tree = Tree(train, test)
preds = [tree.classify(t) for t in test]
acc = [a == b for a, b in zip(preds, y_test)]
print('Accuracy:', sum(acc) / len(acc) * 100)