## Instructions

### Objective

Write a Python homework program to implement SVM classification.

## Requirements and Specifications

**Source Code**

```
import numpy as np
class Tree_node:
"""
Data structure for nodes in the decision-tree
"""
def __init__(self,):
self.is_leaf = False # whether or not the current node is a leaf node
self.feature = None # index of the selected feature (for non-leaf node)
self.label = -1 # class label (for leaf node)
self.left_child = None # left child node
self.right_child = None # right child node
class Decision_tree:
"""
Decision tree with binary features
"""
def __init__(self,min_entropy):
self.min_entropy = min_entropy # min node entropy
self.root = None
def fit(self,train_x,train_y):
# construct the decision-tree with recursion
self.root = self.generate_tree(train_x,train_y)
def predict(self,test_x):
# iterate through all samples
prediction = np.zeros([len(test_x),]).astype('int') # placeholder
for i in range(len(test_x)):
#pass # placeholder
node = self.root
data = test_x[i,:]
while node.left_child or node.right_child:
if data[node.feature] == 1:
node = node.right_child
else:
node = node.left_child
prediction[i] = node.label
return prediction
def generate_tree(self,data,label):
# initialize the current tree node
cur_node = Tree_node()
# compute the node entropy
node_entropy = self.compute_node_entropy(label)
if node_entropy < self.min_entropy:
cur_node.isleaf = True
mostFrequent = np.argmax(np.bincount(label))
cur_node.label = mostFrequent
return cur_node
# select the feature that will best split the current non-leaf node
selected_feature = self.select_feature(data,label)
cur_node.feature = selected_feature
# split the data based on the selected feature and start the next level of recursion
featureData = data[:,selected_feature]
zeros = np.asarray(np.where(featureData == 0))[0]
ones = np.asarray(np.where(featureData == 1))[0]
leftData = data[zeros]
leftLabel = label[zeros]
rightData = data[ones]
rightLabel = label[ones]
cur_node.left_child = self.generate_tree(leftData, leftLabel)
cur_node.right_child = self.generate_tree(rightData, rightLabel)
return cur_node
def select_feature(self,data,label):
# iterate through all features and compute their corresponding entropy
best_feat = 0
lowestEntropy = float("inf")
for i in range(len(data[0])):
featureData = data[:,i]
zeros = np.asarray(np.where(featureData == 0))
ones = np.asarray(np.where(featureData == 1))
zerosLabels = label[zeros[0]]
onesLabels = label[ones[0]]
entropy = self.compute_split_entropy(zerosLabels, onesLabels)
if entropy < lowestEntropy:
lowestEntropy = entropy
best_feat = i
return best_feat
def compute_split_entropy(self,left_y, right_y):
# compute the entropy of a potential split, left_y and right_y are labels for the two branches
split_entropy = 0 # placeholder
leftEntropy = self.compute_node_entropy(left_y)
rightEntropy = self.compute_node_entropy(right_y)
leftSamples = len(left_y)
rightSamples = len(right_y)
total = leftSamples + rightSamples
split_entropy = leftEntropy * leftSamples/total + rightEntropy * rightSamples/total
return split_entropy
def compute_node_entropy(self,label):
# compute the entropy of a tree node (add 1e-15 inside the log2 when computing the entropy to prevent numerical issue)
node_entropy = 0 # placeholder
e = 1e-12
totalSamples = len(label)
count = np.bincount(label)
count = count / totalSamples
for j in range(len(count)):
node_entropy += -count[j] * np.log2(count[j] + e)
return node_entropy
```

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