good stuff coming
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+44
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@@ -2,85 +2,10 @@
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"cells": [
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"cells": [
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{
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{
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"cell_type": "code",
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"cell_type": "code",
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"execution_count": 3,
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"execution_count": null,
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"id": "d2aa9221",
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"id": "d2aa9221",
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"metadata": {},
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"metadata": {},
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"outputs": [
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"outputs": [],
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"\n",
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"===== Banknote Authentication =====\n",
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]
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},
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{
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"data": {
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"image/png": 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"text/plain": [
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"<Figure size 640x480 with 1 Axes>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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truncated
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"text/plain": [
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"<Figure size 640x480 with 1 Axes>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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||||||
{
|
|
||||||
"name": "stdout",
|
|
||||||
"output_type": "stream",
|
|
||||||
"text": [
|
|
||||||
"k-NN error after PCA (k=5): 0.1238\n",
|
|
||||||
"Best k via CV: 15\n",
|
|
||||||
"CV accuracy: 0.9993\n",
|
|
||||||
"Leave-One-Out error: 0.0015\n",
|
|
||||||
"SVM accuracy: 1.0\n",
|
|
||||||
"\n",
|
|
||||||
"===== Seeds =====\n",
|
|
||||||
"[0.17460317460317465, 0.17460317460317465, 0.12698412698412698, 0.12698412698412698, 0.15873015873015872, 0.15873015873015872, 0.15873015873015872, 0.1428571428571429] [0.09523809523809523, 0.12698412698412698, 0.12698412698412698, 0.12698412698412698, 0.11111111111111116, 0.1428571428571429, 0.1428571428571429, 0.1428571428571429]\n"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
{
|
|
||||||
"data": {
|
|
||||||
"image/png": 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truncated
|
|
||||||
"text/plain": [
|
|
||||||
"<Figure size 640x480 with 1 Axes>"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
"metadata": {},
|
|
||||||
"output_type": "display_data"
|
|
||||||
},
|
|
||||||
{
|
|
||||||
"data": {
|
|
||||||
"image/png": 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truncated
|
|
||||||
"text/plain": [
|
|
||||||
"<Figure size 640x480 with 1 Axes>"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
"metadata": {},
|
|
||||||
"output_type": "display_data"
|
|
||||||
},
|
|
||||||
{
|
|
||||||
"name": "stdout",
|
|
||||||
"output_type": "stream",
|
|
||||||
"text": [
|
|
||||||
"k-NN error after PCA (k=5): 0.1587\n",
|
|
||||||
"Best k via CV: 11\n",
|
|
||||||
"CV accuracy: 0.9238\n",
|
|
||||||
"Leave-One-Out error: 0.0762\n",
|
|
||||||
"SVM accuracy: 0.873\n"
|
|
||||||
]
|
|
||||||
}
|
|
||||||
],
|
|
||||||
"source": [
|
"source": [
|
||||||
"from typing import Callable, Literal\n",
|
"from typing import Callable, Literal\n",
|
||||||
"import numpy as np\n",
|
"import numpy as np\n",
|
||||||
@@ -92,9 +17,16 @@
|
|||||||
"from sklearn.preprocessing import StandardScaler\n",
|
"from sklearn.preprocessing import StandardScaler\n",
|
||||||
"from sklearn.decomposition import PCA\n",
|
"from sklearn.decomposition import PCA\n",
|
||||||
"from sklearn.metrics import accuracy_score\n",
|
"from sklearn.metrics import accuracy_score\n",
|
||||||
"from sklearn.svm import SVC\n",
|
"from sklearn.svm import SVC\n"
|
||||||
"\n",
|
]
|
||||||
"\n",
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": null,
|
||||||
|
"id": "e4c07993",
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [],
|
||||||
|
"source": [
|
||||||
"# ---------- Utility functions ----------\n",
|
"# ---------- Utility functions ----------\n",
|
||||||
"\n",
|
"\n",
|
||||||
"\n",
|
"\n",
|
||||||
@@ -121,9 +53,16 @@
|
|||||||
" df = pd.read_csv(url, sep=r\"\\s+\", names=cols)\n",
|
" df = pd.read_csv(url, sep=r\"\\s+\", names=cols)\n",
|
||||||
" X = df.iloc[:, :-1].values\n",
|
" X = df.iloc[:, :-1].values\n",
|
||||||
" y = df[\"class\"].values\n",
|
" y = df[\"class\"].values\n",
|
||||||
" return X, y, \"Seeds\"\n",
|
" return X, y, \"Seeds\"\n"
|
||||||
"\n",
|
]
|
||||||
"\n",
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": null,
|
||||||
|
"id": "00c062bd",
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [],
|
||||||
|
"source": [
|
||||||
"def knn_error(X, y, k):\n",
|
"def knn_error(X, y, k):\n",
|
||||||
" Xtr, Xte, ytr, yte = train_test_split(\n",
|
" Xtr, Xte, ytr, yte = train_test_split(\n",
|
||||||
" X, y, test_size=0.3, random_state=42, stratify=y\n",
|
" X, y, test_size=0.3, random_state=42, stratify=y\n",
|
||||||
@@ -167,9 +106,16 @@
|
|||||||
" )\n",
|
" )\n",
|
||||||
" svm = SVC(kernel=kernel, C=1, gamma=\"scale\")\n",
|
" svm = SVC(kernel=kernel, C=1, gamma=\"scale\")\n",
|
||||||
" svm.fit(Xtr, ytr)\n",
|
" svm.fit(Xtr, ytr)\n",
|
||||||
" return svm.score(Xte, yte)\n",
|
" return svm.score(Xte, yte)\n"
|
||||||
"\n",
|
]
|
||||||
"\n",
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": null,
|
||||||
|
"id": "66947987",
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [],
|
||||||
|
"source": [
|
||||||
"# ---------- Plotting ----------\n",
|
"# ---------- Plotting ----------\n",
|
||||||
"\n",
|
"\n",
|
||||||
"\n",
|
"\n",
|
||||||
@@ -190,9 +136,16 @@
|
|||||||
" plt.title(title)\n",
|
" plt.title(title)\n",
|
||||||
" plt.xlabel(\"PC1\")\n",
|
" plt.xlabel(\"PC1\")\n",
|
||||||
" plt.ylabel(\"PC2\")\n",
|
" plt.ylabel(\"PC2\")\n",
|
||||||
" plt.show()\n",
|
" plt.show()\n"
|
||||||
"\n",
|
]
|
||||||
"\n",
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": null,
|
||||||
|
"id": "bf07447a",
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [],
|
||||||
|
"source": [
|
||||||
"# ---------- Main pipeline ----------\n",
|
"# ---------- Main pipeline ----------\n",
|
||||||
"\n",
|
"\n",
|
||||||
"\n",
|
"\n",
|
||||||
@@ -242,32 +195,12 @@
|
|||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 4,
|
"execution_count": null,
|
||||||
"id": "bbd5e7a8",
|
"id": "bbd5e7a8",
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [
|
"outputs": [],
|
||||||
{
|
|
||||||
"name": "stdout",
|
|
||||||
"output_type": "stream",
|
|
||||||
"text": [
|
|
||||||
"=== Dataset Sizes ===\n",
|
|
||||||
"Banknote: 1372 samples, 4 features\n",
|
|
||||||
"Seeds: 210 samples, 7 features\n",
|
|
||||||
"\n",
|
|
||||||
"=== PCA Explained Variance (2 components) ===\n",
|
|
||||||
"Banknote: 54.5% + 32.3% = 86.8% total\n",
|
|
||||||
"Seeds: 71.9% + 17.1% = 89.0% total\n",
|
|
||||||
"\n",
|
|
||||||
"=== Feature Ranges (min-max span) ===\n",
|
|
||||||
"Banknote: ['13.87', '26.72', '23.21', '11.00']\n",
|
|
||||||
"Seeds: ['10.59', '4.84', '0.11', '1.78', '1.40', '7.69', '2.03']\n"
|
|
||||||
]
|
|
||||||
}
|
|
||||||
],
|
|
||||||
"source": [
|
"source": [
|
||||||
"# Additional data for report\n",
|
"# Additional data for report\n",
|
||||||
"from sklearn.decomposition import PCA\n",
|
|
||||||
"\n",
|
|
||||||
"# Load datasets\n",
|
"# Load datasets\n",
|
||||||
"X_bank, y_bank, _ = load_banknote()\n",
|
"X_bank, y_bank, _ = load_banknote()\n",
|
||||||
"X_seeds, y_seeds, _ = load_seeds()\n",
|
"X_seeds, y_seeds, _ = load_seeds()\n",
|
||||||
|
|||||||
@@ -0,0 +1,22 @@
|
|||||||
|
# Data Mining - Classification II
|
||||||
|
|
||||||
|
## Decision Tree - DT
|
||||||
|
|
||||||
|
Select two datasets with labels available to perform the following experiments:
|
||||||
|
|
||||||
|
- Analyze and pre-process the data (if any).
|
||||||
|
- Divide the original dataset into two subsets: one for training (80%) and one for testing (20%).
|
||||||
|
- Build a DT for the training subset and test the built model for data from the testing subset.
|
||||||
|
Note: Try the “tree” package from sklearn in Python or the function fitctree() in Matlab.
|
||||||
|
- Calculate the error of classification.
|
||||||
|
|
||||||
|
## Random Forest - RF
|
||||||
|
|
||||||
|
Select two datasets with labels available to perform the following experiments:
|
||||||
|
|
||||||
|
- Analyze and pre-process the data (if any).
|
||||||
|
- Create K = 100 training set (using cross-validation or bagging technique), and build 1 testing
|
||||||
|
set.
|
||||||
|
- Build an RF for each training set. Classify data from the testing set using RF and calculate
|
||||||
|
the error of classification.
|
||||||
|
- Compare the results of RF and DT for the testing dataset. Comment.
|
||||||
@@ -0,0 +1,15 @@
|
|||||||
|
@misc{banknote_authentication_267,
|
||||||
|
author = {Lohweg, Volker},
|
||||||
|
title = {{Banknote Authentication}},
|
||||||
|
year = {2013},
|
||||||
|
howpublished = {UCI Machine Learning Repository},
|
||||||
|
note = {{DOI}: https://doi.org/10.24432/C55P57}
|
||||||
|
}
|
||||||
|
|
||||||
|
@misc{seeds_236,
|
||||||
|
author = {Charytanowicz, Malgorzata and Niewczas, Jerzy and Kulczycki, Piotr and Kowalski, Piotr and Lukasik, Szymon and Zak, Slawomir},
|
||||||
|
title = {{Seeds}},
|
||||||
|
year = {2012},
|
||||||
|
howpublished = {UCI Machine Learning Repository},
|
||||||
|
note = {{DOI}: https://doi.org/10.24432/C5H30K}
|
||||||
|
}
|
||||||
+11135
File diff suppressed because it is too large.
Load diff
+294
@@ -0,0 +1,294 @@
|
|||||||
|
```python
|
||||||
|
import numpy as np
|
||||||
|
import pandas as pd
|
||||||
|
import matplotlib.pyplot as plt
|
||||||
|
|
||||||
|
from sklearn.model_selection import train_test_split
|
||||||
|
from sklearn.tree import DecisionTreeClassifier, plot_tree
|
||||||
|
from sklearn.ensemble import RandomForestClassifier, BaggingClassifier
|
||||||
|
from sklearn.metrics import accuracy_score, classification_report
|
||||||
|
from sklearn.preprocessing import StandardScaler
|
||||||
|
|
||||||
|
#
|
||||||
|
from matplotlib_inline.backend_inline import set_matplotlib_formats
|
||||||
|
set_matplotlib_formats('pdf', 'svg')
|
||||||
|
|
||||||
|
# ---------- Data Loading ----------
|
||||||
|
|
||||||
|
def load_banknote():
|
||||||
|
url = "https://archive.ics.uci.edu/ml/machine-learning-databases/00267/data_banknote_authentication.txt"
|
||||||
|
df = pd.read_csv(url, header=None)
|
||||||
|
X = df.iloc[:, :-1].values
|
||||||
|
y = df.iloc[:, -1].values
|
||||||
|
feature_names = ["Variance", "Skewness", "Kurtosis", "Entropy"]
|
||||||
|
return X, y, "Banknote Authentication", feature_names
|
||||||
|
|
||||||
|
|
||||||
|
def load_seeds():
|
||||||
|
url = "https://archive.ics.uci.edu/ml/machine-learning-databases/00236/seeds_dataset.txt"
|
||||||
|
cols = [
|
||||||
|
"area",
|
||||||
|
"perimeter",
|
||||||
|
"compactness",
|
||||||
|
"length",
|
||||||
|
"width",
|
||||||
|
"asymmetry",
|
||||||
|
"groove",
|
||||||
|
"class",
|
||||||
|
]
|
||||||
|
df = pd.read_csv(url, sep=r"\s+", names=cols)
|
||||||
|
X = df.iloc[:, :-1].values
|
||||||
|
y = df["class"].values
|
||||||
|
return X, y, "Seeds", cols[:-1]
|
||||||
|
|
||||||
|
|
||||||
|
# ---------- Decision Tree ----------
|
||||||
|
|
||||||
|
|
||||||
|
def train_decision_tree(X_train, y_train, max_depth=None):
|
||||||
|
dt = DecisionTreeClassifier(max_depth=max_depth, random_state=42)
|
||||||
|
dt.fit(X_train, y_train)
|
||||||
|
return dt
|
||||||
|
|
||||||
|
|
||||||
|
def evaluate_model(model, X_test, y_test):
|
||||||
|
y_pred = model.predict(X_test)
|
||||||
|
acc = accuracy_score(y_test, y_pred)
|
||||||
|
error = 1 - acc
|
||||||
|
return acc, error, y_pred
|
||||||
|
|
||||||
|
|
||||||
|
def plot_decision_tree(dt, feature_names, class_names, title):
|
||||||
|
plt.figure(figsize=(20, 10))
|
||||||
|
plot_tree(
|
||||||
|
dt,
|
||||||
|
feature_names=feature_names,
|
||||||
|
class_names=class_names,
|
||||||
|
filled=True,
|
||||||
|
rounded=True,
|
||||||
|
fontsize=10,
|
||||||
|
)
|
||||||
|
plt.title(title)
|
||||||
|
plt.tight_layout()
|
||||||
|
plt.show()
|
||||||
|
|
||||||
|
|
||||||
|
# ---------- Random Forest ----------
|
||||||
|
|
||||||
|
|
||||||
|
def train_random_forest(X_train, y_train, n_estimators=100):
|
||||||
|
rf = RandomForestClassifier(n_estimators=n_estimators, random_state=42)
|
||||||
|
rf.fit(X_train, y_train)
|
||||||
|
return rf
|
||||||
|
|
||||||
|
|
||||||
|
def plot_feature_importance(model, feature_names, title):
|
||||||
|
importances = model.feature_importances_
|
||||||
|
indices = np.argsort(importances)[::-1]
|
||||||
|
|
||||||
|
plt.figure(figsize=(10, 6))
|
||||||
|
plt.bar(range(len(importances)), importances[indices])
|
||||||
|
plt.xticks(
|
||||||
|
range(len(importances)), [feature_names[i] for i in indices], rotation=45
|
||||||
|
)
|
||||||
|
plt.xlabel("Feature")
|
||||||
|
plt.ylabel("Importance")
|
||||||
|
plt.title(title)
|
||||||
|
plt.tight_layout()
|
||||||
|
plt.show()
|
||||||
|
|
||||||
|
|
||||||
|
# ---------- Comparison ----------
|
||||||
|
|
||||||
|
|
||||||
|
def compare_dt_rf(X_train, X_test, y_train, y_test, feature_names, dataset_name):
|
||||||
|
results = {}
|
||||||
|
|
||||||
|
# Decision Tree
|
||||||
|
dt = train_decision_tree(X_train, y_train)
|
||||||
|
dt_acc, dt_err, _ = evaluate_model(dt, X_test, y_test)
|
||||||
|
results["Decision Tree"] = {"accuracy": dt_acc, "error": dt_err}
|
||||||
|
|
||||||
|
# Random Forest (K=100)
|
||||||
|
rf = train_random_forest(X_train, y_train, n_estimators=100)
|
||||||
|
rf_acc, rf_err, _ = evaluate_model(rf, X_test, y_test)
|
||||||
|
results["Random Forest (100)"] = {"accuracy": rf_acc, "error": rf_err}
|
||||||
|
|
||||||
|
return results, dt, rf
|
||||||
|
|
||||||
|
|
||||||
|
def plot_comparison(results, dataset_name):
|
||||||
|
models = list(results.keys())
|
||||||
|
errors = [results[m]["error"] for m in models]
|
||||||
|
|
||||||
|
plt.figure(figsize=(8, 5))
|
||||||
|
plt.bar(models, errors, color=["steelblue", "coral"])
|
||||||
|
plt.ylabel("Classification Error")
|
||||||
|
plt.title(f"{dataset_name} — DT vs RF Error Comparison")
|
||||||
|
plt.ylim(0, max(errors) * 1.3 + 0.01)
|
||||||
|
for i, v in enumerate(errors):
|
||||||
|
plt.text(i, v + 0.005, f"{v:.3f}", ha="center")
|
||||||
|
plt.tight_layout()
|
||||||
|
plt.show()
|
||||||
|
|
||||||
|
|
||||||
|
# ---------- Main Pipeline ----------
|
||||||
|
|
||||||
|
|
||||||
|
def run_pipeline(loader_fn):
|
||||||
|
X, y, name, feature_names = loader_fn()
|
||||||
|
print(f"\n{'=' * 50}")
|
||||||
|
print(f"Dataset: {name}")
|
||||||
|
print(f"Samples: {X.shape[0]}, Features: {X.shape[1]}")
|
||||||
|
print(f"{'=' * 50}")
|
||||||
|
|
||||||
|
# 80/20 split
|
||||||
|
X_train, X_test, y_train, y_test = train_test_split(
|
||||||
|
X, y, test_size=0.2, random_state=42, stratify=y
|
||||||
|
)
|
||||||
|
print(f"Training set: {len(X_train)}, Testing set: {len(X_test)}")
|
||||||
|
|
||||||
|
# Compare DT vs RF
|
||||||
|
results, dt, rf = compare_dt_rf(
|
||||||
|
X_train, X_test, y_train, y_test, feature_names, name
|
||||||
|
)
|
||||||
|
|
||||||
|
# Print results
|
||||||
|
print(f"\nResults:")
|
||||||
|
for model, metrics in results.items():
|
||||||
|
print(
|
||||||
|
f" {model}: Accuracy = {metrics['accuracy']:.4f}, Error = {metrics['error']:.4f}"
|
||||||
|
)
|
||||||
|
|
||||||
|
# Visualizations
|
||||||
|
class_names = [str(c) for c in np.unique(y)]
|
||||||
|
|
||||||
|
# Plot decision tree (limited depth for readability)
|
||||||
|
dt_viz = train_decision_tree(X_train, y_train, max_depth=4)
|
||||||
|
plot_decision_tree(
|
||||||
|
dt_viz, feature_names, class_names, f"{name} — Decision Tree (max_depth=4)"
|
||||||
|
)
|
||||||
|
|
||||||
|
# Plot feature importance
|
||||||
|
plot_feature_importance(
|
||||||
|
rf, feature_names, f"{name} — Random Forest Feature Importance"
|
||||||
|
)
|
||||||
|
|
||||||
|
# Plot comparison
|
||||||
|
plot_comparison(results, name)
|
||||||
|
|
||||||
|
return results, dt, rf
|
||||||
|
|
||||||
|
|
||||||
|
# ---------- Run ----------
|
||||||
|
|
||||||
|
if __name__ == "__main__":
|
||||||
|
results_bank, dt_bank, rf_bank = run_pipeline(load_banknote)
|
||||||
|
results_seeds, dt_seeds, rf_seeds = run_pipeline(load_seeds)
|
||||||
|
```
|
||||||
|
|
||||||
|
|
||||||
|
==================================================
|
||||||
|
Dataset: Banknote Authentication
|
||||||
|
Samples: 1372, Features: 4
|
||||||
|
==================================================
|
||||||
|
Training set: 1097, Testing set: 275
|
||||||
|
|
||||||
|
Results:
|
||||||
|
Decision Tree: Accuracy = 0.9927, Error = 0.0073
|
||||||
|
Random Forest (100): Accuracy = 0.9964, Error = 0.0036
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
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||||||
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||||||
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||||||
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||||||
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|
||||||
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|
||||||
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|
||||||
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|
||||||
|
==================================================
|
||||||
|
Dataset: Seeds
|
||||||
|
Samples: 210, Features: 7
|
||||||
|
==================================================
|
||||||
|
Training set: 168, Testing set: 42
|
||||||
|
|
||||||
|
Results:
|
||||||
|
Decision Tree: Accuracy = 0.8810, Error = 0.1190
|
||||||
|
Random Forest (100): Accuracy = 0.9048, Error = 0.0952
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
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||||||
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||||||
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|
||||||
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||||||
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||||||
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||||||
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||||||
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|
||||||
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||||||
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||||||
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||||||
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||||||
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||||||
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||||||
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|
||||||
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||||||
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|
||||||
|
|
||||||
|
```python
|
||||||
|
# Export decision trees as vector PDFs for report (scales cleanly)
|
||||||
|
from sklearn.tree import plot_tree
|
||||||
|
import os
|
||||||
|
|
||||||
|
os.makedirs("lw4_files", exist_ok=True)
|
||||||
|
|
||||||
|
|
||||||
|
def export_tree_pdf(loader_fn, filename):
|
||||||
|
X, y, name, feature_names = loader_fn()
|
||||||
|
X_train, _, y_train, _ = train_test_split(
|
||||||
|
X, y, test_size=0.2, random_state=42, stratify=y
|
||||||
|
)
|
||||||
|
|
||||||
|
dt = DecisionTreeClassifier(max_depth=4, random_state=42)
|
||||||
|
dt.fit(X_train, y_train)
|
||||||
|
|
||||||
|
class_names = [str(c) for c in np.unique(y)]
|
||||||
|
|
||||||
|
# Vector PDF - will scale up cleanly in LaTeX
|
||||||
|
fig, ax = plt.subplots(figsize=(16, 10))
|
||||||
|
plot_tree(
|
||||||
|
dt,
|
||||||
|
feature_names=feature_names,
|
||||||
|
class_names=class_names,
|
||||||
|
filled=True,
|
||||||
|
rounded=True,
|
||||||
|
fontsize=9,
|
||||||
|
ax=ax,
|
||||||
|
)
|
||||||
|
ax.set_title(f"{name} — Decision Tree (max_depth=4)", fontsize=14)
|
||||||
|
plt.tight_layout()
|
||||||
|
plt.savefig(f"lw4_files/{filename}", format="pdf", bbox_inches="tight")
|
||||||
|
plt.close()
|
||||||
|
print(f"Saved: lw4_files/{filename}")
|
||||||
|
|
||||||
|
|
||||||
|
export_tree_pdf(load_banknote, "banknote_tree.pdf")
|
||||||
|
export_tree_pdf(load_seeds, "seeds_tree.pdf")
|
||||||
|
```
|
||||||
|
|
||||||
|
Saved: lw4_files/banknote_tree.pdf
|
||||||
|
Saved: lw4_files/seeds_tree.pdf
|
||||||
|
|
||||||
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|
|||||||
|
---
|
||||||
|
title: Classification II — Decision Trees and Random Forests
|
||||||
|
author:
|
||||||
|
- "Lương Đức Anh - 23BI14021"
|
||||||
|
bibliography: "cite.bib"
|
||||||
|
header-includes:
|
||||||
|
- \usepackage{float}
|
||||||
|
nocite: "[@*]"
|
||||||
|
---
|
||||||
|
|
||||||
|
# 1. Decision Tree Classification
|
||||||
|
|
||||||
|
## 1.1 Selected datasets
|
||||||
|
|
||||||
|
Two labeled datasets were selected (same as Classification I for consistency):
|
||||||
|
|
||||||
|
- **Banknote Authentication** [@banknote_authentication_267]
|
||||||
|
- Binary classification (genuine vs forged banknotes)
|
||||||
|
- 1,372 samples with 4 continuous features
|
||||||
|
- Well-separated classes
|
||||||
|
|
||||||
|
- **Seeds Dataset** [@seeds_236]
|
||||||
|
- Multi-class classification (3 types of wheat seeds)
|
||||||
|
- 210 samples with 7 continuous features
|
||||||
|
- Moderate class overlap
|
||||||
|
|
||||||
|
## 1.2 Data preprocessing and split
|
||||||
|
|
||||||
|
Each dataset was divided into **80% training** and **20% testing** subsets using stratified sampling to preserve class distributions.
|
||||||
|
|
||||||
|
No normalization was applied, as decision trees are invariant to feature scaling.
|
||||||
|
|
||||||
|
## 1.3 Decision Tree construction
|
||||||
|
|
||||||
|
A decision tree was built using the CART algorithm (sklearn's `DecisionTreeClassifier`). The tree recursively partitions the feature space by selecting splits that maximize information gain.
|
||||||
|
|
||||||
|
### Banknote Authentication
|
||||||
|
|
||||||
|
{latex-placement="H"}
|
||||||
|
|
||||||
|
- The root node splits on **Variance $\leq$ 0.765**, confirming it as the most discriminative feature
|
||||||
|
- Tree structure shows clear separation paths with low Gini impurity at leaf nodes
|
||||||
|
- Most leaves achieve pure classification (gini = 0.0)
|
||||||
|
|
||||||
|
### Seeds Dataset
|
||||||
|
|
||||||
|
{latex-placement="H"}
|
||||||
|
|
||||||
|
- The root node splits on **groove $\leq$ 5.576**, effectively separating class 2 from classes 1 and 3
|
||||||
|
- Subsequent splits use area, width, and asymmetry to distinguish remaining classes
|
||||||
|
- Some leaves retain impurity (gini > 0), reflecting the inherent class overlap in this dataset
|
||||||
|
|
||||||
|
## 1.4 Classification error
|
||||||
|
|
||||||
|
| Dataset | DT Accuracy | DT Error |
|
||||||
|
| -------- | ----------- | -------- |
|
||||||
|
| Banknote | 99.3% | 0.7% |
|
||||||
|
| Seeds | 88.1% | 11.9% |
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
# 2. Random Forest Classification
|
||||||
|
|
||||||
|
## 2.1 Random Forest construction
|
||||||
|
|
||||||
|
A Random Forest was built with **K = 100** decision trees. Each tree is trained on a bootstrap sample (bagging), and at each split, a random subset of features is considered.
|
||||||
|
|
||||||
|
This ensemble approach reduces variance compared to a single decision tree.
|
||||||
|
|
||||||
|
## 2.2 Feature importance
|
||||||
|
|
||||||
|
Random Forests provide feature importance scores based on how much each feature contributes to reducing impurity across all trees.
|
||||||
|
|
||||||
|
### Banknote Authentication
|
||||||
|
|
||||||
|
{latex-placement="H"}
|
||||||
|
|
||||||
|
- **Variance** dominates with ~56% importance, consistent with its role as the root split in the decision tree
|
||||||
|
- **Skewness** contributes ~24%, providing secondary discrimination
|
||||||
|
- **Kurtosis** (~15%) and **Entropy** (~6%) play minor roles
|
||||||
|
- The skewed distribution suggests that a single feature carries most of the predictive power
|
||||||
|
|
||||||
|
### Seeds Dataset
|
||||||
|
|
||||||
|
{latex-placement="H"}
|
||||||
|
|
||||||
|
- Importance is **more evenly distributed** across features compared to Banknote
|
||||||
|
- **Area**, **perimeter**, and **groove** each contribute ~20%
|
||||||
|
- **Width** (~16%) and **length** (~14%) provide moderate contribution
|
||||||
|
- **Asymmetry** (~7%) and **compactness** (~3%) are least important
|
||||||
|
- This distribution explains why Seeds is harder to classify — no single feature dominates
|
||||||
|
|
||||||
|
## 2.3 Classification error
|
||||||
|
|
||||||
|
| Dataset | RF Accuracy | RF Error |
|
||||||
|
| -------- | ----------- | -------- |
|
||||||
|
| Banknote | 99.6% | 0.4% |
|
||||||
|
| Seeds | 90.5% | 9.5% |
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
# 3. Comparison: Decision Tree vs Random Forest
|
||||||
|
|
||||||
|
## 3.1 Error comparison
|
||||||
|
|
||||||
|
### Banknote Authentication
|
||||||
|
|
||||||
|
{latex-placement="H"}
|
||||||
|
|
||||||
|
### Seeds Dataset
|
||||||
|
|
||||||
|
{latex-placement="H"}
|
||||||
|
|
||||||
|
## 3.2 Summary
|
||||||
|
|
||||||
|
| Dataset | DT Error | RF Error | Improvement |
|
||||||
|
| -------- | -------- | -------- | ----------- |
|
||||||
|
| Banknote | 0.7% | 0.4% | 43% |
|
||||||
|
| Seeds | 11.9% | 9.5% | 20% |
|
||||||
|
|
||||||
|
## 3.3 Discussion
|
||||||
|
|
||||||
|
- **Random Forest reduces variance:** By averaging predictions from 100 trees trained on bootstrap samples, RF is less prone to overfitting than a single DT.
|
||||||
|
|
||||||
|
- **Single DT is interpretable:** A decision tree provides a clear, human-readable set of rules. RF sacrifices this interpretability for improved accuracy.
|
||||||
|
|
||||||
|
- **Feature importance:** RF provides robust feature importance estimates by aggregating across many trees.
|
||||||
|
|
||||||
|
- **Banknote benefits less from RF:** The single DT already achieves 99.3% accuracy due to the dominant Variance feature. RF provides marginal improvement (0.3 percentage points).
|
||||||
|
|
||||||
|
- **Seeds benefits more from RF:** With no dominant feature and class overlap, the ensemble approach reduces error by 2.4 percentage points (20% relative improvement).
|
||||||
|
|
||||||
|
---
|
||||||
|
|
||||||
|
# Overall Conclusion
|
||||||
|
|
||||||
|
- Decision Trees provide fast, interpretable models but can overfit on small or noisy datasets
|
||||||
|
- Random Forests improve generalization by ensembling multiple trees via bagging
|
||||||
|
- The variance reduction from RF is most noticeable on datasets with higher complexity or class overlap
|
||||||
|
- For Banknote (well-separated, dominant feature), both DT and RF achieve near-perfect accuracy
|
||||||
|
- For Seeds (overlapping classes, distributed importance), RF provides meaningful improvement over a single DT
|
||||||
|
- Feature importance analysis reveals dataset structure: concentrated importance suggests easy classification, distributed importance suggests complexity
|
||||||
|
|
||||||
|
# References
|
||||||
LFS
BIN
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Reference in new issue
Block a user