most minor wording changes
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@@ -24,7 +24,7 @@
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},
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{
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"data": {
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"image/svg+xml": [
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"<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
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"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
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@@ -34,7 +34,7 @@
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" <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
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" <cc:Work>\n",
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" <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
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" <dc:date>2026-01-24T17:24:22.064489</dc:date>\n",
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" <dc:date>2026-01-25T01:27:41.418741</dc:date>\n",
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" <dc:format>image/svg+xml</dc:format>\n",
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" <dc:creator>\n",
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" <cc:Agent>\n",
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@@ -3632,7 +3632,7 @@
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},
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{
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"image/svg+xml": [
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"<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
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"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
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@@ -5866,7 +5866,7 @@
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" <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
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" <cc:Work>\n",
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" <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
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" <dc:date>2026-01-24T17:24:23.355297</dc:date>\n",
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" <dc:date>2026-01-25T01:27:43.299660</dc:date>\n",
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" <dc:format>image/svg+xml</dc:format>\n",
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" <dc:creator>\n",
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" <cc:Agent>\n",
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@@ -8618,7 +8618,7 @@
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{
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" <defs>\n",
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" <path id=\"m198a62db0b\" d=\"M 0 0 \n",
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" <path id=\"mbe305c08ec\" d=\"M 0 0 \n",
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"L 0 3.5 \n",
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"\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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" </defs>\n",
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" <use xlink:href=\"#mbe305c08ec\" x=\"176.625619\" y=\"327.558125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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" </g>\n",
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@@ -10021,7 +10021,7 @@
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" <g id=\"xtick_2\">\n",
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" <g>\n",
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" <use xlink:href=\"#m198a62db0b\" x=\"434.751881\" y=\"327.558125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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" </g>\n",
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" <g id=\"text_2\">\n",
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@@ -10268,12 +10268,12 @@
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" <g id=\"ytick_1\">\n",
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" <g id=\"line2d_3\">\n",
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" <defs>\n",
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" <path id=\"m22fea275c5\" d=\"M 0 0 \n",
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"L -3.5 0 \n",
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"\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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" <use xlink:href=\"#m188ca62a8d\" x=\"50.14375\" y=\"327.558125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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@@ -10298,7 +10298,7 @@
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@@ -10377,7 +10377,7 @@
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@@ -10425,7 +10425,7 @@
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@@ -10482,7 +10482,7 @@
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@@ -10514,7 +10514,7 @@
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@@ -10530,7 +10530,7 @@
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@@ -10851,7 +10851,7 @@
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@@ -10872,9 +10872,8 @@
|
||||
"\n",
|
||||
"from sklearn.model_selection import train_test_split\n",
|
||||
"from sklearn.tree import DecisionTreeClassifier, plot_tree\n",
|
||||
"from sklearn.ensemble import RandomForestClassifier, BaggingClassifier\n",
|
||||
"from sklearn.metrics import accuracy_score, classification_report\n",
|
||||
"from sklearn.preprocessing import StandardScaler\n",
|
||||
"from sklearn.ensemble import RandomForestClassifier\n",
|
||||
"from sklearn.metrics import accuracy_score\n",
|
||||
"\n",
|
||||
"# the trix are out of hand\n",
|
||||
"from matplotlib_inline.backend_inline import set_matplotlib_formats\n",
|
||||
@@ -11056,7 +11055,7 @@
|
||||
},
|
||||
{
|
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"cell_type": "code",
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"execution_count": 10,
|
||||
"execution_count": 2,
|
||||
"id": "146bb611",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
|
||||
+3
-4
@@ -5,11 +5,10 @@ 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 sklearn.ensemble import RandomForestClassifier
|
||||
from sklearn.metrics import accuracy_score
|
||||
|
||||
#
|
||||
# the trix are out of hand
|
||||
from matplotlib_inline.backend_inline import set_matplotlib_formats
|
||||
set_matplotlib_formats('pdf', 'svg')
|
||||
|
||||
|
||||
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+9
-8
@@ -1,7 +1,6 @@
|
||||
---
|
||||
title: Classification II — Decision Trees and Random Forests
|
||||
author:
|
||||
- "Lương Đức Anh - 23BI14021"
|
||||
author: lda
|
||||
bibliography: "cite.bib"
|
||||
header-includes:
|
||||
- \usepackage{float}
|
||||
@@ -28,11 +27,11 @@ Two labeled datasets were selected (same as Classification I for consistency):
|
||||
|
||||
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.
|
||||
No normalization was applied, as decision trees base splits on feature thresholds rather than distances, making them 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.
|
||||
A decision tree was built using the CART algorithm (sklearn's `DecisionTreeClassifier`). The tree recursively partitions the feature space by selecting splits that minimize Gini impurity.
|
||||
|
||||
### Banknote Authentication
|
||||
|
||||
@@ -63,13 +62,13 @@ A decision tree was built using the CART algorithm (sklearn's `DecisionTreeClass
|
||||
|
||||
## 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.
|
||||
A Random Forest was built with **K = 100** decision trees. Each tree is trained on a bootstrap sample (random sampling with replacement), 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.
|
||||
Random Forests provide feature importance scores based on how much each feature contributes to reducing impurity across all trees. Specifically, importance reflects the average reduction in Gini impurity contributed by each feature.
|
||||
|
||||
### Banknote Authentication
|
||||
|
||||
@@ -126,9 +125,9 @@ Random Forests provide feature importance scores based on how much each feature
|
||||
|
||||
- **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).
|
||||
- **Banknote benefits less from RF:** The dominance of the Variance feature results in a shallow, highly effective decision tree, leaving limited room for improvement through ensembling. RF provides only 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).
|
||||
- **Seeds benefits more from RF:** With no dominant feature and class overlap, the ensemble approach reduces error by 2.4 percentage points (20% relative error reduction).
|
||||
|
||||
---
|
||||
|
||||
@@ -141,4 +140,6 @@ Random Forests provide feature importance scores based on how much each feature
|
||||
- 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
|
||||
|
||||
Overall, ensemble methods provide the greatest benefit when datasets exhibit class overlap and distributed feature importance, while simpler models suffice for well-structured problems.
|
||||
|
||||
# References
|
||||
LFS
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Reference in new issue
Block a user