shi

2026-01-14 03:23:02 +07:00
1 parent 234350b6d6
commit 66c4d588be
@@ -0,0 +1,21 @@
+@misc{communities_and_crime_183,
+  author       = {Redmond, Michael},
+  title        = {{Communities and Crime}},
+  year         = {2002},
+  howpublished = {UCI Machine Learning Repository},
+  note         = {{DOI}: https://doi.org/10.24432/C53W3X}
+}
+@misc{abalone_1,
+  author       = {Nash, Warwick, Sellers, Tracy, Talbot, Simon, Cawthorn, Andrew, and Ford, Wes},
+  title        = {{Abalone}},
+  year         = {1994},
+  howpublished = {UCI Machine Learning Repository},
+  note         = {{DOI}: https://doi.org/10.24432/C55C7W}
+}
+@misc{covertype_31,
+  author       = {Blackard, Jock},
+  title        = {{Covertype}},
+  year         = {1998},
+  howpublished = {UCI Machine Learning Repository},
+  note         = {{DOI}: https://doi.org/10.24432/C50K5N}
+}
@@ -2,7 +2,7 @@
 "cells": [
  {
   "cell_type": "code",
-   "execution_count": 54,
+   "execution_count": 106,
   "id": "e377bc9b",
   "metadata": {},
   "outputs": [],
@@ -20,7 +20,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 55,
+   "execution_count": 107,
   "id": "d7275d15",
   "metadata": {},
   "outputs": [
@@ -30,7 +30,7 @@
       "WindowsPath('c:/Users/Admin/Documents/lecture ass shit/3/ml2/lw2')"
      ]
     },
-     "execution_count": 55,
+     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
@@ -51,7 +51,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 56,
+   "execution_count": 108,
   "id": "4de18adb",
   "metadata": {},
   "outputs": [],
@@ -78,7 +78,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 57,
+   "execution_count": 109,
   "id": "50b3eb52",
   "metadata": {},
   "outputs": [],
@@ -105,7 +105,45 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 58,
+   "execution_count": 110,
+   "id": "a89a6974",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "([0.4307184563069171,\n",
+       "  0.3308881531841743,\n",
+       "  0.34454881088271005,\n",
+       "  0.3330973959780588,\n",
+       "  0.37350567261284556,\n",
+       "  0.39200932042425607,\n",
+       "  0.3905976225423938,\n",
+       "  0.38566484346143776,\n",
+       "  0.3910649022379036],\n",
+       " [18066.00920712765,\n",
+       "  13418.727667404704,\n",
+       "  11157.455698492053,\n",
+       "  9330.808564389003,\n",
+       "  7660.230080453761,\n",
+       "  6764.331897239782,\n",
+       "  5939.9031003732325,\n",
+       "  5315.323604570619,\n",
+       "  4805.410264465899])"
+      ]
+     },
+     "execution_count": 110,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "silhouettes, inertias"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 111,
   "id": "c70bfa21",
   "metadata": {},
   "outputs": [],
@@ -116,13 +154,13 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 59,
+   "execution_count": 112,
   "id": "926a255e",
   "metadata": {},
   "outputs": [
    {
     "data": {
-      "image/png": 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truncated
+      "image/png": "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 truncated
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
@@ -135,19 +173,19 @@
    "plt.plot(ks, inertias, marker=\"o\")\n",
    "plt.xlabel(\"k\")\n",
    "plt.ylabel(\"Inertia (WCSS)\")\n",
-    "plt.title(\"Elbow Method\")\n",
+    "plt.title(\"Elbow Method - Abalone\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
-   "execution_count": 60,
+   "execution_count": 113,
   "id": "7b8c1750",
   "metadata": {},
   "outputs": [
    {
     "data": {
-      "image/png": "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 truncated
+      "image/png": "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 truncated
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
@@ -160,13 +198,13 @@
    "plt.plot(ks, silhouettes, marker=\"o\")\n",
    "plt.xlabel(\"k\")\n",
    "plt.ylabel(\"Silhouette Score\")\n",
-    "plt.title(\"Silhouette Analysis\")\n",
+    "plt.title(\"Silhouette Analysis - Abalone\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
-   "execution_count": 61,
+   "execution_count": 114,
   "id": "acab8d95",
   "metadata": {},
   "outputs": [
@@ -199,7 +237,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 62,
+   "execution_count": 90,
   "id": "92b692bc",
   "metadata": {},
   "outputs": [],
@@ -214,7 +252,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 63,
+   "execution_count": 91,
   "id": "e6bbfcb7",
   "metadata": {},
   "outputs": [],
@@ -239,7 +277,41 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 64,
+   "execution_count": 92,
+   "id": "05d4bd31",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "([-0.030689560868985374,\n",
+       "  0.014267829228328097,\n",
+       "  0.052170441001039715,\n",
+       "  0.0763160133542805,\n",
+       "  0.05712772597563029,\n",
+       "  0.11281790580873496,\n",
+       "  0.1241172489653034],\n",
+       " [1033855.8510931745,\n",
+       "  983031.2462602488,\n",
+       "  933199.3143504256,\n",
+       "  914886.5211138967,\n",
+       "  889334.3440412064,\n",
+       "  868852.814198654,\n",
+       "  848656.9204411206])"
+      ]
+     },
+     "execution_count": 92,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "silhouettes, inertias"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 93,
   "id": "da938557",
   "metadata": {},
   "outputs": [
@@ -264,7 +336,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 65,
+   "execution_count": 94,
   "id": "0070102e",
   "metadata": {},
   "outputs": [
@@ -289,7 +361,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 66,
+   "execution_count": 95,
   "id": "c312a24a",
   "metadata": {},
   "outputs": [],
@@ -308,7 +380,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 67,
+   "execution_count": 96,
   "id": "bc26af01",
   "metadata": {},
   "outputs": [],
@@ -336,7 +408,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 68,
+   "execution_count": 97,
   "id": "a3e10a92",
   "metadata": {},
   "outputs": [
@@ -372,7 +444,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 69,
+   "execution_count": 98,
   "id": "69a1249a",
   "metadata": {},
   "outputs": [
@@ -405,7 +477,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 70,
+   "execution_count": 99,
   "id": "f41491b4",
   "metadata": {},
   "outputs": [],
@@ -429,7 +501,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 71,
+   "execution_count": 100,
   "id": "873caac5",
   "metadata": {},
   "outputs": [],
@@ -454,7 +526,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 72,
+   "execution_count": 101,
   "id": "6846b929",
   "metadata": {},
   "outputs": [
@@ -489,7 +561,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 73,
+   "execution_count": 102,
   "id": "fc244f0c",
   "metadata": {},
   "outputs": [
@@ -522,7 +594,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 74,
+   "execution_count": 103,
   "id": "813e9b68",
   "metadata": {},
   "outputs": [],
@@ -535,7 +607,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 75,
+   "execution_count": 104,
   "id": "6aa93bec",
   "metadata": {},
   "outputs": [],
@@ -558,7 +630,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 76,
+   "execution_count": 105,
   "id": "1fb883f8",
   "metadata": {},
   "outputs": [
@@ -74,6 +74,35 @@ for k in ks:
 ```


+```python
+silhouettes, inertias
+```
+
+
+
+
+    ([0.4307184563069171,
+      0.3308881531841743,
+      0.34454881088271005,
+      0.3330973959780588,
+      0.37350567261284556,
+      0.39200932042425607,
+      0.3905976225423938,
+      0.38566484346143776,
+      0.3910649022379036],
+     [18066.00920712765,
+      13418.727667404704,
+      11157.455698492053,
+      9330.808564389003,
+      7660.230080453761,
+      6764.331897239782,
+      5939.9031003732325,
+      5315.323604570619,
+      4805.410264465899])
+
+
+
+
 ```python
 best_k = ks[np.argmax(silhouettes)]
 best_labels = labels_per_k[best_k]
@@ -84,13 +113,13 @@ best_labels = labels_per_k[best_k]
 plt.plot(ks, inertias, marker="o")
 plt.xlabel("k")
 plt.ylabel("Inertia (WCSS)")
-plt.title("Elbow Method")
+plt.title("Elbow Method - Abalone")
 plt.show()
 ```


    
-![png](lw2_files/lw2_6_0.png)
+![png](lw2_files/lw2_7_0.png)
    


@@ -99,13 +128,13 @@ plt.show()
 plt.plot(ks, silhouettes, marker="o")
 plt.xlabel("k")
 plt.ylabel("Silhouette Score")
-plt.title("Silhouette Analysis")
+plt.title("Silhouette Analysis - Abalone")
 plt.show()
 ```


    
-![png](lw2_files/lw2_7_0.png)
+![png](lw2_files/lw2_8_0.png)
    


@@ -121,7 +150,7 @@ plt.show()


    
-![png](lw2_files/lw2_8_0.png)
+![png](lw2_files/lw2_9_0.png)
    


@@ -160,6 +189,31 @@ for k in ks:
 ```


+```python
+silhouettes, inertias
+```
+
+
+
+
+    ([-0.030689560868985374,
+      0.014267829228328097,
+      0.052170441001039715,
+      0.0763160133542805,
+      0.05712772597563029,
+      0.11281790580873496,
+      0.1241172489653034],
+     [1033855.8510931745,
+      983031.2462602488,
+      933199.3143504256,
+      914886.5211138967,
+      889334.3440412064,
+      868852.814198654,
+      848656.9204411206])
+
+
+
+
 ```python
 plt.plot(ks, inertias, marker="o")
 plt.xlabel("k")
@@ -170,7 +224,7 @@ plt.show()


    
-![png](lw2_files/lw2_12_0.png)
+![png](lw2_files/lw2_14_0.png)
    


@@ -185,7 +239,7 @@ plt.show()


    
-![png](lw2_files/lw2_13_0.png)
+![png](lw2_files/lw2_15_0.png)
    


@@ -232,7 +286,7 @@ plt.show()


    
-![png](lw2_files/lw2_18_0.png)
+![png](lw2_files/lw2_20_0.png)
    


@@ -251,7 +305,7 @@ plt.show()


    
-![png](lw2_files/lw2_20_0.png)
+![png](lw2_files/lw2_22_0.png)
    


@@ -303,7 +357,7 @@ plt.show()


    
-![png](lw2_files/lw2_26_0.png)
+![png](lw2_files/lw2_28_0.png)
    


@@ -322,7 +376,7 @@ plt.show()


    
-![png](lw2_files/lw2_28_0.png)
+![png](lw2_files/lw2_30_0.png)
    


@@ -367,6 +421,6 @@ plt.show()


    
-![png](lw2_files/lw2_33_0.png)
+![png](lw2_files/lw2_35_0.png)
    

@@ -0,0 +1,160 @@
+---
+title: Clustering Analysis Report
+author:
+  - "Mai Minh Vũ - 22BI13477"
+  - "Lương Đức Anh - 23BI14021"
+header-includes:
+  - \usepackage{float}
+  - \usepackage{tabularx}
+  - \usepackage{booktabs}
+references:
+- author:
+  - family: Redmond
+    given: Michael
+  id: communities_and_crime_183
+  issued: 2002
+  note: "DOI: https://doi.org/10.24432/C53W3X"
+  publisher: UCI Machine Learning Repository
+  title: "[Communities and Crime]{.nocase}"
+- author:
+  - family: Nash
+    given: Sellers
+    suffix: Warwick
+  - family: Ford
+    given: Wes
+  id: abalone_1
+  issued: 1994
+  note: "DOI: https://doi.org/10.24432/C55C7W"
+  publisher: UCI Machine Learning Repository
+  title: Abalone
+- author:
+  - family: Blackard
+    given: Jock
+  id: covertype_31
+  issued: 1998
+  note: "DOI: https://doi.org/10.24432/C50K5N"
+  publisher: UCI Machine Learning Repository
+  title: Covertype
+nocite: "[@*]"
+---
+
+# Part 1 — K-means Clustering
+
+## 1.1 Dataset: Abalone [@abalone_1]
+
+### Experimental Protocol
+
+We applied K-means clustering to the Abalone dataset. Preprocessing included:
+
+- One-hot encoding of the categorical `Sex` feature.
+- Standard scaling of all numeric features to zero mean and unit variance.
+- Exclusion of the target `Rings` from clustering.
+
+We varied k from 2 to 10, used the **k-means++** centroid initialization, and ran each clustering with multiple initializations (`n_init = 10`) to reduce random seed sensitivity.
+
+### Results
+
+#### Silhouette Analysis
+
+This plot shows the average silhouette score for different values of k:
+
+![Abalone Silhouette](lw2_files/lw2_8_0.png){latex-placement="H"}
+
+#### Elbow Plot
+
+The elbow plot showing inertia (within-cluster sum of squares) across k:
+
+![Abalone Elbow](lw2_files/lw2_7_0.png){latex-placement="H"}
+
+### Interpretation
+
+The silhouette score peaked at _k = 2_, indicating that this value of k yields the best separation given the dataset. The elbow plot shows diminishing returns after this point. Overall, the clustering quality suggests moderate structure in the data.
+
+---
+
+## 1.2 Dataset: Covertype [@covertype_31]
+
+### Experimental Protocol
+
+For the Covertype dataset, which is large in size, we performed:
+
+- Subsampling (e.g., 20,000 random samples) to make computations feasible.
+- Standard scaling of all features.
+- Clustering using **MiniBatchKMeans** with k-means++ initialization.
+
+We tested k from 2 to 8, tracked inertia and silhouette scores, and recorded results for comparison.
+
+### Results
+
+#### Silhouette Analysis
+
+![Covtype Silhouette](lw2_files/lw2_15_0.png){latex-placement="H"}
+
+#### Elbow Plot
+
+![Covtype Elbow](lw2_files/lw2_14_0.png){latex-placement="H"}
+
+### Interpretation
+
+The Covertype silhouette scores remained relatively low across k values, indicating weak separation in the original feature space. The elbow plot does not show a clear bend, further suggesting that classic k-means struggles with high dimensionality and feature noise in this dataset.
+
+---
+
+# Part 2 — Subspace Clustering
+
+## 2.1 Dataset: Communities & Crime [@communities_and_crime_183]
+
+The Communities & Crime dataset contains more than 100 numeric socio-economic and crime rate features, making it suitable for subspace clustering analysis.
+
+### Preprocessing
+
+Before clustering:
+
+- Dropped non-numeric identification columns (`communityname`, `state`, `county`, `community`, `fold`) and the target `ViolentCrimesPerPop`.
+- Replaced missing values (`?`) with column means.
+- Standard scaled all features.
+
+## 2.2 PCA Variance Explained
+
+We applied PCA to analyze variance distribution across components and determine an appropriate dimensionality for visualization/clustering.
+
+![PCA Variance Explained](lw2_files/lw2_20_0.png){latex-placement="H"}
+
+## 2.3 PCA Visualization (2D)
+
+The data projected onto the first two principal components:
+
+![PCA Projection](lw2_files/lw2_22_0.png){latex-placement="H"}
+
+## 2.4 Clustering After PCA vs Original
+
+We applied k-means clustering with varying k to:
+
+- The original high-dimensional space.
+- The 2D PCA projection.
+
+The silhouette scores for both are shown below:
+
+![Subspace Clustering Comparison](lw2_files/lw2_28_0.png){latex-placement="H"}
+
+### Best PCA Clustering Visualization
+
+For the PCA space, the best silhouette score occurred at _k = 3_. The clusters are visualized here:
+
+![PCA Clusters (k=3)](lw2_files/lw2_30_0.png){latex-placement="H"}
+
+## 2.5 Random Subspace Clustering
+
+We also selected a random subset of 30 features and repeated k-means clustering, comparing silhouette scores with previous methods. This helped assess the impact of arbitrary feature selection vs. PCA-based dimensionality reduction.
+
+### Random Subspace Results
+
+The random subspace silhouette scores are included in the comparison plot above.
+
+---
+
+# Conclusion
+
+We successfully ran k-means clustering on two UCI datasets (Abalone and Covertype). For Abalone, moderate cluster structure was identified, while Covertype presented weak separability in the original space.
+
+In the subspace clustering section, PCA significantly improved clustering quality relative to both original and random subspace clustering. This demonstrates that **dimensionality reduction can reveal latent structure** that is otherwise obscured in high-dimensional data.