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Redmond, Michael. 2002. Communities and Crime. UCI Machine Learning Repository. https://doi.org/10.24432/C53W3X.
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fixed by copilot:
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@misc{abalone_1,
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author = {Nash, Warwick, Sellers, Tracy, Talbot, Simon, Cawthorn, Andrew, and Ford, Wes},
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author = {Nash, Warwick and Sellers, Tracy and Talbot, Simon and Cawthorn, Andrew and Ford, Wes},
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title = {{Abalone}},
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year = {1994},
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howpublished = {UCI Machine Learning Repository},
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+109
-62
@@ -5,10 +5,13 @@ import matplotlib.pyplot as plt
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from sklearn.cluster import KMeans, MiniBatchKMeans
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from sklearn.decomposition import PCA
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from sklearn.preprocessing import StandardScaler
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from sklearn.metrics import silhouette_score
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from sklearn.metrics import (
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silhouette_score,
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davies_bouldin_score,
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calinski_harabasz_score,
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)
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from pathlib import Path
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```
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@@ -75,30 +78,13 @@ for k in ks:
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```python
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silhouettes, inertias
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f"{silhouettes = }, {inertias = }"
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```
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([0.4307184563069171,
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0.3308881531841743,
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0.34454881088271005,
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0.3330973959780588,
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0.37350567261284556,
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0.39200932042425607,
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0.3905976225423938,
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0.38566484346143776,
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0.3910649022379036],
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[18066.009207127645,
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13418.727667404704,
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11157.455698492053,
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9330.808564389003,
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7660.230080453761,
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6764.331897239782,
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5939.9031003732325,
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5315.323604570619,
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4805.410264465898])
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'silhouettes = [0.4307184563069171, 0.3308881531841743, 0.34454881088271005, 0.3330973959780588, 0.37350567261284556, 0.39200932042425607, 0.3905976225423938, 0.38566484346143776, 0.3910649022379036], inertias = [18066.00920712765, 13418.727667404704, 11157.455698492053, 9330.808564389003, 7660.230080453761, 6764.331897239782, 5939.903100373233, 5315.323604570618, 4805.410264465897]'
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@@ -154,6 +140,23 @@ plt.show()
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```python
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# Abalone dataset stats
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print(f"Abalone: n_samples={X.shape[0]}, n_features={X.shape[1]}")
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print(f"Best k: {best_k}")
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print(f"Cluster sizes: {np.bincount(best_labels)}")
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print(f"Davies-Bouldin Index: {davies_bouldin_score(X, best_labels):.4f}")
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print(f"Calinski-Harabasz Index: {calinski_harabasz_score(X, best_labels):.4f}")
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```
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Abalone: n_samples=4177, n_features=9
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Best k: 2
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Cluster sizes: [1940 2237]
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Davies-Bouldin Index: 0.8836
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Calinski-Harabasz Index: 4512.6320
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## Covertype
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@@ -190,26 +193,13 @@ for k in ks:
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```python
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silhouettes, inertias
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f"{silhouettes = }, {inertias = }"
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```
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([-0.030689560868985374,
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0.014267829228328097,
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0.052170441001039715,
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0.0763160133542805,
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0.05712772597563029,
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0.11281790580873496,
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0.1241172489653034],
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[1033855.8510931745,
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983031.2462602488,
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933199.3143504256,
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914886.5211138967,
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889334.3440412064,
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868852.814198654,
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848656.9204411206])
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'silhouettes = [-0.030689560868985374, 0.014267829228328097, 0.052170441001039715, 0.0763160133542805, 0.05712772597563029, 0.11281790580873496, 0.1241172489653034], inertias = [1033855.8510931745, 983031.2462602488, 933199.3143504256, 914886.5211138967, 889334.3440412064, 868852.814198654, 848656.9204411206]'
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@@ -224,7 +214,7 @@ plt.show()
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@@ -239,7 +229,7 @@ plt.show()
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@@ -249,6 +239,23 @@ best_k = ks[np.argmax(silhouettes)]
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best_labels = labels_per_k[best_k]
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```
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```python
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# Covertype dataset stats
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print(f"Covertype: n_samples={X.shape[0]}, n_features={X.shape[1]}")
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print(f"Best k: {best_k}")
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print(f"Cluster sizes: {np.bincount(best_labels)}")
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print(f"Davies-Bouldin Index: {davies_bouldin_score(X, best_labels):.4f}")
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print(f"Calinski-Harabasz Index: {calinski_harabasz_score(X, best_labels):.4f}")
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```
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Covertype: n_samples=20000, n_features=54
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Best k: 8
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Cluster sizes: [1407 6092 3757 2258 1139 4226 88 1033]
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Davies-Bouldin Index: 2.3425
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Calinski-Harabasz Index: 714.6171
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# community
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@@ -286,10 +293,26 @@ plt.show()
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```python
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# Communities dataset stats + PCA 90% variance
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print(f"Communities: n_samples={X.shape[0]}, n_features={X.shape[1]}")
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n_90 = np.argmax(np.cumsum(pca.explained_variance_ratio_) >= 0.90) + 1
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print(f"Components for 90% variance: {n_90}")
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print(
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f"First 2 components explain: {pca.explained_variance_ratio_[:2].sum() * 100:.1f}%"
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)
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```
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Communities: n_samples=1994, n_features=122
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Components for 90% variance: 30
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First 2 components explain: 35.0%
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## PCA to 2D (no clustering yet)
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@@ -305,7 +328,7 @@ plt.show()
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@@ -357,7 +380,7 @@ plt.show()
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@@ -376,7 +399,7 @@ plt.show()
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@@ -421,35 +444,59 @@ plt.show()
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```python
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sil_orig, sil_pca, sil_sub
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f"{sil_orig = }, {sil_pca = }, {sil_sub = }"
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```
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([0.1447573886443752,
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0.1513815804645033,
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0.1622363759648628,
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0.10473845344821518,
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0.11854956392780605,
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0.11689825990588008],
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[0.3885783888959868,
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0.43308922486937373,
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0.3730220026311381,
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0.38759443998496274,
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0.35733354404743983,
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0.36750626178240353],
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[0.16609258945009867,
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0.13111313797495522,
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0.13898110095002836,
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0.12515895253959083,
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0.12109768667928446,
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0.10798315908348614])
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'sil_orig = [0.1447573886443752, 0.1513815804645033, 0.1622363759648628, 0.10473845344821518, 0.11854956392780605, 0.11689825990588008], sil_pca = [0.3885783888959868, 0.43308922486937373, 0.3730220026311381, 0.38759443998496274, 0.35733354404743983, 0.36750626178240353], sil_sub = [0.16609258945009867, 0.13111313797495522, 0.13898110095002836, 0.12515895253959083, 0.12109768667928446, 0.10798315908348614]'
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```python
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# Full metrics table for all k values - Communities
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print("Communities & Crime - Full Metrics Table")
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print("-" * 70)
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print(f"{'k':<4} {'Orig Sil':<12} {'PCA Sil':<12} {'Rand Sil':<12}")
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print("-" * 70)
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for i, k in enumerate(ks):
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print(f"{k:<4} {sil_orig[i]:<12.4f} {sil_pca[i]:<12.4f} {sil_sub[i]:<12.4f}")
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```
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Communities & Crime - Full Metrics Table
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----------------------------------------------------------------------
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k Orig Sil PCA Sil Rand Sil
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----------------------------------------------------------------------
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2 0.1448 0.3886 0.1661
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3 0.1514 0.4331 0.1311
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4 0.1622 0.3730 0.1390
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5 0.1047 0.3876 0.1252
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6 0.1185 0.3573 0.1211
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7 0.1169 0.3675 0.1080
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```python
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# Best PCA clustering - additional metrics
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best_pca_k = ks[np.argmax(sil_pca)]
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best_pca_labels = labels_pca[best_pca_k]
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print(f"Best PCA k: {best_pca_k}")
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print(f"Cluster sizes (PCA): {np.bincount(best_pca_labels)}")
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print(f"Davies-Bouldin (PCA): {davies_bouldin_score(Xp, best_pca_labels):.4f}")
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print(f"Calinski-Harabasz (PCA): {calinski_harabasz_score(Xp, best_pca_labels):.4f}")
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```
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Best PCA k: 3
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Cluster sizes (PCA): [786 253 955]
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Davies-Bouldin (PCA): 0.7937
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Calinski-Harabasz (PCA): 1704.2171
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+7
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#### Silhouette Analysis
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{latex-placement="H"}
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{latex-placement="H"}
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#### Elbow Plot
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{latex-placement="H"}
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{latex-placement="H"}
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### Interpretation
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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.
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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. Additionally, the cluster size distribution is highly imbalanced (one cluster contains only 88 samples while another has 6,092), indicating potential outliers or that k-means is not finding natural groupings in this data.
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### Dataset Statistics
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@@ -166,13 +166,13 @@ Before clustering:
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We applied PCA to analyze variance distribution across components and determine an appropriate dimensionality for visualization/clustering.
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{latex-placement="H"}
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{latex-placement="H"}
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## 2.3 PCA Visualization (2D)
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The data projected onto the first two principal components:
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{latex-placement="H"}
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{latex-placement="H"}
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## 2.4 Clustering After PCA vs Original
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@@ -183,13 +183,13 @@ We applied k-means clustering with varying k to:
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The silhouette scores for both are shown below:
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{latex-placement="H"}
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{latex-placement="H"}
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### Best PCA Clustering Visualization
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For the PCA space, the best silhouette score occurred at _k = 3_. The clusters are visualized here:
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{latex-placement="H"}
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{latex-placement="H"}
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## 2.5 Random Subspace Clustering
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LFS
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# Classification I
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## K-nearest neighbor classification
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The objective is to study the use of the method k-nn and
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1. Select two datasets with labels.
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2. Run k-nn on these two datasets. Calculate the classification error (by comparing the class
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labels obtained with the prediction and the original labels of test data).
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3. Vary the value of k, comment on the results
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4. Try to normalize the input dataset, is the performance better?
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5. Apply PCA and SVD on the dataset, then what is the performance of k-nn on the new
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projected data? Justify the answer.
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6. Propose an approach to improve the performance of k-nn with the use of k-cross validation.
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7. Apply leave-one-out and calculate the error of classification.
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## SVM classifier
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Suppose that we use the SVM classifier from sklearn in Python.
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- Select two datasets with labels.
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- Analyze the dataset. How is the data distribution? linearly separable or non-linearly seperable?
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- Set up the SVM parameters suitable to the selected datasets.
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- What is the performance of SVMs?
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- How can SVM handle multi-class datasets?
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