The data

  • Four dataset (sheets TEST1, TEST4, TEST5, and TEST7 of the Excel file)
    • 1017 samples with 10 features
    • 287 samples with 10 features
    • 144 samples with 5 features
    • 287 samples with 10 features
      • First nine of second dataset and thorium
  • All data are normalised by using the Z-score normalisation
    • Z-score: (x-mean)/standard deviation

First dataset

Clustering

  • Running k-means and hierarchical clustering for k between 2 and 10
k Cluster sizes
2 300, 717
3 294, 348, 375
4 107, 254, 286, 370
5 78, 89, 237, 248, 365
6 77, 79, 89, 159, 244, 369
7 34, 79, 80, 81, 163, 287, 293
8 35, 77, 79, 81, 153, 159, 183, 250
9 4, 35, 78, 78, 78, 154, 157, 184, 249
10 4, 34, 70, 78, 78, 131, 146, 146, 157, 173
k Cluster sizes
2 316, 701
3 316, 346, 355
4 82, 234, 346, 355
5 82, 105, 234, 250, 346
6 79, 82, 105, 155, 250, 346
7 20, 79, 82, 105, 155, 250, 326
8 4, 20, 79, 82, 101, 155, 250, 326
9 4, 20, 79, 82, 101, 124, 155, 202, 250
10 4, 20, 69, 79, 82, 101, 124, 133, 155, 250

k-means

hierarchical

Dendogram

Silhouette

k-means

hierarchical

Clustering similarity

  • Dice index of two sets \(A\) and\(B\): \(\frac{2|A\cap B|}{|A|+|B|}\)
Dice index for h in [1,k]
k=2 0.99,0.97
k=3 0.93,0.96,0.91
k=4 0.61,0.96,0.83,0.88
k=5 0.81,0.88,0.82,0.89,0.99
k=6 0.8,0.95,0.97,0.82,0.88,0.92
k=7 0.96,0.86,0.89,0.74,0.95,0.89,0.88
k=8 0.95,0.63,0.97,0.73,0.76,0.84,0.55,0.92
k=9 0.92,0.76,0.58,0.59,0.73,0.97,1.0,0.96,0.85
k=10 0.74,0.97,0.63,0.58,1.0,0.66,0.49,0.8,0.96,0.92

Second dataset

Feature Pearson correlation

0.22 -0.26 0.13 -0.26 -0.37 -0.12 0.30 0.09 -0.03
0.54 0.68 0.28 0.20 -0.35 0.21 0.44 -0.09
0.88 0.54 0.84 -0.69 0.03 0.15 0.03
0.38 0.66 -0.71 0.07 0.29 0.06
0.73 -0.02 -0.17 -0.12 -0.26
-0.50 -0.20 -0.05 -0.06
-0.24 -0.28 -0.07
0.05 -0.08
0.01

Dy/Yb

Zr/Y

La/Sm

La/Yb

Th/Ta

Th/Zr

Zr/Nb

Nb/Ta

Zr/Hf

Zr/Y

La/Sm

La/Yb

Th/Ta

Th/Zr

Zr/Nb

Nb/Ta

Zr/Hf

K/Th

Clustering

k Cluster sizes
2 65, 222
3 59, 112, 116
4 3, 57, 110, 117
5 3, 11, 57, 96, 120
6 3, 11, 30, 57, 89, 97
7 3, 11, 24, 30, 34, 89, 96
8 3, 11, 21, 22, 29, 34, 78, 89
9 3, 7, 11, 21, 21, 26, 34, 82, 82
10 2, 3, 7, 11, 21, 21, 34, 44, 66, 78
  • Running k-means and hierarchical clustering for k between 2 and 10

k-means

k Cluster sizes
2 67, 220
3 9, 67, 211
4 3, 9, 64, 211
5 3, 9, 64, 81, 130
6 3, 9, 36, 64, 81, 94
7 3, 9, 23, 36, 41, 81, 94
8 3, 9, 20, 21, 23, 36, 81, 94
9 3, 8, 9, 20, 21, 23, 28, 81, 94
10 2, 3, 8, 9, 20, 21, 23, 26, 81, 94

hierarchical

Dendogram

Silhouette

k-means

hierarchical

Clustering similarity

  • Dice index of two sets \(A\) and\(B\): \(\frac{2|A\cap B|}{|A|+|B|}\)
Dice index for h in [1,k]
k=2 0.89,0.97
k=3 0.64,0.92,0.66
k=4 1.0,0.93,0.68,0.61
k=5 0.83,0.79,1.0,0.9,0.93
k=6 0.9,0.93,0.82,1.0,0.86,0.89
k=7 0.89,0.86,0.9,1.0,0.88,0.89,0.82
k=8 1.0,0.9,0.95,0.7,0.86,0.81,0.83,0.98
k=9 0.85,0.93,1.0,0.95,0.82,1.0,0.9,0.74,0.9
k=10 1.0,0.93,1.0,0.74,0.76,0.79,0.66,0.95,1.0,0.9

Third dataset

Clustering

  • Running k-means and hierarchical clustering for k between 2 and 10
k Cluster sizes
2 15, 129
3 11, 51, 82
4 1, 11, 50, 82
5 1, 3, 17, 51, 72
6 1, 3, 17, 28, 42, 53
7 1, 3, 4, 12, 28, 41, 55
8 1, 3, 5, 5, 19, 29, 39, 43
9 1, 2, 3, 4, 7, 22, 27, 36, 42
10 1, 2, 3, 4, 10, 12, 13, 30, 34, 35
k Cluster sizes
2 53, 91
3 10, 53, 81
4 1, 10, 52, 81
5 1, 3, 7, 52, 81
6 1, 3, 7, 17, 52, 64
7 1, 3, 5, 7, 17, 47, 64
8 1, 3, 5, 7, 17, 27, 37, 47
9 1, 2, 3, 3, 7, 17, 27, 37, 47
10 1, 2, 3, 3, 7, 15, 17, 27, 32, 37

k-means

hierarchical

Dendogram

Silhouette

k-means

hierarchical

Clustering similarity

  • Dice index of two sets \(A\) and\(B\): \(\frac{2|A\cap B|}{|A|+|B|}\)
Dice index for h in [1,k]
k=2 0.73,0.21
k=3 0.95,0.99,0.98
k=4 0.99,0.98,0.95,1.0
k=5 1.0,0.97,1.0,0.58,0.94
k=6 1.0,1.0,0.89,0.77,0.58,0.76
k=7 0.67,0.63,0.76,0.89,1.0,1.0,0.79
k=8 1.0,0.91,0.83,0.82,0.79,0.6,1.0,0.89
k=9 0.87,0.86,0.94,0.75,1.0,1.0,0.86,1.0,0.86
k=10 0.95,0.64,0.83,0.96,0.71,0.82,0.86,1.0,1.0,1.0

Fourth dataset

Clustering

k Cluster sizes
2 63, 224
3 54, 111, 122
4 11, 46, 101, 129
5 3, 11, 56, 106, 111
6 3, 11, 25, 30, 107, 111
7 2, 3, 11, 21, 34, 106, 110
8 2, 3, 11, 24, 25, 26, 86, 110
9 2, 3, 12, 24, 25, 26, 31, 78, 86
10 2, 3, 10, 12, 15, 22, 26, 37, 74, 86
  • Running k-means and hierarchical clustering for k between 2 and 10

k-means

k Cluster sizes
2 53, 234
3 53, 94, 140
4 9, 53, 94, 131
5 3, 9, 50, 94, 131
6 3, 9, 39, 50, 55, 131
7 3, 9, 12, 38, 39, 55, 131
8 2, 3, 9, 12, 38, 39, 55, 129
9 2, 3, 9, 12, 17, 21, 39, 55, 129
10 2, 3, 9, 12, 17, 21, 34, 39, 55, 95

hierarchical

Dendogram

Silhouette

k-means

hierarchical

Clustering similarity

  • Dice index of two sets \(A\) and\(B\): \(\frac{2|A\cap B|}{|A|+|B|}\)
Dice index for h in [1,k]
k=2 0.86,0.97
k=3 0.8,0.92,0.82
k=4 0.87,0.95,0.85,0.9
k=5 0.85,0.81,0.9,0.9,1.0
k=6 0.4,0.68,0.9,0.9,1.0,0.75
k=7 1.0,0.67,0.92,0.68,0.9,0.9,0.03
k=8 0.46,0.9,0.9,1.0,0.65,1.0,0.81,0.52
k=9 0.46,0.65,0.36,0.75,0.52,1.0,1.0,0.86,0.72
k=10 0.82,1.0,1.0,0.95,0.72,0.44,0.86,0.26,0.64,0.82

SismaCluster

By Pierluigi Crescenzi

Made with Slides.com

SismaCluster

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