abcde

1. Tugas Siskomul
Riyani Jana Yanti
18113002
Soal:
Perhatikan suatu deretan sampel-sampel berikut:
3 4 5 4 4 6 7 6 13 6 3 7
5 7 6 8 9 8 8 9 10 10 10 13
6 14 8 14 11 15 14 15 9 16
Untuk N=2, disain codebook dg k-means algorithm dg jumlah codebook = 3. Lakukan sampai iterasi ke 3,
nyatakan masing-masing vektor representatifnya (codebook) dan berapa distorsinya?
Jawaban :
A. Iterasi1
Dipilih 𝑦1, 𝑦2, 𝑑𝑎𝑛 𝑦3 dengan menggunakan prinsip kuartal 𝑄1, 𝑄2,𝑑𝑎𝑛 𝑄3 sebagai berikut :
𝑄1 = 𝑦1 = 6
𝑄2 = 𝑦2 = 8
𝑄3 = 𝑦3 = 11
𝑑( 𝑥, 𝑦1) =
1
2
(( 𝑥1 − 6)2+( 𝑥2 − 6)2)
𝑑( 𝑥, 𝑦2) =
1
2
(( 𝑥1 − 8)2+( 𝑥2 − 8)2)
𝑑( 𝑥, 𝑦3) =
1
2
(( 𝑥1 − 11)2+( 𝑥2 − 11)2)

2. Code Rep.Vector 𝒅(𝒙,𝒚 𝟏) 𝒅(𝒙,𝒚 𝟐) 𝒅(𝒙,𝒚 𝟑) 𝑴𝑰𝑵(𝒅(𝒙,𝒚)) 𝒚 𝒌
3 3.5 6.5 20.5 56.5 6.5 𝑦1
4
5 4.5 2.5 12.5 42.5 2.5 𝑦1
4
4 5 2 10 37 2 𝑦1
6
7 6.5 0.5 2.5 20.5 0.5 𝑦1
6
13 9.5 24.5 14.5 14.5 14.5 𝑦3
6
3 5 5 13 40 5 𝑦1
7
5 6 1 5 26 1 𝑦1
7
6 7 2 2 17 2 𝑦1
8
9 8.5 6.5 0.5 6.5 0.5 𝑦2
8
8 8.5 6.5 0.5 6.5 0.5 𝑦2
9
10 10 16 4 1 1 𝑦3
10
10 11.5 32.5 14.5 2.5 2.5 𝑦3
13
6 10 32 20 17 17 𝑦3
14
8 11 34 18 9 9 𝑦3
14
11 13 53 29 8 8 𝑦3
15
14 14.5 72.5 42.5 12.5 12.5 𝑦3
15
9 12.5 54.5 32.5 14.5 14.5 𝑦3
16
𝑅1 = {3.5,4.5, 5,6.5,5,6, 7}
𝑅2 = {8.5,8.5}
𝑅3 = {9.5,10,11.5, 10, 11,13,,14.5, 12.5}

3. 𝐷 = 99.5
B. Iterasi 2
Dipilih 𝑦1, 𝑦2, 𝑑𝑎𝑛 𝑦3 dengan menggunakan
𝑦1 = 𝑀𝑒𝑎𝑛( 𝑅1) = 5.357142857
𝑦2 = 𝑀𝑒𝑎𝑛( 𝑅2) = 8.5
𝑦3 = 𝑀𝑒𝑎𝑛( 𝑅3) = 11.5
𝑑( 𝑥, 𝑦1) =
1
2
(( 𝑥1 − 5.36)2+( 𝑥2 − 5.36)2)
𝑑( 𝑥, 𝑦2) =
1
2
(( 𝑥1 − 8.5)2+( 𝑥2 − 8.5)2)
𝑑( 𝑥, 𝑦3) =
1
2
(( 𝑥1 − 11.5)2+( 𝑥2 − 11.5)2)
Code Rep.Vector 𝒅(𝒙,𝒚 𝟏) 𝒅(𝒙,𝒚 𝟐) 𝒅(𝒙,𝒚 𝟑) 𝑴𝑰𝑵(𝒅(𝒙,𝒚)) 𝒚 𝒌
3 3.5 3.7096 25.25 64.25 3.7096 𝑦1
4
5 4.5 0.9896 16.25 49.25 0.9896 𝑦1
4
4 5 1.1296 13.25 43.25 1.1296 𝑦1
6
7 6.5 1.5496 4.25 25.25 1.5496 𝑦1
6
13 9.5 29.3896 13.25 16.25 13.25 𝑦2
6
3 5 4.1296 16.25 46.25 4.1296 𝑦1
7
5 6 1.4096 7.25 31.25 1.4096 𝑦1
7
6 7 3.6896 3.25 21.25 3.25 𝑦2
8
9 8.5 10.1096 0.25 9.25 0.25 𝑦2
8

4. 8 8.5 10.1096 0.25 9.25 0.25 𝑦2
9
10 10 21.5296 2.25 2.25 2.25 𝑦3
10
10 11.5 39.9496 11.25 2.25 2.25 𝑦3
13
6 10 37.5296 18.25 18.25 18.25 𝑦3
14
8 11 40.8096 15.25 9.25 9.25 𝑦3
14
11 13 62.3696 24.25 6.25 6.25 𝑦3
15
14 14.5 83.7896 36.25 9.25 9.25 𝑦3
15
9 12.5 63.2296 28.25 13.25 13.25 𝑦3
16
𝑅1 = {3.5,4.5, 5,6.5,5, 6,}
𝑅2 = {9.5,7, 8.5, 8.5}
𝑅3 = { 10, 11.5,10,11, 13,14.5,12.5}
𝐷 = 90.6676
𝑪. 𝑰terasi3
Dipilih 𝑦1, 𝑦2, 𝑑𝑎𝑛 𝑦3 dengan menggunakan
𝑦1 = 𝑀𝑒𝑎𝑛( 𝑅1) = 5.083333333
𝑦2 = 𝑀𝑒𝑎𝑛( 𝑅2) = 8.375
𝑦3 = 𝑀𝑒𝑎𝑛( 𝑅3) = 11.78571429
𝑑( 𝑥, 𝑦1) =
1
2
(( 𝑥1 − 5.083)2+( 𝑥2 − 5.083)2)
𝑑( 𝑥, 𝑦2) =
1
2
(( 𝑥1 − 8.375)2+( 𝑥2 − 8.375)2)

5. 𝑑( 𝑥, 𝑦3) =
1
2
(( 𝑥1 − 11.78)2 + ( 𝑥2 − 11.78)2
Code Rep.Vector 𝑑(𝑥, 𝑦1) 𝑑(𝑥, 𝑦2) 𝑑(𝑥, 𝑦3) 𝑀𝐼𝑁(𝑑(𝑥, 𝑦)) 𝑦 𝑘
3
3.5 3.7096 25.25 64.25 3.7096 y14
5
4.5 0.9896 16.25 49.25 0.9896 y14
4
5 1.1296 13.25 43.25 1.1296 y16
7
6.5 1.5496 4.25 25.25 1.5496 y16
13
9.5 29.3896 13.25 16.25 13.25 y26
3
5 4.1296 16.25 46.25 4.1296 y17
5
6 1.4096 7.25 31.25 1.4096 y17
6
7 3.6896 3.25 21.25 3.25 y28
9
8.5 10.1096 0.25 9.25 0.25 y28
8
8.5 10.1096 0.25 9.25 0.25 y29
10
10 21.5296 2.25 2.25 2.25 y310
10
11.5 39.9496 11.25 2.25 2.25 y313
6
10 37.5296 18.25 18.25 18.25 y314
8
11 40.8096 15.25 9.25 9.25 y314
11
13 62.3696 24.25 6.25 6.25 y315
14
14.5 83.7896 36.25 9.25 9.25 y315
9
12.5 63.2296 28.25 13.25 13.25 y316

6. 𝑅1 = {3.5, 4.5,5, 6.5, 5,6, }
𝑅2 = {9.5, 7, 8.5, 8.5}
𝑅3 = { 10,11.5,10, 11, 13,,14.5,12.5}
𝐷 = 88.47613