written 2.5 years ago by | modified 20 months ago by |

Object | Attribute 1 (X) | Attribute 2 (Y) |
---|---|---|

A | 2 | 2 |

B | 3 | 2 |

C | 1 | 1 |

D | 3 | 1 |

E | 1.5 | 1.5 |

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Consider the data given below. Create adjacency matrix. Apply single link algorithm to cluster the given data set and draw the dendogram.

written 2.5 years ago by | modified 20 months ago by |

Object | Attribute 1 (X) | Attribute 2 (Y) |
---|---|---|

A | 2 | 2 |

B | 3 | 2 |

C | 1 | 1 |

D | 3 | 1 |

E | 1.5 | 1.5 |

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written 2.5 years ago by | • modified 2.5 years ago |

Solution:

Object | Attribute 1 (X) | Attribute 2 (Y) |
---|---|---|

A | 2 | 2 |

B | 3 | 2 |

C | 1 | 1 |

D | 3 | 1 |

E | 1.5 | 1.5 |

For simplicity we can find the adjacency matrix which gives distances of all object from each other. Using Euclidean distance we have

$\begin{aligned} \mathrm{D}(\mathrm{i}, \mathrm{j}) &=\sqrt{\left|\mathrm{x}_{2}-\mathrm{x}_{1}\right|^{2}+\left|\mathrm{y}_{2}-\mathrm{y}_{1}\right|^{2}} \\ \mathrm{D}(\mathrm{A}, \mathrm{B}) &=\sqrt{(2-3)^{2}+(2-2)^{2}}=1 \end{aligned}$

Similarly we can compute for the rest.

A | B | C | D | E | |
---|---|---|---|---|---|

A | 0 | ||||

B | 1 | 0 | |||

C | 1.41 | 2.24 | 0 | ||

D | 1.41 | 1 | 2 | 0 | |

E | 1.58 | 2.12 | 0.71 | 1.58 | 0 |

(i) Singlelink:

step 1: Since $C, E$ is minimum we can combine clusters $C, E$

- | A | B | (C,E) | D |
---|---|---|---|---|

A | 0 | |||

B | 1 | 0 | ||

C | 1.41 | 2.12 | 0 | |

D | 1.41 | 1 | 1.58 | 0 |

Step 2: Now $\mathrm{A}$ and $\mathrm{B}$ is having minimum value therefore we merge these two clusters.

- | (A,B) | (C,E) | D |
---|---|---|---|

(A,B) | 0 | ||

(C,E) | 1.41 | 0 | |

D | 1 | 1.58 | 0 |

Step 3 : Cluster $(\mathrm{A}, \mathrm{B})$ and $\mathrm{D}$ can be merged together as they are having minimum distance value

- | (A,B,D) | (C,E) |
---|---|---|

(A,B,D) | 0 | |

(C,E) | 1.41 | 0 |

Step 4 : In the last step there are only two clusters to be combined they are, $(\mathrm{A}, \mathrm{B}, \mathrm{D})$ and $(\mathrm{C}, \mathrm{E})$

Now the final dendrogram is

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