SoSe 2014: M-TANI: Big Data Analytics
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1 SoSe 2014: M-TANI: Big Data Analytics Lecture 4 21/05/2014 Sead Izberovic Dr. Nikolaos Korfiatis
2 Agenda Recap from the previous session Clustering Introduction Distance mesures Hierarchical Clustering Partitional Clustering
3 Introduction Given a set of objects, with a notion of distance between those objects. The task of a clustering algorithm is to group those objects into some number of clusters, so that: Members of a cluster are similar to each other Members of different clusters are dissimilar High dimensionality may be hard to interpret from [2]
4 Introduction Clustering Classification Classification Assigning objects to predifined classes Requires supervised learning Clustering No predifined classes Assigning objects to clusters (based on distance)
5 Introduction Clustering applications Clustering DNA sequences Image segmentation Customer segmentation...
6 Distance mesures Calculate similarity Large distance = low similarity Small distance = high similarity Conditions 1. dddd x, y = d with d: X X R and x, y, z ϵ X 2. dddd x, y 0 3. dddd x, y = 0 if x = y 4. dddd x, y = dddd y, x 5. dddd x, z dddd x, y + dddd(y, z) from [1] and [3]
7 Distance mesures Euclidian distance: dddd eeeeee X, Y = n i=1 (x i y i ) 2 Jaccard distance: dddd jjjjjjj x, y = 1 SSS x, y Cosine distance: dddd ccc X, Y = n i=1 x i y i n i=1 (x i ) 2 n i=1(x i ) 2 Edit distance: smallest number of insertions and deletions of single characters that will convert string x to string y from [2] and [3]
8 Distance between clusters Centroid Medoid/Clustroid
9 Distance between clusters Single-linkage
10 Distance between clusters Complete-linkage
11 Distance between clusters Average-linkage
12 Clustering approches Clustering Hierarchical Partitional adapted from [4]
13 Hierarchical Agglomerative 1. Every Object is a cluster 2. Calculate the minimal distance between to clusters 3. Merge clusters with minimal distance 4. Repeat 2. and 3. until we have one big cluster Single Link
14 Hierarchical Agglomerative 1. Every Object is a cluster 2. Calculate the minimal distance between to clusters 3. Merge clusters with minimal distance Single Link 4. Repeat 2. and 3. until we have one big cluster
15 Hierarchical Agglomerative 1. Every Object is a cluster 2. Calculate the minimal distance between to clusters 3. Merge clusters with minimal distance 4. Repeat 2. and 3. until we have one big cluster Single Link
16 Hierarchical Agglomerative 1. Every Object is a cluster 2. Calculate the minimal distance between to clusters 3. Merge clusters with minimal distance 4. Repeat 2. and 3. until we have one big cluster Single Link
17 Hierarchical Agglomerative 1. Every Object is a cluster 2. Calculate the minimal distance between to clusters 3. Merge clusters with minimal distance 4. Repeat 2. and 3. until we have one big cluster Single Link
18 Hierarchical Agglomerative 1. Every Object is a cluster 2. Calculate the minimal distance between to clusters 3. Merge clusters with minimal distance 4. Repeat 2. and 3. until we have one big cluster Single Link
19 Hierarchical Agglomerative 1. Every Object is a cluster 2. Calculate the minimal distance between to clusters 3. Merge clusters with minimal distance 4. Repeat 2. and 3. until we have one big cluster Single Link
20 Hierarchical Agglomerative 1. Every Object is a cluster 2. Calculate the minimal distance between to clusters 3. Merge clusters with minimal distance 4. Repeat 2. and 3. until we have one big cluster Single Link
21 Hierarchical Agglomerative 1. Every Object is a cluster 2. Calculate the minimal distance between to clusters 3. Merge clusters with minimal distance 4. Repeat 2. and 3. until we have one big cluster Single Link
22 Hierarchical Agglomerative 1. Every Object is a cluster 2. Calculate the minimal distance between to clusters 3. Merge clusters with minimal distance 4. Repeat 2. and 3. until we have one big cluster Single Link
23 Hierarchical Agglomerative 1. Every Object is a cluster 2. Calculate the minimal distance between to clusters 3. Merge clusters with minimal distance 4. Repeat 2. and 3. until we have one big cluster Single Link
24 Hierarchical Divisive 1. Find max. distance between objects 2. Split those clusters 3. Repeat 1. and 2. until we have clusters which contain just one object Single Link
25 Hierarchical Divisive 1. Find max. distance between objects 2. Split those clusters 3. Repeat 1. and 2. until we have clusters which contain just one object Single Link
26 Hierarchical Divisive 1. Find max. distance between objects 2. Split those clusters 3. Repeat 1. and 2. until we have clusters which contain just one object Single Link
27 Hierarchical Divisive 1. Find max. distance between objects 2. Split those clusters 3. Repeat 1. and 2. until we have clusters which contain just one object Single Link
28 Hierarchical Divisive 1. Find max. distance between objects 2. Split those clusters 3. Repeat 1. and 2. until we have clusters which contain just one object Single Link
29 Hierarchical Divisive 1. Find max. distance between objects 2. Split those clusters 3. Repeat 1. and 2. until we have clusters which contain just one object Single Link
30 Hierarchical Divisive 1. Find max. distance between objects 2. Split those clusters 3. Repeat 1. and 2. until we have clusters which contain just one object Single Link
31 Hierarchical Divisive 1. Find max. distance between objects 2. Split those clusters 3. Repeat 1. and 2. until we have clusters which contain just one object Single Link
32 Cluster Visualization Dendrogram Distance adopted from [3]
33 Cluster Visualization Dendrogram Distance adopted from [3]
34 Cluster Visualization Dendrogram Distance adopted from [3]
35 Cluster Visualization Dendrogram Distance adopted from [3]
36 Cluster Visualization Dendrogram Distance adopted from [3]
37 Cluster Visualization Dendrogram Distance adopted from [3]
38 Cluster Visualization Dendrogram Distance adopted from [3]
39 Cluster Visualization Dendrogram Distance adopted from [3]
40 Clustering approches Clustering Hierarchical Partitional adapted from [4]
41 K-Means 1. Place k centroids randomly 2. If distance to centroid min. merge to cluster 3. Move the k centroids to the new cluster center 4. Repeat 2. and 3. until we fulfil the stop criteria k=3
42 K-Means 1. Place k centroids randomly 2. If distance to centroid min. merge to cluster 3. Move the k centroids to the new cluster center 4. Repeat 2. and 3. until we fulfil the stop criteria k=3
43 K-Means 1. Place k centroids randomly 2. If distance to centroid min. merge to cluster 3. Move the k centroids to the new cluster center 4. Repeat 2. and 3. until we fulfil the stop criteria k=3
44 K-Means 1. Place k centroids randomly 2. If distance to centroid min. merge to cluster 3. Move the k centroids to the new cluster center 4. Repeat 2. and 3. until we fulfil the stop criteria k=3
45 K-Means 1. Place k centroids randomly 2. If distance to centroid min. merge to cluster 3. Move the k centroids to the new cluster center 4. Repeat 2. and 3. until we fulfil the stop criteria k=3
46 K-Means How to choose the right k? Try different k, looking at the change in the average distance to centroid as k increases Average falls rapidly until right k, then changes little Average distance to centroid k from [2]
47 Clustering on graphs Create the MST Remove k-1 edges with the highest weights Create the clusters k=3
48 Clustering on graphs 3 Create the MST 6 Remove k-1 edges with the highest weights Create the clusters 1 k=3
49 Clustering on graphs 3 Create the MST Remove k-1 edges with the highest weights 2 4 Create the clusters 1 k=3
50 Clustering on graphs 3 Create the MST Remove k-1 edges with the highest weights 2 4 Create the clusters 1 k=3
51 Literature 1. Anand Rajaraman, Jeffrey D. Ullman, Jure Leskovec Mining of Massive Datasets Cambridge University Press 2. Jure Leskovec Slides: Mining Massive Data Sets URL: 3. Martin Ester, Jörg Sander Knowledge Discovery in Databases Springer Verlag Berlin Heidelberg 4. A. K. Jain, M. N. Murty, and P. J. Flynn Data clustering: a review ACM Comput. Surv., 31(3):
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