1. Azhar Ali Shah @ Interdisciplinary Optimization and Decision Making Journal Club (IODMJC) IODMJC, March 20 , 2009
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3. Introduction: authors Azhar A Shah Efficient algorithms for accurate hierarchical clustering of huge datasets: tackling the entire protein space /31
4. Introduction: Hierarchical Clustering Azhar A Shah Efficient algorithms for accurate hierarchical clustering of huge datasets: tackling the entire protein space /31
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6. Introduction: about the topic Azhar A Shah Efficient algorithms for accurate hierarchical clustering of huge datasets: tackling the entire protein space /31 There is no guideline for selecting the best linkage method. In practice, people almost always use average linkage. UPGMA (Unweighted Pair Group Method using arithmetic Averages) Scalable to large datasets as it requires only (O(1)) edges in memory. BUT Highly susceptible to outliers!
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8. Introduction: UPGMA -Sparse input N=11 input singletons ( vertices ): {1,2,3,4,11,12,13,14,21,22,23} and 14 edges in the sparse input. The input is considered sparse since not all pairs are given e.g. there is no edge b/w 1 and 22. Clusters 1,2,3,4 form a clique A. Clusters 11,12,13,14 are missing edge < 11,14 > to form clique B. Clusters 21,22,23 are loosely connected to each other and to the cluster of clique A. In total there are two connected components in the input graph: ({1,2,3,4,21,22,23}) (producing 6 merges for 7 vertices) and {11,12,13,14} (producing 4 merges for 3 nodes), which therefore forms a forest of two disjoint trees , rather than the full tree of N-1=10 merges. UPGMA-input 90 23 1 70 23 22 50 22 21 30 14 13 20 14 12 12 13 12 11 13 11 1e+01 12 11 4e-10 4 3 1e-50 4 2 1e-80 3 2 2e-40 4 1 1e-40 3 1 1e-100 2 1 UPGMA-tree 32 99.167 31 26 31 85 29 23 30 50 28 14 29 50 22 21 28 11.5 27 13 27 10 12 11 26 1.33e-10 25 4 25 5e-41 24 3 24 1e-100 2 1
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10. Methodology: 1) Sparse-UPGMA Azhar A Shah Efficient algorithms for accurate hierarchical clustering of huge datasets: tackling the entire protein space /31 Can’t cope with huge datasets, where an O ( E ) memory requirement is intolerable (e.g. Table 1). UPGMA (mean): New eq: Time and memory improvement:
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14. Methodology: 2) Single-Round MC-UPGMA Azhar A Shah Efficient algorithms for accurate hierarchical clustering of huge datasets: tackling the entire protein space /31 Requires O(n) memory for holding forming tree!
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