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LinkClus: Efficient Clustering via Heterogeneous Semantic Links

LinkClus: Efficient Clustering via Heterogeneous Semantic Links. Xiaoxin Yin, Jiawei Han Univ. of Illinois at Urbana-Champaign Philip S. Yu IBM T.J. Watson Research Center. A Motivating Example. Questions: Q1: How to cluster each type of objects?

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LinkClus: Efficient Clustering via Heterogeneous Semantic Links

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  1. LinkClus: Efficient Clustering via Heterogeneous Semantic Links Xiaoxin Yin, Jiawei Han Univ. of Illinois at Urbana-Champaign Philip S. Yu IBM T.J. Watson Research Center

  2. A Motivating Example Questions: Q1: How to cluster each type of objects? Q2: How to define similarity between each type of objects? Authors Proceedings Conferences Tom sigmod03 sigmod04 sigmod Mike sigmod05 vldb03 Cathy vldb04 vldb vldb05 John aaai04 aaai Mary aaai05

  3. Tom sigmod03 sigmod04 sigmod Mike sigmod05 vldb03 Cathy vldb04 vldb John vldb05 Link-based Similarities • Two objects are similar if they are linked with similar objects Jeh & Widom, 2002 - SimRank The similarity between two objects x and y is defined as the average similarity between objects linked with x and those with y. sigmod03 Tom sigmod04 sigmod Mary sigmod05 Very expensive to compute: For a dataset of N objects and M links, it takes O(N2) space and O(M2) time to compute all similarities.

  4. A hierarchical structure of products in Walmart All grocery electronics apparel TV DVD camera Observation 1: Hierarchical Structures • Hierarchical structures often exist naturally among objects (e.g., taxonomy of animals) Relationships between articles and words (Chakrabarti, Papadimitriou, Modha, Faloutsos, 2004) Articles Words

  5. Observation 2: Distribution of Similarity • Power law distribution exists in similarities • 56% of similarity entries are in [0.005, 0.015] • 1.4% of similarity entries are larger than 0.1 • Our goal: Design a data structure that stores the significant similarities and compresses insignificant ones Distribution of SimRank similarities among DBLP authors

  6. Canon A40 digital camera Sony V3 digital camera Our Data Structure: SimTree Each leaf node represents an object Each non-leaf node represents a group of similar lower-level nodes Similarities between siblings are stored Digital Cameras Consumer electronics Apparels TVs

  7. Average similarity between x and all other nodes Average similarity between x’s parent and all other nodes Similarity Defined by A SimTree • simp(n7,n8) = • Path-based node similarity • Similarity between two nodes is the average similarity between objects linked with them in other SimTrees • Adjustment ratio forx = Similarity between two sibling nodes n1 and n2 0.2 n1 n2 n3 0.8 0.9 0.9 Adjustment ratio for node n7 0.3 n4 n5 n6 0.9 0.8 1.0 n7 n8 n9 s(n7,n4) x s(n4,n5) xs(n5,n8)

  8. Overview of LinkClus • Initialize a SimTree for objects of each type • Repeat • For each SimTree, update the similarities between its nodes using similarities in other SimTrees • Similarity between two nodes x and y is the average similarity between objects linked with them • Adjust the structure of each SimTree • Assign each node to the parent node that it is most similar to

  9. Initialization of SimTrees • The “SimTrees” before initialization • Each leaf nodes have similarity 1 to itself and 0 to others • Initializing a SimTree • Repeatedly find groups of tightly related nodes, which are merged into a higher-level node ST2 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 ST1 l m n o p q r s t u v w x y

  10. (continued) • Tightness of a group of nodes • For a group of nodes {n1, …, nk}, its tightness is defined as the number of leaf nodes in other SimTrees that are connected to all of {n1, …, nk} Leaf nodes in another SimTree Nodes 1 n1 The tightness of {n1, n2} is 3 2 3 4 n2 5

  11. Transactions {n1} 1 n1 g1 {n1, n2} 2 {n2} 3 n2 {n1, n2} 4 {n1, n2} 5 {n2, n3, n4} n3 6 {n4} g2 7 {n3, n4} n4 8 {n3, n4} 9 (continued) • Finding tight groups Frequent pattern mining • Procedure of initializing a tree • Start from leaf nodes (level-0) • At each level l, find non-overlapping groups of similar nodes with frequent pattern mining Reduced to The tightness of a group of nodes is the support of a frequent pattern

  12. ST2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 ST1 z sim(na,nb) = average similarity between and 10 13 c d e 11 14 a b f g h k 12 l m n o p q r s t u v w x y Updating Similarities Between Nodes • The initial similarities can seldom capture the relationships between objects • Iteratively update similarities • Similarity between two nodes is the average similarity between objects linked with them takes O(3x2) time

  13. 0.2 ST2 4 5 0.9 0.8 0.9 1.0 1.0 10 11 12 13 14 ST1 a b Aggregation-based Similarity Computation For each node nk∈{n10,n11,n12} and nl∈{n13,n14}, their path-based similarity simp(nk, nl) = s(nk, n4)·s(n4, n5)·s(n5, nl). takes O(3+2) time After aggregation, we reduce quadratic time computation to linear time computation.

  14. 0.9+1.0+0.8 3 simweight(na, n4)= ( , 3 ) Simweights of Linkages Simweight between nodes na and n4: the average similarity and total weight of linkages between them a:(0.9,3) b:(0.95,2) 0.2 SC2 4 5 0.9 0.8 0.9 1.0 1.0 10 11 12 13 14 na has a linkage of weight 1 and similarity 1 to each leaf node it is linked with a:(1,1) a:(1,1) a:(1,1) b:(1,1) b:(1,1) SC1 a b weighted average similarity of linkages between naand children of n4 total weight of linkages between naand children of n4

  15. Computing Similarity with Simweights To compute sim(na,nb): • Find all pairs of sibling nodes ni and nj, so that na linked with ni and nb with nj. • Calculate similarity (and weight) between na and nb w.r.t. ni and nj. • Calculate weighted average similarity between na and nb w.r.t. all such pairs. a:(0.9,3) b:(0.95,2) sim(na, nb) can be computed from aggregated similarities 0.2 4 5 10 11 12 13 14 a b sim(na, nb) = simweight(na,n4).sim xs(n4, n5) x simweight(nb,n5).sim = 0.9 x 0.2 x 0.95 = 0.171

  16. 0.9 0.8 n7 n7 Adjusting SimTree Structures • After similarity changes, the tree structure also needs to be changed • If a node is more similar to its parent’s sibling, then move it to be a child of that sibling • Try to move each node to its parent’s sibling that it is most similar to, under the constraint that each parent node can have at most c children n1 n2 n3 n4 n5 n6 n8 n9

  17. Complexity For two types of objects, N in each, and M linkages between them.

  18. Empirical Study • Generating clusters using a SimTree • Suppose K clusters are to be generated • Find a level in the SimTree that has number of nodes closest to K • Merging most similar nodes or dividing largest nodes on that level to get K clusters • Accuracy • Measured by manually labeled data • Accuracy of clustering: Percentage of pairs of objects in the same cluster that share common label • Efficiency and scalability • Scalability w.r.t. number of objects, clusters, and linkages

  19. Approaches in Comparison • SimRank (Jeh & Widom, KDD 2002) • Computing pair-wise similarities • Pruned-SimRank (P-SimRank) • Only compute similarities between objects that are linked to the same object • SimRank with FingerPrints (F-SimRank) • Fogaras & R´acz, WWW 2005 • pre-computes a large sample of random paths from each object and uses the samples of two objects to estimate their SimRank similarity • ReCom (Wang et al. SIGIR 2003) • Iteratively clustering objects using cluster labels of linked objects

  20. DBLP Dataset • We use 4170 most productive authors, and 154 well-known conferences with most proceedings • Manually labeled research areas of 400 most productive authors according to their home pages (or publications) • Manually labeled areas of 154 conferences according to their call for papers Authors Publishes Publications Proceedings Conferences author-id author-id paper-id proc-id conference author-name paper-id title conference publisher email proc-id year location

  21. Accuracy

  22. (continued) • Accuracy vs. Running time • LinkClus is almost as accurate as SimRank (most accurate), and is much more efficient

  23. Email Dataset • F. Nielsen. Email dataset. http://www.imm.dtu.dk/∼rem/data/Email-1431.zip • 370 emails on conferences, 272 on jobs, and 789 spam emails

  24. Scalability (1) • Tested on synthetic datasets, with randomly generated clusters • Scalability w.r.t. number of objects • Number of clusters is fixed (40)

  25. Scalability (2) • Scalability w.r.t. number of objects & clusters • Each cluster has fixed size (100 objects)

  26. Scalability (3) • Scalability w.r.t. number of linkages from each object

  27. Conclusions • With our data structure SimTree, LinkClus can compress the pair-wise similarities while achieving high accuracy • Experimental results show that LinkClus is a highly accurate and scalable approach for clustering multi-typed linked objects

  28. Thank you • Questions and comments

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