1. Efficient Data Mining for Path Traversal Patterns CS401 Paper Presentation Chaoqiang chen Guang Xu

2. Overview Introduction Problem Formulation Algorithm for Traversal Pattern 1. Identifying Maximal Forward References 2. Determining Large Reference Sequences Performance Results 1. Generation of Synthetic Traversal Paths 2. Performance Comparison Between FS and SS 3. Sensitivity Analysis Advantages and Disadvantages Conclusions

3. Introduction Analysis of past transaction data can provide very valuable information on customer buying behavior, and thus improve the quality of business decisions. It is essential to collect a sufficient amount of sales data before any meaningful conclusion can be drawn. Efficient algorithms are needed to conduct mining on these huge data. One of the most important data mining problems is mining association rules. The presence of some items in a transaction will imply the presence of other items in the same transaction.

4. Introduction Mining access patterns in a distributed information providing environment where objects are linked together to facilitate interactive access. 1. Improve the system design: provide efficient access between highly correlated objects etc. 2. Better marketing decisions: putting advertisements in proper places etc. Algorithms for mining traversal patterns: 1. Algorithm MF (standing for maximal forward references) to convert the original sequence of log data into a set of maximal forward references. 2. Algorithms FS (full-scan) and SS (selective-scan) for determining large reference sequences.

5. Problem Formulation Traversal path for a user: {A,B,C,D,C,B,E,G,H,G, W,A,O,U,O,V} Maximal forward references: {ABCD, ABEGH, ABEGW, AOU, AOV}

6. Problem Formulation Some nodes might be revisited because of its location, rather than its content. Assume that a backward reference is mainly for ease of traveling but not for browsing When a backward references occur, a forward reference path terminates, this resulting forward reference path is termed as maximal forward reference. A large reference sequence is a reference sequence that appeared in a sufficient number of times in a set of maximal forward references The number of times a reference sequence has to appear in order to be qualified as a large reference sequence is called the minimal support.

7. Problem Formulation A large k-reference is a large reference sequence with k elements. Set of large k-references is denoted as L K, its candidate set as C K. A maximal reference sequence corresponds to a “hot” access pattern in an information providing service A maximal reference sequences is a large reference sequence that is not contained in any other maximal reference sequence. Suppose that {AB, BE, AD, CG, GH, BG} is the set of large 2-references (i.e. L 2 ) and {ABE, CGH} is the set of large 3-references (i.e. L 3 ), then, the resulting maximal reference sequences are {AD, BG, ABE, CGH}

8. Problem Formulation Procedure for mining traversal patterns: Step 1: Determine maximal forward references from the original log data. Step 2: Determine large reference sequences (i.e., L K, K >= 1) from the set of maximal forward references. Step 3: Determine maximal reference sequences from large reference sequences. Extraction of maximal reference sequences from large reference sequences (i.e. Step 3) is straightforward Focus on Steps 1 and 2

9. Problem Formulation L i : set of large reference sequences Support = 2 D: set of maximal forward references C i : candidate set of large reference sequences

10. Algorithm for Traversal Pattern --- Identifying Maximal Forward References A traversal log database contains, for each link traversed, a pair of (source, destination) The traversal log database is sorted by user id’s, resulting in a traversal path, {(s 1,d 1 ),(s 2,d 2 ), …,(s n,d n )}, for each user, where pairs of (s i,d i ) are ordered by time. Then algorithm MF is applied to determine the maximal forward references.

11. Algorithm for Traversal Pattern --- Identifying Maximal Forward References

12. Algorithm for Traversal Pattern --- Determining large Reference Sequences (FS) Algorithm FS utilizes key ideas of the DHP (i.e., hashing and pruning) technique DHP: efficient generation for large itemsets, effective reduction on transaction database size after each scan. C k can be generated from joining L k-1 with itself Different from DHP, in FS, for any two distinct reference sequences in L k-1, say r 1,…,r k-1 and s 1,…,s k-1, we join them to form a k-reference sequence only if either r 1,…,r k- 1 contains s 1,…,s k-2 or s 1,…,s k-1 contains r 1,…,r k-2

13. Algorithm for Traversal Pattern --- Determining large Reference Sequences (FS) D: set of maximal forward references C i : candidate set of large reference sequences L i : set of large reference sequences Support = 2

14. Algorithm for Traversal Pattern --- Determining large Reference Sequences (SS) Utilizing the information in candidate reference in prior passes to avoid database scans in some passes, thus further reducing the disk I/O cost. Generate a C 3 ’ from C 2 * C 2, instead of from L 2 * L 2, and both C 2 and C 3 ’ can stored in the main memory, we can find L 2 and L 3 together when the next scan of the database is performed. If | C k+1 ’|>| C k ’ | for some k >= 2, it is usually beneficial to have a database scan to obtain L k+1 before the set of candidate references becomes too big.

15. Performance Results --- Generation of Synthetic Traversal Paths

16. The browsing scenario in a World Wide Web (WWW) environment is simulated. A traversal tree is constructed to mimic WWW structure whose starting position is a root node of the tree. The traversal tree consists of internal nodes and leaf nodes The number of child nodes at each internal node, referred to as fanout, is determined from a uniform distribution with a given range The height of a subtree whose subroot is a child node of the root node is determined from a Poisson distribution A traversal path consists of nodes accessed by a user. The size of each traversal path is picked from a Possion distribution.

17. Performance Results --- Generation of Synthetic Traversal Paths With the first node being the root node, a traversal path is generated probabilistically within the traversal tree. 1. For internal nodes: p 0 : probability go back to parent node p 1, p 2, p 3, p 4 …: probability go to the child nodes p j : probability jump to another internal node 2. For leaf node: 25% to parent, 75% jump to internal node The number of internal nodes with internal jumps is denoted by N J, which is set to 3% of all the internal nodes in general cases. Sensitivity of varying N J will be analyzed.

18. Performance Results --- Generation of Synthetic Traversal Paths

19. Performance Results --- Performance Comparison between FS and SS |D| = 200,000, N J = 3%, and p j = 0.1 The fanout at each internal node is between 4 and 7. The root node consists of 7 child nodes The number of internal nodes is 16,200, the number of leaf nodes is 73,006 Algorithm SS in general outperforms FS, and their performance difference becomes prominent when the I/O cost is taken into account

20. Performance Results --- Performance Comparison between FS and SS

22. Algorithm SS consistently outperforms FS as the database size increases

23. Performance Results --- Sensitivity Analysis |D| = 200,000, |P| = 10, the minimum support is 0.75% As the probability to backward at an internal node, p 0, increases, the number of large reference sequences decreases because the possibility of having forward traveling becomes smaller.

24. Performance Results --- Sensitivity Analysis The number of large reference sequences decreases as the number of child nodes of internal nodes (fanout) increases Because with a larger fanout the traversal paths are more likely to be dispersed to several branches, thus resulting in fewer large reference sequences.

25. Performance Results --- Sensitivity Analysis The probability of traveling to each child node from an internal node is determined from a Zipf-like distribution The number of large reference sequences increases when the corresponding probabilities are more skewed..

26. Performance Results --- Sensitivity Analysis

27. Advantages and Disadvantages Advantages 1. Make use of the concept of DHP (i.e., hashing and pruning) technique, thus the proposed algorithms are very efficient in generating set of large reference sequences L k and in reducing size of the database of maximal forward references after each scan. By this way, both CPU and I/O costs are reduced. 2. By utilizing the information in candidate references in prior passes, algorithm SS avoids database scans in some passes, thus further reducing the disk I/O cost.

28. Advantages and Disadvantages Disadvantages 1. Since user’s backward browsing is treated as for ease of traveling, there exist a possibility that some information about the user’s browsing behavior get lost. It is better that the backward traversal pattern can also be mined to reflect the user’s real behavior. 2. When traversal log record only contains destination references instead of a pair of references. The MF algorithm can not identify the breakpoint where the user picks a new URL to begin a new traversal path. This could increase the computational complexity because the paths considered become longer, especially in an environment where users jump from sites to sites frequently. Thus some complement method should be employed to deal with this problem.

29. Conclusions A new data mining capability is explored. It involves mining traversal patterns in an information providing environment where documents or objects are linked together to facilitate interactive access. Algorithm MF is employed to convert the original sequence of log data into a set of maximal forward references. Algorithms FS and SS are developed to determine large reference sequences from the maximal forward references obtained. FS is based on some hashing and pruning techniques, and SS is a further improvement of FS. Performance of FS and SS has been comparatively analyzed. Algorithm SS in general outperforms algorithm FS. Sensitivity analysis on various parameters was also conducted.