Efficient Data Mining for Path Traversal Patterns

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 LK , its candidate set as CK .
• 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. L2) and ABE, CGH is
  the set of large 3-references (i.e. L3), then,
  the resulting maximal reference sequences are
  AD, BG, ABE, CGH

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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., LK , K gt 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

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Problem Formulation
D set of maximal forward references Ci
candidate set of large reference sequences
Li set of large reference
sequences Support 2
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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
  ids, resulting in a traversal path,
  (s1,d1),(s2,d2), ,(sn,dn), for each user,
  where pairs of (si,di) are ordered by time.
• Then algorithm MF is applied to determine the
  maximal forward references.

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Algorithm for Traversal Pattern ---Identifying
Maximal Forward References
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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.
• Ck can be generated from joining Lk-1 with itself
• Different from DHP, in FS, for any two distinct
  reference sequences in Lk-1 , say r1,,rk-1 and
  s1,,sk-1 , we join them to form a k-reference
  sequence only if either r1,,rk-1 contains
  s1,,sk-2 or s1,,sk-1 contains r1,,rk-2

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Algorithm for Traversal Pattern --- Determining
large Reference Sequences (FS)
Li set of large reference
sequences Support 2
D set of maximal forward references Ci
candidate set of large reference sequences
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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 C3 from C2 C2, instead of from L2
  L2, and both C2 and C3 can stored in the main
  memory, we can find L2 and L3 together when the
  next scan of the database is performed.
• If Ck1gt Ck for some k gt 2, it is
  usually beneficial to have a database scan to
  obtain Lk1 before the set of candidate
  references becomes too big.

15
Performance Results --- Generation of Synthetic
Traversal Paths
16
Performance Results --- Generation of Synthetic
Traversal Paths

• 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.

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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
• p0 probability go back to parent node
• p1, p2, p3, p4 probability go to the
  child nodes
• pj 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 NJ, which is set to 3 of all the
  internal nodes in general cases.
• Sensitivity of varying NJ will be analyzed.

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Performance Results --- Generation of Synthetic
Traversal Paths
19
Performance Results --- Performance Comparison
between FS and SS

• D 200,000, NJ 3, and pj 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
21
Performance Results --- Performance Comparison
between FS and SS
22
Performance Results --- Performance Comparison
between FS and SS

• 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, p0, increases, the number of large
  reference sequences decreases because the
  possibility of having forward traveling becomes
  smaller.

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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 Lk 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.

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Advantages and Disadvantages

• Disadvantages
• 1. Since users backward browsing is treated as
  for ease of traveling, there exist a possibility
  that some information about the users browsing
  behavior get lost. It is better that the backward
  traversal pattern can also be mined to reflect
  the users 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.

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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.