From Path Tree To Frequent Patterns

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From Path Tree To Frequent Patterns

• -A Framework for Mining Frequent Patterns

Yabo Xu1, Jeffrey Xu Yu1, Guimei Liu2, Hongjun
Lu2 1.Chinese University of Hongkong 2.
Hongkong University of Science and Technology
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Outline

• Frequent pattern mining
• Mining in memory PP-Mine
• Performance Study
• Framework under multi-user environments
• Experimental Results
• Conclusion

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Frequent Pattern Mining

• Problem Definition
• find frequent patterns whose support is greater
  than a threshold ?
• An essential task in many data mining problems,
  e.g. Association, correlation, causality
• Two Main Approaches
• Generation and Test Approach( Apriori-like
  algorithms)
• Pattern Growth Approach

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Pattern Growth Approach

• FP-Growth, H-Mine and our approach PP-Mine
• Strength
• Compress database into a compact structure, and
  project the database on its frequent patterns,
  thus reduce the database scan
• Extend patterns without candidate generation,
  avoid candidate generating cost
• Weakness
• FP-Growth need extra space and cost to generate
  conditional FP-Tree
• H-Mine cant do with the dense dataset
• Deficient in multi-user environment one scan to
  construct the structure

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Mining in memory?PP-Mine

• Main features
• two pushing operations and a no-counting
  strategy below
• Push-down Operation ( Apriori Heuristic )
• Pushing-down to one of its children is to check
  the itemset with one more item, e.g ab-gtabc
• Push-right Operation (Dynamic link-justification)
• Pushing-right is to push the child to its
  corresponding sibling, that helps to identify sub
  trees for a pattern transitively
• No-counting
• Counting is done as a side-effort of
  pushing-right in an accumulated manner

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PP-Mine(cont)-An example
root
1.push-down from node a, to mine subtrees a.b,
a.c, a.d
c
a
b
d
2.after mining these subtrees, push-right these
subtrees to as right-siblings
c
d
d
d
3.after mining subtrees of node-b, push-right
them to bs right-siblings.
d
4. All 4 subtrees( a.b.c, a.c, b.c, c ) are
collected for pattern c
A complete prefix-path tree with 4 items
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Mining in memory?PPM-Tree
TID Items bought (ordered) frequent
path 100 c,d,e,f,g,i c, d, e,
g 200 a,c,d,e,m a,c,d,e 300
a,b,d,g,k a,d,e,g 400 a,c,h a,c
min_support threshold 2

• Build Procedure
• 1. Frequent items list( frequency order) a3,
  c3, d3, e2, g2
• Insert every frequent path into the prefix tree.
• PPM-Tree(Prefix-Path Tree)
• Every node in the tree represents a path and the
  frequency of this path.

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PP-Mine(cont)-A Running Example

• Construct the initial header-table from the
  children of the root, output pattern a3
• Push-down from node a, and construct
  sub-header-table, output pattern ac2

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PP-Mine(cont)-A Running Example

• After mining a.c-prefix, push-right a.cs
  children to a.cs right siblings.
• Mining a.d-prefix, output pattern ad3

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Algorithm Analysis

• PP-Mine Vs FP-Growth
• FP-Tree link all the nodes with same item-names,
  while PP-Tree is node-link free while
  constructed.
• FP-Growth explore the tree using bottom-up
  fashion, construct conditional FP-Tree, and
  PP-Mine follow depth-first order, conditional
  FP-Tree replaced by dynamic link adjusting
• PP-Mine Vs H-Mine
• H-Mine dynamic hyper-link adjusting using
  hyper-structure
• Hyper-structure not so compact as tree structure
• After hyperlink adjusting, it need to count the
  projected database, while PP-tree do it in an
  accumulation fashion.

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Performance Study on PP-Mine
General dataset
Dense dataset
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Framework -From Path Tree To Frequent Pattern

Loading
Loading
dataset
Disk PP-Tree
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Framework -Four Components
1. PPM-Tree an efficient mining algorithm on it
2.Three loading algorithms

3.Coding Strategy (PPM-Tree ? PPD-Tree)
dataset
Disk PP-Tree
4.Coded prefix-path tree on disk (PPD-Tree)

• The advantages
• Reduce the cost of constructing trees
• Load only the relative portion of the whole tree
• Use an even faster algorithm in memory

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Comparison with FP-Tree and H-Struct

• Simple than FP-Tree( node-link free)
• Compact than H-Struct

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Code PP-Tree into Disk

• A complete prefix-path tree of rank 5, each node
  is encoded with a number( of the pre-order of
  traversal of tree)
• The node with shadow is the actual existing node
• For every node with number M, we can calculate
  following easily.
• the path-gtM(code)
• M -gtthe path this node represent ( restore)

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PPD-Tree representation

• A PPD-Tree with rank N is represented by
• (T, F, I, ?m)
• T- a heap for the tree structure, where an
  element consists of a code and its count
• F- N frequent 1-itemsets with their counts in
  order
• I- an index indicating the ranges of codes in
  disk-pages
• ?m -This PPD-Tree can be used for mining frequent
  itemsets with a minimum threshold ?m

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Efficient Loading

• Three tasks
• Frequent Itemsets Mining
• mining frequent patterns whose support is
  greater than or equal to ?
• Frequent Superitemsets Mining
• mining frequent patterns that include all items
  in V, and have a support that is greater than or
  equal to ?.
• Frequent Subitemsets Mining
• mining frequent patterns that are included all
  items in V, and have a support that is greater
  than or equal to ?.
• Load algorithm
• Push constraint into loading phase
• Load a sub PPD-tree from disk
• Construct a minimum PPm-Tree in memory

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Efficient Loading PPt-load

• Example
• Constraints t3
• load only items with frequencies greater than 3

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Efficient Loading PP?-load

• Example
• Constraints
• ttm,Va,d
• find all the paths that contain a and d, and
  merge them

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Efficient Loading PP?-load

• Example
• Constraints
• t tm,Va,d,e
• find all the part of paths that are contained in
  a,d,e, and merge them

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Performance Study for Loading

• Loading Vs Constructing
• X-the tree size we load and construct.
• Y- the time we use
• The building cost are much larger than loading
• The loading time is proportional to the size of
  the tree loaded

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Performance Study for Loading

• Pruning power of PP?-load
• X - the item numbers in the constraint
• Y - the loading PP-Tree size
• Choose different items from different
  regions(top, high, middle, low)
• The loaded part are decreased greatly

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Conclusion

• A new framework for mining frequent patterns in
  multi-user environment
• A novel algorithm PP-Mine
• Two prefix-path tree representation(PPM-Tree, and
  PPD-Tree) and a coding strategy for the
  transformation
• Push constraints into loading phase, reduce the
  I/O cost and CPU cost.