nonordfp: An FPgrowth variation without rebuilding the FPtree

1
nonordfp An FP-growth variation without
rebuilding the FP-tree

• Balázs Rácz
• Computer and Automation Research Institute of the
  Hungarian Academy of Sciences

2
Outline

• Introduction FP-growth
• New core data structure
• Traversing strategies
• Implementational aspects
• Future work and thoughts

3
About the title

• nonordfp An FP-growth variation without
  rebuilding the FP-tree
• What varies
• Core data structure
• Memory layout
• Simpler recursion the same trie is used for
  more/all levels of recursion
• nonord item ordering does not change

4
FP-growth

• Han, Pei, Yin, 2000
• Pattern growth approach
• Keep a representation of the (projected/conditiona
  l) database in memory
• Data structure FP-tree (trie extra data)
• Core recursion
• Determine support of items
• Calculate projections onto single items
• Recurse on them

5
Projection

• Conditional database for itemset X all
  transactions that contain X with the elements of
  X removed.

6
New core data structure

• Trie
• Original FP-tree node
• item ID
• children map, or
• first child next sibling pointer
• counter
• parent pointer
• New node counter, parent pointer
• separately

7
New core data structure (2)

• New node counter, parent pointer
• Stored in separate arrays
• projection replace counters, structure remains
• Nodes are placed in an array contiguously
• no dynamic allocation
• no pointers (just indices)
• traversal sequential memory read

8
New core data structure (3)

• Hey, we dropped item identifiers!
• Node array is filled with nodes of the same item
  being adjacent
• Only starts of item intervals are stored
• A sequential scan of this array is a
  bottom-to-top traversal of the trie
• sequential memory read

9
Aggregation on the new data structure

• Aggregation calculation of new counters
• By default, recursion proceeds with the same
  structural information and new set of counters
• Dense
• Default aggregation mode, visits each node once
• Problem deleted nodes of the previous iterations
• Sparse
• For first (few) recursions or skewed datasets
• Ignores nodes with zero counter (deleted nodes)
• Dynamically builds header chain
• Typically projection follows

10
Aggregation on the new data structure

• Single path optimization
• If the FP-tree is only a single chain (path) of
  nodes, then easy fast recursion
• Extension if at most one node of each item
• Skewed datasets
• Real-life market basket data
• Very large trie (up to millions of nodes)
• First level of projection dominates the time
  (gt80)
• Specialized, simultaneous projection

11
Projection/compacting

• Compact counters and parents arrays to remove
  space used by deleted nodes
• both for sparse and dense aggregation
• results in new structural data
• spare memory (traversal) time
• not a real projection no new trie is built, item
  order remains the same but can be done only
  using the parent pointers
• Experimental results
• on dense datasets projection costs and benefits
  are surprisingly well balanced
• on sparse datasets projection is important on the
  first few levels (see simultaneous projection)

12
Implementation

• Auxiliary and library routines take 90 of the
  time
• Especially core recursion
• input/output routines
• memory management

13
Impl. Input/output

• 100 million fprintf is ssslllooowww
• Improvements
• buffer output file
• use specialized number conversion
• utilize recursion

14
(No Transcript)
15
Impl. memory management

• Allocating and freeing an array in each recursion
  step is too ssslllooowww
• C librarys memory management functions are too
  general for the purpose
• Solution reuse arrays
• Note fill with zero the array before/after use
  only when necessary
• Block oriented memory allocators
• sometimes allocated memory is unused

16
(No Transcript)
17
Experimental results

• On dense datasets the fast traversal routines
  take advantage
• On sparse datasets the performance is still
  competitive
• Test runs against some of the best competitors of
  FIMI03

18
(No Transcript)
19
(No Transcript)
20
Future work questions

• Code is not yet mature
• Use top-down approach
• reuses counter arrays in-place
• Simultaneous projection is not very efficient
• how hard is it to do the first level of
  projections?
• especially on sparse datasets

21
New direction of research

• SIMD
• stands for Single Instruction Multiple Data
• vector processing ability of modern processors
• Supported by all mainstream CPUs
• In x86 since Pentium MMX (1997)
• MMX 7 years old
• APRIORI 10 years old
• FP-growth 4 years old

22
New direction of research (contd)

• Give an FIM algorithm/implementation that can be
  SIMD parallelized!
• Use parallel CPU resources
• Most important
• eliminate conditional branches
• fits superscalar processors
• Revise FIMI rules?

23
Thank you!