The document summarizes the CARPENTER algorithm for finding frequent closed patterns in datasets with many features and few rows, such as biological datasets. CARPENTER uses a row-wise enumeration approach instead of column-wise. It first transposes the dataset and then performs a depth-first search of the row enumeration tree, using three pruning methods to improve efficiency. Experimental results on a lung cancer dataset show CARPENTER outperforms other algorithms like CHARM and CLOSET that use column enumeration.

1. ROW ENUMERATION
METHOD-CARPENTER
Presented By : Submitted To:
Aniket Choudhury Prof. Ompriya Kale
140320702501(C.E)

2. OUTLINE:
 Introduction
 Problem statement
 Related work
 Preliminaries
 The carpenter algorithm
 Pruning methods
 Pruning method 1
 Pruning method 2
 Pruning method 3
 Comparative study
 Conclusion

3. INTRODUCTION
 CARPENTER[1] stands for Closed Pattern Discovery by
Transposing Tables that are Extremely Long; the “ar” in
the name is silent.
 Bioinformatics datasets typically contain large number of
features with small number of rows.
 For example, many gene expression dataset may contain
10K to 100K columns or items but usually have only
100-1000 rows.
 Such datasets pose a great challenge for existing frequent
pattern discovery algorithms.

4. CONTI..
 Running time of most of the previous algorithms will
increase exponentially with the average length of the
transactions.
 CARPENTER’s search space is much smaller than that
of the previous algorithms on these kind of datasets and
therefore has a better performance.
 CRAPENTER is specially designed to handle dataset
having large number of attributes and relatively small
number of rows.

5. CONTI..
 In other words CARPENTER[1] is defined as an
algorithm which discovers frequent closed patterns by
performing depth-first row wise enumeration combined
with efficient search pruning techniques to generate
highly optimized algorithm.

6. PROBLEM STATEMENT
 Discover all the frequent closed patterns with respect to
user specified support threshold in such biological
datasets efficiently.

7. RELATED WORK
 To reduce the frequent patterns to a compact size, mining
frequent closed patterns has been proposed.
 The followings are some new advances for mining closed
frequent patterns.
 Close and Pascal are two algorithms which discover closed
patterns by performing breadth first, column enumeration.
 Similarly the CLOSET algorithm was proposed for mining
closed frequent patterns. Unlike Close and Pascal, CLOSET
performs depth first, column enumeration.
 CLOSET uses a frequent pattern tree (FP-structure) for a
compressed representation of the datasets.

8. PRELIMINARIES
 Let F = {f1,f2,f3….fn} be set of items, which is called
features.
 Our dataset D consists of a set of rows R = {r1,r2…rn},
where each row ri is a set of features, i.e ri ⊆ F(feature).

9. CONTI..
 In the previous figure there are 5 rows, r1,r2,r3,r4,r5.
 The first row r1 contains the feature set {a,b,c,l,o,s}.
 Given a set of features FꞋ ⊆ F from this we can define the
feature support set which is denoted by F(RꞋ)⊂F.
 This indicates the maximum set of rows that contain FꞋ.
 For example, let FꞋ=aeh(features) then R(FꞋ)=234 as all
these rows contain (FꞋ=aeh).

10. CONTI..
 Like wise ,given a set of rows RꞋ⊂R, we define the row
support set, denoted as F(RꞋ)⊂F, as the maximum set of
features common to all the rows in RꞋ.
 For example, RꞋ=23, then F(RꞋ)=aeh since it is the max set of
features common to both r2 and r3.
 Given a set of features (FꞋ=aeh), the no. of rows (r2,r3,r4) in
the dataset that contains (FꞋ=aeh) is called support of FꞋ.
 A set of features FꞋ⊂F, it is called a closed pattern if there
exists no FꞋꞋ such that (FꞋ⊂FꞋꞋ) and |R(FꞋꞋ)| = |R(FꞋ)| i.e., there is
no superset of FꞋ with the same support.

11. CONTI…
 Put another way, the row set that contains superset FꞋꞋ must not
be exactly the same as the row set of FꞋ. A feature set FꞋ is
called a frequent closed pattern, if it is i) closed, ii) |R(FꞋ) ≥
minsup.
 where minsup is a user specified lower support threshold.
 For example, given minsup = 2, the feature set aeh is a
frequent closed pattern in above figure since it occurs three
times.
 ae, on the other hand, is not a frequent closed pat- tern, since
it is not closed (|R(aeh)| = |R(ae)|), although its support is
more than minsup.

12. THE CARPENTER ALGORITHM
 The main idea of CARPENTER[1] is to mine the
dataset row-wise.
 2 steps:
 First, transpose the dataset
 Second , search in the row enumeration tree.

13. CONTI…

14. ROW ENUMERATION TREE

15. CONTI…
 Bottom-up row enumeration tree is based on conditional
table.
 Each node is a conditional table.
 23-conditional table represents node 23.

16. CONTI..
 Recursively generation of conditional transposed table,
performing a depth-first traversal of row-enumeration
tree in order to find the frequent closed patterns.

17. CONTI…
 Without pruning strategies, minsup=3

18. EXAMPLE

19. PRUNE METHODS[1]
 It is obvious that complete traversal of row enumerations
tree is not efficient.
 CARPENTER[1] proposes 3 prune methods.

20. PRUNE METHOD 1
 Prune out the branch which can never generate closed
pattern over minsup threshold.
 In the enumeration tree, the depth of a node is the
corresponding support value.
 Prune a branch if there won’t be enough depth in that
branch, which means the support of patterns found in the
branch will not exceed the minimum support.

21. CONTI…
In this case the minsup = 4
Max support value in branch “13”
will be 3, therefore prune this
branch.

22. PRUNE METHOD 2
 If same rows appear in all tuples of the conditional
transposed table, then such branch needs to prune.
 Row r4 has 100% support in the projected table of
 r2 and r3, hence, branch 234 is pruned and reconstructed.

23. PRUNE METHOD 3
 In each node, if corresponding support features is found,
prune out the branch.

24. COMPARATIVE STUDY WITH SIMILAR
TECHNOLOGIES
 CARPENTER is compared with CHARM and CLOSET
 Both CHARM and CLOSET use column enumeration
approach
 Use lung cancer dataset
 181 samples with 12533 features
 Two parameters: minsup and length ratio
 Length ratio is the percentage of column from original dataset

25. CONTI…
 Length ratio =60%, varying minsup

26. CONTI…
 Minsup=4% varying length ratio

27. CONCLUSION
 CARPENTER[1] is used to find the frequent closed
pattern in biological dataset.
 CARPENTER[1] uses row enumeration instead of
column enumeration to overcome the high
dimensionality of biological datasets.

28. REFERENCES
Research paper:
[1] Feng Pan, Gao Cong, Anthony K. H. Tung, Jiong Yang
and Mohammed J. Zaki “CARPENTER: Finding Closed
Patterns in Long Biological Datasets”. In Proc. 2003 ACM
SIGKDD Int. Conf. on Knowledge Discovery and Data
Mining (KDD'03), Washington, D.C., Aug 2003.

29. THANK YOU