Decision Tree Clustering : A Columnstores Tuple Reconstruction

DECISION TREE CLUSTERING: A COLUMNSTORES TUPLE RECONSTRUCTION
Tejaswini Apte1, Dr. Maya Ingle2 and Dr. A.K. Goyal2
1

Symbiosis Institute of Computer Studies and Research
apte.tejaswini@gmail.com
2

Devi Ahilya Vishwavidyalaya, Indore

maya_ingle@rediffmail.com, goyalkcg@yahoo.com

ABSTRACT
Column-Stores has gained market share due to promising physical storage alternative for
analytical queries. However, for multi-attribute queries column-stores pays performance
penalties due to on-the-fly tuple reconstruction. This paper presents an adaptive approach for
reducing tuple reconstruction time. Proposed approach exploits decision tree algorithm to
cluster attributes for each projection and also eliminates frequent database scanning.
Experimentations with TPC-H data shows the effectiveness of proposed approach.

GENERAL TERMS
Performance, Clustering, Projection

KEYWORDS
Tuple Reconstruction, Support

1. INTRODUCTION
Tuple reconstruction time is a major factor to affect the query performance in column-stores [1,
2]. For large data requirement, traditional row-id based tuple construction time pays heavy
performance penalty. Two materialization strategies for tuple reconstruction exists in literature
namely; Early materialization and Late Materialization. Early Materialization is a technique to
stitch the columns into partial tuples as early as possible, Late materialization provides significant
performance advantages for analytical queries, since there are fewer row-ids to fetch off the disk
for each join [16], hence results in significant disk I/O savings for large tables. In late
materialization, schedule to materialize columns according to need, requires awareness in the
optimizer, execution engine, and cost model during query optimization. For the very large tables,
late materialization involves multiple I/O operations other than the join. In contrast, an early
materialized plan involves single scan of complete data.

Sundarapandian et al. (Eds) : ICAITA, SAI, SEAS, CDKP, CMCA-2013
pp. 295–303, 2013. © CS & IT-CSCP 2013

DOI : 10.5121/csit.2013.3824

Computer Science & Information Technology (CS & IT)

296

Therefore, researching and designing a time effective tuple reconstruction approach adapted to
column-stores is of great significance. Exploiting projections to support tuple reconstruction is
included in C-Store. A relation is divided according to required attributes by query, into subrelations called projections. Each attribute may appear in more than one projection and stored on
different sorted order. Since all the attributes are not the part of projection, thus tuple
reconstruction pays penalty [4].
Decision tree algorithm is a popular approach for classifying data of various classes. A purity
function to partition the data space into several different classes is a requirement for Decision tree
algorithm. Although, as datasets have no pre-assigned labels, the decision tree partitioning
approach is not directly applicable to clustering. The partitioning of data space into cluster and
empty regions is carried through CLTree, as it efficiently finds cluster in large high dimensional
spaces [15]. Proposed approach inherits CLTree to reduce the tuple reconstruction time by
clustering frequently used attributes with available projection techniques.
It has been observed that attribute projection plays vital role for tuple reconstruction. Proposed
approach i.e. Decision Tree Frequent Clustering Algorithm (DTFCA) uses some existing
projection techniques to reduce tuple reconstruction time. These techniques are discussed in
Section 2. Some notations and terminology are necessary to review the correlation amongst query
attributes and are discussed in Section 3. Methodology to understand DTFCA is presented in
Section 4. Section 5 presents the detail description of DTFCA. To exploit DTFCA, experimental
data based on TPC-H schema is used as an input in suitable experimental environment. The
experimental results thus obtained are analyzed, and discussed in Section 6. Finally, paper
conclude with concluding remarks in Section 7.

2. RELATED WORK
All column-stores databases require tuple reconstruction to process multi-column queries.
Literature reveals that much work has been performed to present the materialization strategies
and their trade-offs [2]. Column-Stores database series C-Store and MonetDB has gained
popularity due to their good performance for analytical queries [4, 5]. Projections are exploited
to logically organize the attributes of the base table. Multiple attributes are involved in each
projection. The objective of projections is to reduce the tuple reconstruction time. MonetDB uses
late tuple materialization. Though partitioning strategies do not guarantee about the better
projection, a good solution is to cluster attributes into sub-relations based on the usage patterns
[5]. CLTree clustering technique performs clustering by partitioning the data space into dense and
sparse regions [15].
The Bond Energy Algorithm (BEA) is used to cluster attributes based on Attribute Usage Matrix
[1, 10, 11]. MonetDB proposed self-organization tuple reconstruction strategy in a main memory
structure called cracker map [5, 7]. Dividing and combining the pieces of existing cracker map
optimize the query performance. But for the large databases, cracker map pays performance
penalty due to high maintenance cost for memory [5]. Therefore, the cracker map is only adapted
to the main memory database systems such as MonetDB.

297


3. DEFINITIONS AND NOTATIONS
In relational Online Analytical Processing Applications, the common format of a query from the
fact table(s) and dimension tables is depicted as follows:
Select <attribute list>
From <Table list>
Where <condition>
Group by <attribute list>
Order by <attribute list>
Definition 1 Strong Correlation
k attributes A1, A2,…, Ak of relation R are strongly correlated if, and only if they appear in the
conjunction in conditional clause and target list of an access query.
Definition 2 Weak Correlation
In a collection of accesses A={a1, a2,…, am}, every ai(1≤i≤m) is an access to a query. If the
correlation among query target attributes is smaller than P, where P is the threshold, the attributes
are considered for weak correlation.
In column-stores, two critical tasks are needed to process a query: First, to determine qualifying
rows based on the conditions in Where clause, and to generate a set of row identifiers; Second, to
merge the qualifying columns of identical row identifiers, and to construct the target rows
according to target expression in Select clause. The attributes appear in conjunction in conditional
clause and query target are considered to be strongly correlative. The strong correlations in the
access list drives the creation of frequent attribute set.

4. METHODOLOGY
This section covers the search space for DTFCA.

4.1 Decision Tree Construction
Divide and conquer strategy has been used to recursively partition the data to build decision tree
[15]. In order to obtain purer regions each successive step chooses the cut to partition the space.
A commonly used criterion for choosing the best cut is the minimum support. It evaluates every
possible value (or cut point) for all projected attributes to find the cut point that gives the best
gain (Figure 1).
for each attribute Ai ∈{A1, A2, …, Ad} of the dataset D do
for each value x of Ai in D do
/* each value is considered as a possible cut */
Compute the information gain at x
end
Select the cut that satisfy the best information gain according to minimum support
Figure 1: The procedure to find the appropriate cluster


298

4.2 Determining Cluster Attributes
This sub-section focuses on determining attributes for tuple reconstruction. A cluster is created
for each data point in the original dataset, and introduce some attributes for support greater than
minimum support. The number of attributes to be added for the cluster E is determined by the
following rule:
If the number of attributes inherited from the parent cluster projection is less than the number of
projected attributes in E then
the number of inherited attributes is increased to E
else
the number of inherited attributes is used for E
The recursive partitioning method will divide the data space until each cluster contains only
attribute of a single class, results in very complex tree that partitions the space more than
necessary. Hence the decision tree needs to be pruned to produce meaningful clusters. This
problem is similar to classification problem, however pruning methods used for classification,
cannot be applied for clustering. Subjective measures are required for pruning, since clustering, to
certain extent is a subjective task [12, 13]. The tree is pruned using the minimum support values.
After pruning, algorithm summarizes the clusters by retrieving only those attributes.

4.3 Scaling-up decision tree algorithm
For the decision tree, whole data must resides in memory. For the large data set, SPRINT, a
scalable technique is proposed by decision tree algorithm, for eliminating the need to have the
entire dataset in memory [23]. A statistical technique to construct a consistent tree based on small
subset of data is discussed in BOAT [22]. Proposed algorithm inherits these techniques to
determine the cluster.

5. DECISION TREE FREQUENT CLUSTERING ALGORITHM (DTFCA)
This section describes the implementation of DTFCA in the MonetDB analytic platform [5].
DTFCA is used to determine the clustering of frequent attribute set. DTFCA algorithm
combines multiple iterations of the original loop into a single loop body, and rearranges the
frequent attribute set.
Let each relation R be grouped into several projections based on empirical knowledge and users’
requirement. After the system is used by users for a period, a set of accesses A={a1, a2,…, am}
are collected by the system. DTFCA uses mainly a set of accesses to cluster frequently projected
attribute-set which are strongly correlated. The input to DTFCA is a variant of AUM (Table 1).
Each element in the output forms attributes of a projection. DTFCA clustering results truly reflect
the strong correlativity between attributes implied in previous collection of accesses for queries,
and conform to the meanings of projection in column-stores.
function DTFCA(String S)
{
/* Decision Tree Frequent Clustering Algorithm*/


，

299

：

Input
a relation R(U={A[1],A[2],…,A[n]})
A={a1,a2,…,am}, the support threshold min_sup.

a collection of strongly correlated accesses

Output: clusters of strongly correlated attributes Cl1,Cl2,…,Clk, which holds support no smaller
than min_sup.
for each access in A //Processing an element per iteration
{
compute frequent attribute set for support > minimum support; // Checking for the limit for
traversal
for i=0 to N-1
{
string ResF[200];
string ResT[200];
ResT [i] = A[i].getName(); //Getting the item name of tree node for frequent attribute set
strcat(ResF,ResT) //Concat columns to build the tuples
}
visit the matching build tuple to compare keys and produce output tuple;
}

6. EXPERIMENT DETAILS
The objective of the experiment is to compare the execution time of existing tuple reconstruction
method with DTFCA for TPC-H schema queries on column-stores DBMS.

6.1. Experimental Environment
Experiments are conducted on 2.20 GHz Intel® Core™2 Duo Processor, 2M Cache, 1G Memory,
5400 RPM Hard Drive, Monet DB, a column oriented database and Windows® XP operating
system.

6.2. Experimental Data
TPC-H data set is used as the experiment data set, which is generated by the data generator.
Given a TPC-H Schema, fourteen different queries are accessed 140 times during a given window
period.

6.3. Experimental Analysis
Let us consider a relation with four attributes namely; S_Supplierkey (A1), P_partkey (A2),
O_orderdate (A3), and L_orderkey (A4). These attributes are accessed by fourteen different
queries of TPC-H schema for varying minimum support. For each attribute AUM has access
frequency generated by the system. The access frequency is derived from three parameters
namely; Minimum access frequency (Min_fq), Maximum access frequency (Max_fq), and
Average access frequency (Avg_fq). Minimum access frequency of query attributes is computed
for initial access of attributes. Maximum access frequency of query attributes is computed on the
system with more processing of queries. Average frequency is computed on the system with less


300

processing of queries. DTFCA uses access frequency to cluster frequent attribute-set. Frequent
attribute-set refers to the set for frequency no smaller than the minimum support.
Table 1: Attribute Usage Matrix
Attr
Que

2
3
4
5
6
7
8
9
10
12
16
17
19
21

S_supplierkey (A1)
Min_
fq
1
0
0
1
0
1
1
0
0
0
0
0
0
0

Max_
Fq
1
0
1
0
1
0
0
1
0
1
0
1
0
1

Ave_
fq
1
0
0
0
0
0
0
0
0
0
0
0
0
0

Acc_
Fq
100123
0
331
331
331
331
331
331
0
331
0
331
0
331

P_partkey
(A2)
Min_
Max
fq
_fq
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
1

Ave
_fq
1
0
0
0
1
0
0
1
0
0
1
1
1
0

Acc
_fq
100123
331
331
0
100123
331
331
100123
0
331
100123
6612
100123
331

O_orderdate
(A3)
Min_
Max_
fq
Fq
0
0
1
1
1
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0

l_orderkey (A4)
Ave_
Fq
0
1
1
1
0
0
1
0
0
0
0
0
0
0

Acc_
Fq
0
100123
100123
100123
0
331
100123
0
331
331
331
331
331
0

Min_
Fq
1
0
1
0
0
1
1
0
0
1
0
0
1
0

Max_
fq
0
1
1
1
0
1
1
0
1
1
1
0
1
1

Ave_
Fq
0
0
1
0
0
1
1
0
0
1
1
0
1
0

Acc_
Fq
331
331
100123
331
0
100123
100123
0
331
100123
6612
0
100123
331

Now, we explain the execution of DTFCA algorithm for different cases of minimum support. We
denote the attribute frequency as a candidate of frequent attribute-set by (int_val) xyz, where
int_val is the integer value of access frequency. Also, x, y and z represent the case variable
numbers respectively. For the given minimum support, the frequent attribute-set will be a
combination of four attributes (A1, A2, A3, and A4).
Case-Study
Let Case 1, Case 2 and Case 3 denote three minimum support case variables. For DTFCA
experiment analysis, let the minimum support values for these variables be 30, 50, and 60
respectively. For the implementation of Case 1, user gains the control to determine the strong
correlation among attributes, and hence formulating the frequent attribute-set. By referring to
Table 1, frequent attribute-sets generated are higher than other cases i.e. out of fourteen pairs or
patterns, thirteen patterns were frequent. This result may be considered as moderate and reduces
tuple reconstruction time for column-stores. However, with Case 2 and Case 3, generated
frequent attribute sets are four and one respectively. The clustering result of DTFCA is more in
conformity with the idea of projection in column-stores.
The experiments are performed on TPC-H dataset queries with the same selectivity and varying
minimum support. As shown in Figure 2 (horizontal axis denotes the minimum support, vertical
axis denotes the execution time), the execution time of TPC-H query schema is inversely
proportional to minimum support, and the system may perform well for query attributes which
are strongly correlative (refer Section 3). As shown in Figure 3, the execution time under DTFCA
is much lower than traditional tuple reconstruction method; hence DTFCA could minimize the
tuple reconstruction time.

301


Figure 2: Minimum Support Time Cost

Figure 3: Tuple Reconstruction Time Cost

7. CONCLUSION
DTFCA approach, exploits decision tree to cluster frequently accessed attributes of a relation. All
the attributes in each cluster form a projection. The experiment shows that proposed approach is
beneficial to cluster projection in column-stores and hence reduces the tuple reconstruction time.
The output of DTFCA is not a partition, but a group of attributes for the clustering into columnstores.


302

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Authors
Tejaswini Apte received her M.C.A(CSE) from Banasthali Vidyapith Rajasthan. She is
pursuing research in the area of Machine Learning from DAU, Indore,(M.P.),INDIA..
Presently she is working as an ASSISTANT PROFESSOR in Symbiosis Institute of
Computer Studies and Research at Pune. She has 4 papers published in
International/National Journals and Conferences. Her areas of interest include Databases,
Data Warehouse and Query Optimization.
Mrs. Tejaswini Apte has a professional membership of ACM
Maya Ingle did her Ph.D in Computer Science from DAU, Indore (M.P.) , M.Tech (CS)
from IIT, Kharagpur, INDIA, Post Graduate Diploma in Automatic Computation,
University of Roorkee, INDIA, M.Sc. (Statistics) from DAU, Indore (M.P.) INDIA.
She is presently working as PROFESSOR, School of Computer Science and Information
Technology, DAU, Indore (M.P.) INDIA. She has over 100 research papers published in
various International / National Journals and Conferences. Her areas of interest
include Software Engineering, Statistical, Natural Language Processing, Usability
Engineering, Agile computing, Natural Language Processing, Object Oriented Software Engineering.
interest include Software Engineering, Statistical Natural Language Processing, Usability Engineering,
Agile computing, Natural Language Processing, Object Oriented Software Engineering.
Dr. Maya Ingle has a lifetime membership of ISTE, CSI, IETE. She has received best teaching Award by
All India Association of Information Technology in Nov 2007.

Dr. Arvind Goyal did his Ph.D. in Physiscs from Bhopal University,Bhopal. (M.P.),
M.C.M from DAU, Indore, M.Sc. (Maths) from U.P. He is presently working as
SENIOR PROGRAMMER, School of Computer Science and Information Technology,
DAU, Indore (M.P.). He has over 10 research papers published in various International /
National Journals and Conferences. His areas of interest include databases and data
structure. Dr. Arvind Goyal has lifetime membership of All India Association of
Education Technology

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