Reconstruction of a Complete Dataset from an Incomplete Dataset by ARA (Attribute Relation Analysis): Some Results

Sameer S. Prabhune & S.R. Sathe
International Journal of Data Engineering (IJDE) Volume (1): Issue (5) 35
Reconstruction of a Complete Dataset from an Incomplete Dataset by
ARA (Attribute Relation Analysis): Some Results
Sameer S. Prabhune ssprabhune@ssgmce.ac.in
Assistant Professor & Head,
Department of Information Technology
S.S.G.M. College of Engineering,
Shegaon-444203, Maharashtra, India
Dr. S. R. Sathe srsathe@cse.vnit.ac.in
Professor,Department of E & CS,
V.N.I.T., Nagpur, Maharashtra, India
Abstract
Preprocessing is crucial steps used for variety of data warehousing and mining Real world data is noisy
and can often suffer from corruptions or incomplete values that may impact the models created from the
data. Accuracy of any mining algorithm greatly depends on the input data sets. Incomplete data sets
have become almost ubiquitous in a wide variety of application domains. The incompleteness in the data
sets may arise from a number of factors: in some cases it may simply be a reflection of certain
measurements not being available at the time; in others the information may be lost due to partial system
failure; or it may simply be a result of users being unwilling to specify attributes due to privacy concerns.
When a significant fraction of the entries are missing in all of the attributes, it becomes very difficult to
perform any kind of interpretation on the original data. And also it overall deteriorates the accuracy of any
classifiers, algorithm for further analysis. For such cases, we introduce the novel idea of attribute
weightage, in which we give weight to every attribute for prediction of the complete data set from
incomplete data sets, on which the data mining algorithms can be directly applied. This simple but robust
mechanism of weighted average gives very precise results, when tested on variety of real world datasets.
This paper describes a theory and implementation of a new filter ARA (Attribute Relation Analysis) to the
WEKA workbench, for finding the complete dataset from an incomplete dataset.
Keywords: Data Mining, Data Preprocessing, Missing Data
1. INTRODUCTION
Many data analysis applications such as data mining, web mining, and information retrieval system
require various forms of data preparation. Mostly all this worked on the assumption that the data they
worked is complete in nature, but that is not true! In data preparation, one takes the data in its raw form,
removes as much as noise, redundancy and incompleteness as possible and brings out that core for
further processing. Common solutions to missing data problem include the use of default [16],imputation,
statistical or regression based procedures [11,15]. We note that, the missing data mechanism would rely
on the fact that the attributes in a data set are not independent from one another, but that there is some
predictive value from one attribute to another [1]. Therefore we used the well-known principle namely,
weightage on attribute instance [11], for predicting the missing values. This paper gives the theory and
implementation details of addition of an ARA filter in the WEKA workbench for estimating the missing
values.

1.1 Contribution of this paper
This paper gives the theory and implementation details of ARA filter addition to the WEKA workbench.
Also it gives the precise results on real datasets.
2. PRELIMENARY TOOLS KNOWLEDGE
To complete our main objective, i.e. to develop the ARA filter for the WEKA workbench we have used the
following technologies. These are as follows:
2.1 WEKA 3-5-4
Weka is an excellent workbench [4] for learning about machine learning techniques. We used this tool
and the package because it was completely written in java and its package gave us the ability to use
ARFF datasets in our filter. The weka package contains many useful classes, which were required to
code our filter. Some of the classes from weka package are as follows [4].
• weka.core
• weka.core.instances
• weka.filters
• weka.core.matrix.package
• weka.filters.unsupervised.attribute;
• weka.core.matrix.Matrix;
• weka.core.matrix.Eigenvalue Decomposition; etc.
We have also studied the working of a simple filter by referring to the filters available in java [9,10].
2.2 JAVA
We used java as our coding language because of two reasons:
1. As the weka workbench is completely written in java and supports the java packages, it is
useful to use java as the coding language.
2. The second reason was that we could use some classes from java package and some from
weka package to create the filter.
3 PSEUDO CODE
This pseudo code is designed to give the user an understanding of the ARA algorithm. ARA is a simple
yet robust technique of weighted average of attribute values. [11,13].

Attribute Relation Analysis Pseudo code
Input: Dataset D with Missing attributes.
Output: Completed dataset D´ with estimated values.
ARA ( Ik , J, AV
k
, It , MAk , PAk , AC
k
)
Where
IK - Instant in AVK
J - Element in AVK
AVK
- Given attributes with Missing values
MAK - Missing attributes
PAk - Predictable attribute
It - Iteration
Step 1
Get input data:-
a. Take ARFF file as input.
b. It will be taken as one-dimensional array.
Step 2
Repeat Until (iteration > CKj)
a. Initially all attribute and instance in iteration is null.
b. Array of instance is initially null.
c. Iteration start from first instance.
d. Initially missing values are null.
e.
Step 3
( Aii…….. Aij ( MAK ) ;
Aii…….. Aij ; { Aii…….. Aij} ≠ [ ] ;
a. Check iteration until missing instances
b. If any missing instances is getting stop the procedure.
Step 4
? AV .......? AVk k
i j← ←
a. In iteration number of instances from {Ai……..Aj} so check entire instances in iteration.
b. Check any missing instance in iteration.
c. In given iteration if no missing value, so stop the procedure and print given iteration in array.
Step 5
If { correct classify (IK.T)} ;

a. Replace the missing value or missing instance by X.
b. And existing instances by Y.
Step 6
(V[chg Num] = AV ........ AVk k
i j+ +
[ chg Num ] ← { Aii --- AiJ }
a. Check given instances is correctly classified or not.
b. If not correctly classify.
c. Restore instances using given dataset.
Step 7
AiK …. Aij; chg Num ++
a. Store the iteration and its changing attribute in an array.
Step 8
Iteration ++
a. Restore old value.
Step 9
if { chgnum ! = 0 }
a. If changing value contains 0, it will be replace by 0.
b. Otherwise replace it by new value.
Step 10
[ ] [ ] [ ]1 2 1 1
0
1
0
( ) ( ) ... ( )
( .... )
n
n n n n
k i
i n
n
i
Ai w Ai Ai w Ai Ai w Ai
Av
w Ai Ai
+ +
=
=
× + × + + ×
=
+ +
∑
∑
a. Take upper sum of instances from missing instances and multiply with its weight.
b. Nearest instances get higher weight and weight will be decrease by 1 for each instance.
c. Sum of upper instances is divided by sum of weight.

Step 11
[ ] [ ] [ ]1 2 1 1
0
1
0
( ) ( ) ... ( )
( .... )
n
n n n n
jk
j n
n
i
Aj w Aj Aj w Aj Aj w Aj
Av
w Aj Aj
+ +
=
=
× + × + + ×
=
+ +
∑
∑
a. Take lower sum of instances from missing instances and multiply with its weight.
b. Nearest instances get higher weight as compared to other and weight will be decrease by 1 for
each instance.
c. Sum of lower instances is divided by sum of weight
Step12
MV
2
K K
k i JAC AC+
=
Finally take average of upper instances and lower instances.
Result is replaced by new value called as predict instance in given attribute.
Step 13
After completion of one instance check next missing instance.
Procedure will be repeated until all value will be predicted.
Figure 1 Shows the ARA psedo code for prediction of the missing values.
4. IMPLEMENTATION
Coding Details
We were using datasets in ARFF format as an input to this algorithm and the ARA filter [2,7,8]. The filter
would then take ARFF dataset as input and estimating out the missing values in the input dataset. After
fixing out the missing values in the given dataset, it would apply the ARA algorithm and predict the
missing values and also reconstruct the whole dataset from an incomplete dataset.
We have created an ARA filter class, which is an extension of the Simple Batch Filter class, which is an
abstract class. Our algorithm first of all takes an ARFF format database as input then read how many
attribute in given data set. It takes each attribute individually and writes it into array format. After that, it
insert all instances into that array, including missing instances and find first missing instance, if it got the
instance replace it by zero. After that it calculates average of all upper instances by using its weight effect
on that particular instance. Nearest instance get more weight and weight will be decreases instance by
instance. After that it also calculates average of all lower instances by using its weight effect on that
particular instance, nearest instance get more weight and weight will be decreases instance by instance
and vice-versa. Finally we are calculating the average of lower as well as upper instances.
5 EXPERIMENTAL SET UP
5.1 Approach
The objective of our experiment is to build the filter as a preprocessing step in Weka Workbench, which
completes the data sets from missing data sets. We did not intentionally select those data sets in UCI

[12], which originally come with missing values because even if they do contain missing values, we don’t
know the accuracy of our approach. For experimental set up, we take the complete dataset from UCI
repository [12], and then missing values are artificially added to the data sets to simulate MCAR missing
values. To introduce m% missing values per attribute xi in a dataset of size n, we randomly selected mn
instances and replaced its xi value with unknown i.e. ?( In WEKA, missing values are denoted as “?”). We
use 10%,20% and 30% missingness for every dataset.
5.2 Results
After preprocessing steps, we use WEKA’s M5Rules classifier for finding the error analysis. The
classification was carried out on 10 fold cross validation technique. In Table 1, we have calculated the
standard errors along with correlation coefficient on UCI[12] database repository. When observing the
correlation coefficient of all the dataset i.e. CPU, Glass and Wine with missingness parameters –
10%,20% and 30%, it has been clear that, as missingness increases the accuracy of the classifier
decreases.
S.
N.
Error
Analysis
Dataset
CPU Glass Wine
10% M 20% M 30% M 10% M 20% M 30% M 10% M 20% M 30% M
1
Correlation
coefficient
0.88 0.66 0.47 0.62 0.59 0.62 0.78 0.78 0.75
2
Mean
absolute
error
36.03 53.85 60.50 0.77 0.76 0.81 144.89 140.69 147.70
3
Root mean
squared
error
74.03 116.22 144.70 2.31 2.39 2.18 198.67 188.66 204.41
4
Relative
absolute
error
43.63% 63.64% 79.63% 40.40% 39.99% 43.23% 57.76% 59.17% 62.67%
5
Root
relative
squared
error
48.68% 75.88% 114.19% 78.06% 80.81% 79.32% 64.36% 63.10% 68.63%
6
Total
Number of
Instances
209 209 209 214 214 214 178 178 178
TABLE-1: After Applying the ARA Filter with M5Rules Classifier in WEKA Workbench on
UCI [12] Datasets.

6. CONCLUSION
In this paper, we provided the theory and implementation details of a new filter viz. ARA in the WEKA
workbench. As seen from the result, this simple but yet robust ARA filter works well to predict the missing
data. We also demonstrate the efficacy of our approach by performing the analysis on real world UCI [12]
data repositories. Thus it proves the extension as a preprocessing filter.
ACKNOWLEDGMENTS
Our special thanks to Mr. Peter Reutemann, of University of Waikato, fracpete@waikato.ac.nz, for
providing us the support as and when required.
REFERENCES
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4. wekaWiki link : http://weka.sourceforge.net/wiki/index.php/Main_Page
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16. C. J. Date and H. Darwen, “The Default Values approach to Missing Information,” Relational
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Reconstruction of a Complete Dataset from an Incomplete Dataset by ARA (Attribute Relation Analysis): Some Results

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Reconstruction of a Complete Dataset from an Incomplete Dataset by ARA (Attribute Relation Analysis): Some Results