A two level approach to discretize cosmetic data using Rough set theory

Abstract

Discrete values play a very prominent role in extracting knowledge. Most of the machines learning algorithms use discrete values. It is also observed that the rules discovered through discrete values are shorter and precise. The predictive accuracy is more when discrete values are used. Cosmetic industry extracts the features from the face images of the customers to analyze their facial skin problems. These values are continuous in nature. A predictive model with high accuracy is required to determine the cosmetic problems of the customers and suggest suitable cosmetic. Existing traditional discretization techniques are not sufficient for deriving discretized data from continuous valued cosmetic data as it has to balance the loss of information intrinsic to process adapted and generating a reasonable number of cut points, that is, a reasonable search space. This paper proposes a two level discretization method which is a combination of traditional k means clustering technique and rough set theory to discretize continuous features of cosmetic data.

Full text

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A two level approach to discretize cosmetic data using Rough set theory
P.M. Prasuna, Dr.Y. Ramadevi, Dr. A.Vinay Babu
Research Scholar JNTU, Hyderabad
prasunamanikya@yahoo.com
Dr.Y. Ramadevi, Professor CBIT, Hyderabad
yrdcse.cbit@gmail.com
Dr. A.Vinay Babu, Professor JNTUHCE, Hyderabad
avb1222@jntuh.ac.in
ABSTRACT
Discrete values play a very prominent role in extracting knowledge. Most of the machine learning algorithms use discrete
values. It is also observed that the rules discovered through discrete values are shorter and precise. The predictive
accuracy is more when discrete values are used. Cosmetic industry extracts the features from the face images of the
customers to analyze their facial skin problems. These values are continuous in nature. A predictive model with high
accuracy is required to determine the cosmetic problems of the customers and suggest suitable cosmetic. Existing
traditional discretization techniques are not sufficient for deriving discretized data from continuous valued cosmetic data as
it has to balance the loss of information intrinsic to process adapted and generating a reasonable number of cut points,
that is, a reasonable search space. This paper proposes a two level discretization method which is a combination of
traditional k means clustering technique and rough set theory to discretize continuous features of cosmetic data.
Indexing terms/Keywords
Rough set Theory, Discretization, cut points, kmeans.
Academic Discipline And Sub-Disciplines
Data Mining and Retrieval
SUBJECT CLASSIFICATION
Discretization technique
TYPE (METHOD/APPROACH)
Rough set theory
Council for Innovative Research
Peer Review Research Publishing System
Journal: INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY
Vol. 14, No. 10
www.ijctonline.com , editorijctonline@gmail.com

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INTRODUCTION
There are huge volumes of data in the cosmetic industry not only to analyze the problems of the customers but also to
rejuvenate a new product basing on the customer problems. Data mining algorithms help us to extract necessary
information for decision making from this cosmetic data. However, many mining algorithms or machine learning algorithms
cannot be applied on them as they are continuous in nature. Numeric data contain large number of values when compared
to discrete values, the rules discovered looks complex and gives less predictive accuracy. As discrete attributes are
represented with simple interval numbers they are understandable and easier to use. The rules of discrete attributes
usually are shorter and easy to understand, hence will increase the accurateness of predictions. Therefore, it is essential
to have good descretization techniques [1] to transform continuous valued features into discrete valued features. This not
only speeds up the mining process but also helps in developing a better model. This paper deals with a two level
discretization technique for cosmetic data which firstly uses the traditional kmeans algorithm and then applies rough set
theory to discrete the data at attribute level.
K means algorithm
Kmeans algorithm: Kmeans is a simple unsupervised clustering technique [2]. It follows simple and easy steps to form the
clusters. Initially number of clusters to be formed is to be determined. Then it follows three steps, initialization, expectation
and maximization. In initialization step k centers are created where k is the number of clusters to be formed which is
predetermined. In expectation step each data point is assigned to the center closest to it and maximization step deals with
computation of new center basing on the data points associated to it. These steps are carried out repeatedly until no more
changes are done to centers.Finally, this clustering technique aims at minimizing an objective function, in this case a
squared error function. The objective function used is
,
where is a chosen distance measure between a data point and the cluster centre is an indicator of the
distance of the data points from their respective cluster centres [3].
Kmeans Algorithm:
Make initial guesses for the centres c1, c2, ..., ck
 Until there are no changes in any centre
o Use the estimated means to classify the samples into clusters
o For i from 1 to k
 Replace mi with the mean of all of the samples for cluster i
o end_for
 end_until
Application of k means algorithm to cosmetic data discretization
Initially kmeans algorithm is applied on sample cosmetic data to form the clusters as it is unsupervised [4]. This completes
the basic discretization step. This step discretizes the data into specified number of intervals .The results are then given to
the second phase which uses Rough set theory[5]
Rough Set Theory
Rough set theory was proposed by Professor Powlak (powlak, 1982:1991 skowron, 1990) [6]. The main goal of the rough
set analysis is induction of (learning) approximations of concepts. It offers mathematical tools to discover patterns hidden
in data. The basic concepts of rough set theory are described below:
Approximation Space: An approximation space is a pair (U, B) where U is a nonempty finite set called the universe and
B is an equivalence relation defined on U.
Information System: An information system is a pair S= (U, A), where U is a nonempty finite set called the universe and
A is a nonempty finite set of attributes, i.e., a: U→Va for aєA, where Va is called the domain of a.
Decision Table (Data Table): A decision table is a special case of information system, S = (U, A= C є {d}), where
attributes in C are called condition attributes and d is a designated attribute called the decision attribute.
Approximations of Sets: Let S = (U, B) be an approximation space and X be a subset of U.

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The lower approximation of X in S is defined as
= {x є X: [x] BєX}
The upper approximation of X in S is defined as
= {x є X: [x] B ∩ X ≠ φ}
For a given set of conditional attributes B, the B- positive region POSB(D) in the relation IND(D) is defined as, POSB(D) =
є{BX : X є [x ]D } . The positive POSB(D) region contains all the objects in U that can be classified without any error into
distinct classes defined by IND (D), based only on information in the relation IND (B). Greater the cardinality POSB(D)
higher the significance of the attributes in the set B with respect to D.
The rough membership function quantifies the degree of relative overlap between X and the equivalence class to which x
belongs. Thus this rough membership function is also a measure of the significance of B⊆A to describe X and is defined
by [7],
Application of rough set theory to refine the cut points generated by Kmeans
algorithm
The traits of the clusters formed by the kmeans algorithm vary. This discretization using clustering technique is not
sufficient to generate cut points with minimum information loss. Hence they are refined using Rough set theory concepts
[8]. The main aim in splitting the cluster is to refine the discretized interval. The refinement is to enhance the significance
of the attribute. In rough set theory the significance of an attribute is measured through rough membership function
POSai(D).Hence maximizing POSai(D) leads to maximizing the significance of the attribute. To maximize POSai (D), the
clusters formed through kmeans are refined further to generate new intervals or cut points. The refinement is processed in
such a way that the maximum number of objects is correctly classified by each of the interval of attribute ai, just as they
are classified by D [9]. This is done by a rough membership function applied to each interval of the attribute ai with respect
to the clusters formed through the kmeans which are further treated as class labels.
Let us take the data set U contains objects of m clusters say {c1, c2, c3 … cm} and let the k distinct values of an attribute
ai in ascending order be {vi1, vi2, vi3 … vik} i.e. the interval [vi1, vik]. The rough membership function of any interval
I= [Vi1, Vij] of the attribute ai for class cp is defined as
f (ai, cp, I) =
where ={x | ai(x) |є I} and, ={x | ai(x) є I, D(x) =cp}.
Maximizing f(ai,cp,I) is maximising which further maximizes POSai(D) [10].To achieve this each cluster
generated by kmeans is examined carefully and if necessary a cluster may be split into two or merged with the
neighbouring cluster. The splitting process uses the rough set membership function such that it maximizes the POSai
(D).in this way the intervals are refined. The refinement takes place as follows. Initially three predetermined parameters
are taken. Max_size determines the maximum no of values that could fall in each cluster. Min_size decides the minimum
number of values to form a cluster and Range gives the length of the cluster. These parameters decide whether the
cluster can be retained or still to be refined. The refinement process takes place if the cluster is large or small. The cluster
is said to be large if its cardinality is greater than the Max_size or the length is greater than the Range. A cluster is treated
as small if its cardinality is less than the Min_size. If the cluster is large it is split into two or else small, merged with other
small clusters thereby generating new cut points or intervals. This process is refined until there is no change in the cut
points or intervals.
Algorithm for the proposed method
Step1: Consider each attribute in the data set, select distinct values and sort them.
Step2: Apply kmeans algorithm to form clusters.
Step3.From the generated clusters determine the class labels as well as intervals.
Step4.Refine the intervals and add new intervals to the interval set.
Refine (I1, I2, …. Ir))
While (no change in no. of intervals) do
For each interval Ij
If SP-C (Ij, Min_size, Range) = True then

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Temp= Cut Point ({vj1, vj2, vj3 … vjk})
Replace the interval Ij with two intervals
Ij1 = [vj1, Temp] and Ij2 = [Temp, vjk]
Else if | Ij | < Min_size then
If for Ik′ either neighbour of Ij
MR_C (Ij, Ik′, Max_size, Min_size) = True then Merge Ij to an interval Ik′
End if
End if
End for
End while
Cut Point ({vi1, vi2, vi3 … vik})
I = [vi1, vik/2]
MAXRMV= Max ({f (Ai, cp, I)}) є cp,
for each vij , j=k/2 to 2
I = [vi1, vij]
Temp = Max ({ f (A i , c p , I) }) є cp;
if Temp> MAXRMV then
MAXRMV=Temp;
else
break;
End if
If (j < k/2) then
return vij as cut point for the cluster
else
for each vij, j=k/2 to k-1
I = [vij, vij]
Temp = Max ({ f (A i , cp , I) }) є cp;
if Temp> MAXRMV then
MAXRMV=Temp;
else
return vij as cut point for the cluster
End if
End for
for each vij, j=k/2 to k-1
I = [vij, vij]
Temp = Max ({ f (Ai , cp , I) })є cp;
if Temp> MAXRMV then

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MAXRMV=Temp;
else
return vij as cut point for the cluster
End if
End for
Results
Cosmetic data has been collected from the customers of different age groups. The facial images of the customers are
captured under sophisticated environment and then the features are extracted. The features are numeric in nature. To
analyse the data collected mining tools are applied. As a preprocessing step to mining process the numeric values are
discretized. To show the experimental results a dataset of 33 samples taken which consists of 17 numeric Features. After
applying the proposed algorithm the results are as shown in Table -1:
Table -1
Complexity
Before we apply kmeans algorithm first distinct values are identified then they are sorted. For carrying out this process
complexity is O(N log N) where N is the number of objects in the dataset. Kmeans is known to have the complexity
which may be in worst situation for the above algorithm i.e. when the attribute values for each object are
distinct. The complexity of the Refine function is bounded by k * N/2, where k is the number of intervals of an attribute and
the running time of the function Cut_Point is bounded by N/2. If n is the number of attribute then the total complexity of the
algorithm is bounded by,
n * (N log N + N log N + k * N /2 + N )
≈ n * (N log N)
Sno
Attribute
Type
Distin
ct
values
(distin
ct
values)
Interva
ls
1
Stype
Numeric
5
3
2
Saa
Numeric
30
7
3
S_Count
Numeric
29
6
4
A_Spots
Numeric
12
4
5
Pimples
Numeric
13
4
6
Pastules
Numeric
3
3
7
Papules
Numeric
5
4
8
Cysts
Numeric
2
2
9
B_Visi
Numeric
23
4
10
A_count
Numeric
20
4
11
p_count
Numeric
33
8
12
V_pores
Numeric
33
4
13
E_lines
Numeric
31
6
14
F_Lines
Numeric
27
7
15
D_lines
Numeric
20
7
16
E_Wrinkle
s
Numeric
1
1
17
h_skin
Numeric
33
5

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The number of attributes n is normally small in comparison to N. The preprocessing of the dataset for selecting relevant
attributes further reduces the value of n to be small compared to N. Therefore, the running time of the proposed algorithm
for labeled data is bounded by N logN.
Conclusion
By the proposed method the natural intervals of the values of the continuous attributes are obtained which maximized the
mutual class-attribute interdependency. The method also generates the possibly minimum number of intervals.
Although the computational effort for the search algorithm for cut point has been reduced to half of N, the size of dataset,
by implementing binary search for the cut point can further reduce the complexity of search step.
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