1. A Novel Approach for imputation of Missing Values for Mining
Medical Datasets
IEEE International Conference on Computational Intelligence and Computing Research(2015 IEEE ICCIC),Madhurai
UshaRani .Y
Dept of Information Technology
VNR Vignana Jyothi Institute of Engineering & Technology,
Hyderabad.
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2. Abstract
Real-world Medical datasets predominantly contain numeric (continuous) attributes and categorical (nominal) attributes with missing values.
In this paper, we propose a novel imputation approach for fixing missing values.The approach is based on clustering concept and aims at dimensionality reduction of the records
use the same records of lower dimension to be used for clustering and classification of medical records to arrive at accurate decision prediction.
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3. Missing values can also cause misleading results.
Missing values are usually associated with the following reasons such as:
the value might be lost (deleted or erased),
not recorded,
incorrect measurements and
equipment errors…etc
Missing values can also cause misleading results.
Missing values(MV) are affecting the classification accuracy of the classifiers.
To overcome these issues we propose a novel imputation approach for fixing missing values.The approach is based on clustering concept and aims at dimensionality reduction of the records.
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4. RESEARCH ISSUES IN MINING MEDICAL DATA
Handling Medical Datasets
Handling and Imputing Missing Values
Choice of Prediction and Classifications algorithms
Finding Nearest Medical Record and Identifying the Class Label
Deciding on Medical Attributes
Removal of Noise
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5. Importance of Present Approach
The method may be used to find missing attribute values from medical records
The same approach for finding missing values may be used to classify medical records
The disease prediction may be achieved using the proposed approach without the need to adopt a separate procedure
Handles all attribute types
Preserves attribute information
May be applied for datasets with and without class labels which is uniqueness of the current approach.
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6. Proposed Approach
Fig 1. Generating Clusters from medical records in group G1 equal to number of class labels in G
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7. The framework for missing value Imputation consists of following steps
1.Generating Clusters from Group G_1
This step involves finding the number of class labels and generating number of clusters equal to number of class labels
The clusters may be generated using k-means algorithm by specifying value of k to be number of class labels. Alternately, we may apply any clustering algorithm which can generate k clusters
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8. 2.Computing distance of normal records to Cluster Centers
Obtain mean of each cluster. This shall be the cluster center
Obtain distance of each medical record to each cluster center.
Sum all distances obtained
The result is all medical records mapped to single value achieving dimensionality reduction.
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9. Fig 2. Computation of distance of medical record, R1 to each cluster center from clusters formed
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10. 3.Computing distance of missing records to Cluster Centers
Obtain distance of each medical record having missing values to each cluster center by discarding those attributes with missing values.
Sum all distances obtained
The result is all medical records mapped to single value achieving dimensionality reduction.
4.Find Nearest Record to Impute Missing Values
Consider each missing record in group, G2 one by one. Find the distance of this record to all the records in group G1.The record to which the distance is minimal, shall be the nearest neighbor. Perform imputation of the missing attribute value by considering the corresponding attribute value of nearest record in that class. The frequency may also be considered for imputation incase, we have more than one nearest neighbors
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11. Proposed Algorithm Input: Medical Records with Missing Values
Output: Imputation of Missing Values
Notations adopted:
R_i ith medical record
R_i (A_K) - k^th attribute value of i^th medical record
〖 G〗_c c^th group
i,k index of medical records and attributes
∅ misisng record or Empty record value
c number of decision classes in medical dataset
D_d d^th decision class
m total number of medical records
n number of attributes in each record
μ_d cluster center of d^th cluster
μ_(dn ) - mean value of n^th attribute
h number of records in group ,G_2
z - number of records in group ,G_1 equal to (m-h)
Begin of Algorithm Procedure
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12. Step-1: Read Medical Dataset
Read the medical dataset consisting of medical records. Find records with and without missing values. Classify records in to two groups, say G1 and G2. The first group, G1 is set of all medical records with no missing values. The second group, G2 is set of all medical records having missing values.
𝐺 1 = 𝑈 { 𝑅 𝑖 | 𝑅 𝑖 ( 𝐴 𝐾 ) ≠∅ , ∀ 𝑖,𝑘 } (3)
𝐺 2 = 𝑈 { 𝑅 𝑖 | 𝑅 𝑖 ( 𝐴 𝐾 ) =∅ / ∃ 𝑖, 𝑘 } (4)
Where 𝑖 𝜖 (1,𝑚−ℎ) and 𝑘 𝜖 (1,𝑛).We may consider group, 𝐺 1 as training set of medical records while group, 𝐺 2 is considered as testing set in this case.
Step-2: Cluster Medical Records with No Missing values
Let, g = |Dd |, be the number of decision classes. Determine the maximum number of decision classes available in the medical dataset being considered. Cluster the medical records in group, 𝐺 1 to a number of clusters equal to g. i.e |Dd|.

13. Step-3: Obtain Cluster Center for each Cluster formed
This may be achieved using K-means clustering algorithm. This is because K-means algorithm requires the number of required clusters to be specified well ahead before clustering process is carried out. The output of step-2 is a set of clusters. i.e Number of output clusters is equal to‘g’.
This is shown in Fig-1 where a set of medical records represented by 𝐺 1 are clustered in to ‘d’ clusters.
computed are summed to obtain a single distance value. This distance is called Type-1distance value given by equation 2 below.
Dist d ( 𝑹 𝒊 , 𝝁 𝒅 ) = ( 𝑅 𝑖1 − µ 𝑑1 ) 𝟐 + ( 𝑅 𝑖2 − µ 𝑑2 ) 𝟐 +… ( 𝑅 𝑖𝑛 − µ 𝑑𝑛 ) 𝟐 (8) ∀ 𝑖 𝜖 (1,𝑛),∀𝑑
At the end of Step-4 we have distance value from each record , 𝑅 𝑖 to each cluster center denoted by 𝜇 𝑑 .
Step-3: Obtain Cluster Center for each Cluster formed
This step involves finding the cluster center for each cluster which is generated using the k-means clustering algorithm. We can obtain the cluster center by finding the mean of each attribute from attribute set, 𝐴 𝐾 of medical attributes.
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14. Let Cluster- Cd denotes dth cluster having the records R1, R6, R8 and R9 with single attribute. Then the cluster center is given by
𝜇 𝑑 = 𝑅 1 ( 𝐴 1 ) + 𝑅 6 ( 𝐴 1 ) + 𝑅 8 ( 𝐴 1 ) + 𝑅 9 ( 𝐴 1 ) 4 (5)
In general the cluster center of gth cluster may be obtained using the generalized equation given below
𝜇 𝑔 = 𝑈 𝑘 [ { ∑ 𝑅 𝑙 𝑘 | 𝑙 𝜖 {1,𝑞} 𝑓𝑜𝑟 𝑒𝑎𝑐ℎ 𝑘 𝜖 {1,𝑛} } |𝑙| ] (6)
𝜇 𝑔 is hence a sequence of ‘n’ values indicating cluster center over ‘n’ attributes. The notation, 𝑈 𝑘 is used to denote set of all values each separated by a symbol comma. The cluster center may hence be formally represented using the representation
𝜇 𝑔 = < 𝜇 𝑔1 , 𝜇 𝑔2 , 𝜇 𝑔3 , 𝜇 𝑔4 ,……. 𝜇 𝑔𝑛 > (7)
Here ‘n’ indicates total number of attributes in each medical record and |g| indicates number of clusters.

15. Fig 4 G1 Before Clustering
Fig 5 Before and After Clustring

16.  case study
In this Section-V, we discuss case study to find missing attributes values of medical records by using the proposed approach. For this, we consider a sample dataset consisting sample values.
Consider Table. I, shown below consisting of sample dataset of medical records having categorical and numerical values. Table. II shows medical records without missing values after normalizing sample dataset. Table.III denotes records with and without missing values. Table IV denotes all records without missing values and Table. V shows records with missing attribute values.
Table.VI depicts clusters generated from group G1 , which consists medical records with no missing values after applying k-means algorithm. There are two clusters generated C1 and C2.
C1 contains set of all medical records {R1,R4,R6,R9} and C2 contains set of all medical records{R2, R7, R8 }. Table.VII gives the distances of records in group, G1 to cluster center of the first cluster. Similarly, Table.VIII gives the distances of records in group, G2 to cluster center of the second cluster.
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17. Table.IX depicts computation values of mapping function of records of group, G1. The mapping function 𝑀𝑎𝑝( 𝑅 𝑖 ) is mapping distance of ith record, which is sum of all distances from record, 𝑅 𝑖 to each of those cluster centers generated from application of clustering algorithm.
Table. X gives the distances of medical records in group, G2 to each of the cluster centers.
Table. XI depicts computation values of mapping function of medical records containing missing values of group, G2. The mapping function 𝑀𝑎𝑝 𝒓 ( 𝑅 𝑗 ) is mapping distance of jth record,
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18. TABLE I. NORMALIZED SAMPLE DATASET OF MEDICAL RECORDS
TABLE II. MEDICAL RECORDS WITH AND WITHOUT MISSING VALUES
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19. TABLE VII. DISTANCE OF MEDICAL RECORDS TO CLUSTER-1
TABLE VIII. DISTANCE OF MEDICAL RECORDS TO CLUSTER-2

20. XIIV DISTANCE OF MEDICAL RECORDS R5 WITH OTHER RECORDS
TABLE XV NEASREST MEDICAL RECORD FOR RECORD R5

21. Conclusion
In the paper we address the first challenge of handling missing values in medical datasets. We also address how the dimensionality reduction of medical datasets may be achieved in a simple approach.
We also discussed with a new approach of finding missing values in datasets not addressed in the literature by aiming at a single dimension. The approach followed does not miss any attribute information while carrying out dimensionality reduction which is the importance of this approach. The proposed approach of imputing missing values in medical records is feasible for both categorical and numerical attributes as discussed in case study.

22. References
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23. Some handy tips to keep in mind: