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040			_aDLC _cUPMin _dupmin
041			_aeng
090		0	_aLG993.5 2009 _bA64 M67
100			_aMoreno, Iresh Granada. _92090
245		2	_aA modified k-means clustering algorithm with Mahalanobis distance for clustering incomplete data sets / _cIresh Granada Moreno.
260			_c2009
300			_a94 leaves.
502			_aThesis (BS Applied Mathematics) -- University of the Philippines Mindanao, 2009
520	3		_aCluster analysis is an art of finding grounds in data in such a way that objects in the same group are similar to each other, whereas objects in different groups are as dissimilar as possible. The most commonly used clustering algorithm is the K-means with Euclidean distance. However, such distance function neglects the covariance among the variables in calculating distances. To account for this issue, the Mahalanobis distance is used. However, occurrence of missing values is inevitable and clustering such kind of data set is impossible. Existing method such as case deletion and mean imputation for treating missing values are very prone to producing erroneous conclusions by imputing unreliable estimates and significantly reducing the data set. To avoid these problems, modifications of the K-means clustering algorithm's two most essential elements, allocation and representation, were made. Allocation, which was defined by the Mahalanobis distance, was modified to compute distances between two vectors and to compute variances with some unknown values. The representation which was defined by arithmetic mean was modified to estimate mean where there are one or more unknown values of the certain attribute. The proposed algorithm was applied to Iris and Bupa incomplete data sets simulated under MCAR and MAR assumptions with different levels of missing values. Under MAR, case deletion has the highest cluster recovery at 5% of the samples. However, it was totally outperformed by the proposed algorithm as the occurrences of missing values in the sample increased. In general, the modified k-means with Mahalanobis distance has outdone the rest of the algorithms when applied to both data sets.
610			_aPhilippine Eagle Foundation. _92091
610			_aPhilippine Eagle Foundation _zDavao City _zPhilippines. _92092
650	1	7	_aClustering. _9366
650	1	7	_aK-means clustering. _92093
650	1	7	_aMahalanobis distance. _92094
650	1	7	_aClustering algorithm. _91300
650	1	7	_aData sets. _91992
650	1	7	_aModified algorithm. _92095
650	1	7	_aIncomplete data. _92096
650	1	7	_aMissing Values. _9990
650	1	7	_aIris data base. _92097
650	1	7	_aBUPA data base. _92098
650	1	7	_aCluster analysis. _92099
650	1	7	_aAdjusted Rand Index. _92100
650	1	7	_aMultivariate techniques. _92101
650	1	7	_aMAR (Missing at random). _92102
650	1	7	_aMCAR (Missing completely at random). _92103
658			_aUndergraduate Thesis _cAMAT200
905			_aFi
905			_aUP
942			_2lcc _cTHESIS
999			_c2269 _d2269