1. Imputation Algorithms for Data Mining: Categorization and New Ideas Aleksandar R. Mihajlovic Technische Universität München mihajlovic@mytum.de +49 176 673 41387 +381 63 183 0081 1

2. Overview Explain input data based imputation algorithm categorization scheme Introduce a new categorization scheme of imputation algorithms Introduce some new ideas for re- categorization and improvement of existing algorithms and creation of new ones

3. Digitization of Microarray Data and the Missing Value Problem Missing SNPs in individual DNA These missing values statistically blur SNP allele association with the disease gene allele 3

4. Earlier Input Data Based Classification of Imputation Algorithms [2] Categorized according to the input data 4

5. Global Approach 5

6. Local Approach 6

7. Hybrid Approach + 7

8. Knowledge Based Approach 8

9. Earlier Input Data Based Classification of Imputation Algorithms Classification example: Imputation Algorithms (briefly describe each) – Global SVDImpute – Local KNNimpute – Hybrid LinCmb – Knowledge GOimpute 9

10. Ideas for Algorithmic Improvement [3] Ideas for new categorization model of algorithms based on the methods they use. – Link between the method used and the input data – Room for subcategories based on methods Revising the categorization model – Mendeleyevization – Hybridization – Transdisciplinarization – Retrajectorization 10

11. Mendeleyevization Catalyst – Probability based algorithms EM: expectation maximization algorithms have not been classified Accelerator – Algebraic based algorithms With more memory and better processing power we can increase the number of subjects to be examined. This would improve the precision of Principle Component Analysis algorithms such as BPCA and Single Value Decomposition SVDimpute. 11

12. Mendeleyevizaiton Imputation Algorithms Global Probability Based Algebra Based 12

13. Hybridization Symbiosis – NN Based and Regression Based: The Local based algorithms can be classified as both symbiotic and synergic. The difference being the varying data types available for the imputation process. Based on the data set, the proper algorithm from statistical closeness category can be selected. Synergy – Statistical Closeness: Both Nearest Neighbor based and Regression based algorithms can be made to work together, they are not too computationally expensive and can thus be used. It can be assumed that Regression based algorithms can be used to correct NN based algorithms by using the regression based result in an average of the two results. 13

14. Hybridization Imputation Algorithms Local NN Based Regression Based Statistical Closeness 14

15. Transdisciplinarization Modification – Modified NN: Modify KNN to include additional parameters – Compare large K to small K or find the average of all plausible K vlaues – Use different number of flanking markers – Average out all possible outcomes Mutation – Modified probability Compare probabilites of flanking markers in sequence of i’th subject j’th SNP allele with the rest. The value along with sequence with the highest probability wins. 15

16. Transdisciplinarization (1) Imputation Algorithms Local NN Based Regression Based Statistical Closeness Modified NN 16

17. Transdisciplinarization (2) Imputation Algorithms Global Probability Based Algebra Based Modified Probability 17

18. Retrajectorization Reparametrization – Proteome Based and Gene Based Algorithms How protein/aminoacid/codon databases can be utilized in gene imputation is being researched Regranularization – Process Based: Data Set Partitioning Checking if there is Linkage Disequilibrium between the i’th subject with missing values and other sets of diseased patients. – Sets are organized by the geographic origin of the subjects Find the frequencies of the j’th SNP alleles (missing SNP allele under scrutiny in one subject) in the other sets – If LD exists between other set and subject then take allele into account if not then don’t 18

19. Retrajectorization Imputation Algorithms Knowledge Gene Based Proteome Based Process Based 19

20. The Whole Categorization Tree Imputation Algorithms KnowledgeGlobal Hybrid Local Probability based Algebra Based Regression based NN based Statistical Closeness Process Based Gene Based Proteome Based Modified Probability Modified NN 20

21. References [1] Frey M., Gierl A., De Angelis, Beckers J., Kieser A., Genomics Lecture; Fakultät für Biowissenschaft, TUM, Weihenstephan, Freising bei München; Winter Semester 2011 [2] Liew A.W., Law N., Yan H., Missing value imputation for gene expression data: computational techniques to recover missing data from available information, Briefings in Bioinformatics, December 14, 2010, pp.3 [3] Milutinovic V., Korolija N., A Short Course for PhD Students in Science and Engineering: How to Write Papers for JCR Journals 21

22. Questions Aleksandar R. Mihajlovic Technisceh Universität München mihajlovic@mytum.de +49 176 673 41387 +381 63 183 0081 The End 22