Exploratory Tools for Follow-up Studies to Microarray Experiments

1. Exploratory Tools for Follow-up Studies to Microarray Experiments Kaushik Sinha Ruoming Jin Gagan Agrawal Helen Piontkivska Ohio State and Kent State Universities

2. Overall Motivation • Biological literature is vast • Need tools to find interesting patterns from literature • Specific Example • Identify genes from DNA microarray and other gene and protein assays • Next step • What is known about these genes? • How are these genes related to each other or other genes identified in similar studies? • Which other genes are most similar

3. Outline • Hypergraph Mining • Similarity Measures • Evaluation and Observations

4. Hypergraph Mining: Motivating Example • Micro array experiment - suspects that a small set of genes are related to a disease • Confirm by searching existing literature - expect related genes to appear together in literature • However, suppose Gene A and C are related and both of them are weakly related to another term B • In literature, one would expect • A,C appear together OR/AND • A,B appear together • B,C appear together • How do we efficiently conclude that A,C are actually related?

5. Hypergraph Mining • Basic Motivation • To find useful “Transitive Relation” (hyperedges) among genes • Example (Gene-Disease Relationship) • Gene A is related to a term B • Term B is related to a gene C • Is Gene A related to Gene C ? • Gene Source • Microarray Experiments • Information Source • Online Literature abstracts

6. Formal Problem Definition • Given • A dictionary KT • A set KM of user provided keywords (KTכKM) • Collection of literature abstracts - each abstract is represented as a set of words from dictionary • Task • To find hyperedges exceeding user defined threshold, each of which involves a set of key words from KM and are potentially connected by another set of linking words from KT-KM

7. Relationship to Work on Frequent Pattern Mining • Frequent itemset mining • Can represent each document abstract as a transaction with several keywords • Find sets of keywords that appear together and often • Cannot capture cross relationships • Differences • How do we define support ? • How do we prune search space

8. Solution Approach • Define • total weight=support + cross support • Support: set of keywords appear together in one document • Cross support: set of keywords can be partitioned • each partition appears in different document • Common linking words • Issues • Since downclosure property does not hold for total weight modified downclosure property can be defined

9. Idea • Support satisfies downclosure property • Let X be a set, Ω be its power set. A function f : Ω→R+satisfies downclosure property if for all A,B ∈ Ω , A כ B ,f(B)>f(A) • Cross support can be designed to be restricted below a particular value, i.e., it is bounded • Form a function h as addition of two functions h=f+g • f satisfies downclosure property • g is bounded • h satisfies modified down closure property • For any θ≥0, if h(Kn) ≥θ then f(Kn-1) ≥ max{0,(θ-sup(g))} • This property can be used to devise efficient algorithm

10. Outline • Hypergraph Mining • Similarity Measures • Evaluation and Observations

11. Similarity Measure among Sets of Genes • Given two list of gene names • Need to find most similar genes, based on literature abstract occurrences • Standard statistics approach • Each file containing gene names can be considered as a Discrete Random Variable (DRV) • Each such DRV can take several values (gene names) • For two such files X,Y and for any pair (x,y), • joint probability mass function p(x,y)=P(X=x,Y=y) • Compute from online abstracts based on co-occurrence

12. Probability Computation • Assume, • File X has n gene names xi, i ∈{1,…,n} • File Y has m gene names yj, j ∈{1,…,m} • M(i,j) is the number of times (xi,yj) appears together in transactions (article abstracts) • Then, • p(xi,yj)=M(i,j)/{∑i∑jM(i,j)}

13. Expectation Computation • Now define, • Z=g(X,Y), where g: X x Y →[0,∞) • Clearly, Z is a random variable • Expectation of Z is, • E(Z)=E(g(X,Y))=∑i∑j (g(xi,yj)M(i,j)/Mt) • Where, Mt=∑i∑jM(i,j) • Expected value of Z can directly be used as a similarity measure • Different choices of g, give rise to different similarity measures

14. Some Choices of function g • First Choice, • Choose g=M(i,j) • This choice leads to similarity measure, se1= ∑i∑j M(i,j)2 /Mt • Second Choice, • Choose g=tot_length(xi,yj), where tot_length (xi,yj) is the sum of transaction lengths where (xi,yj) co-occur • The idea is longer the transaction length, higher the chance of having related linking key words • This choice leads to similarity measure, se2= ∑i∑j tot_length(xi,yj)*M(i,j)/Mt

15. Extending the notion towards gene ranking • Extend to rank genes from a list Y • Most similar to the genes from list X • Here, instead of Y as a random variable, for each yj ∈Y, consider Uj as a random variable taking value only yj • Find the similarity measure between X and Uj for all j∈{1,…,m} • Sort the genes from list Y according to decreasing similarity measure

16. Datasets Used two sets of 21 and 31 genes • These genes are differentially expressed between prostate epithelial and stromal cells in prostate cancer patients • Dr Gail Frazer’s lab, Kent State University • A standard dictionary, as reported in literature, containing 300 genes was used • These genes were significantly up or down regulated in tumor and adjacent normal tissues when compared with a normal donor tissue • Each literature abstract was represented in a bag of word format containing words, • where each word comes from a dataset or the dictionary or is a GO term

17. Results: Hypergraph Mining • Results show the linking GO terms and linking genes from the dictionary for 21 and 31 dataset obtained by hypergraph mining

18. Results: Similarity Measures • 4 sets of 300 genes each ,- A,B,C,D were formed • A is the dictionary of 300 genes as mentioned before • B,C,D were randomly chosen from superarray’s DNA micro-array experiments • The task is to identify which of A,B,C,D is most similar to the 21 or 31 dataset • As one would expect, A is most similar to the 21 dataset as shown below • It also shows that some naïve similarity measure, such as s1, fails to capture this • Sometimes, this tool discovers some interesting result,- • For 31 dataset, randomly chosen list C was most similar • This has been justified by checking the functionalities of top ranked genes from list C

19. Results: Ranking • Results of the ranked genes from the most similar list to either 21 or 31 data set • Linking words from hypergraph mining were also found within top 20 genes

20. Summary • Biological Literature is large and complex • Need data mining tools to summarize interesting patterns • Proposed hypergraph mining and similarity metrics • Initial results are promising