Discovering Pair-wise Synergies in Microarray Data

Abstract

Informative gene selection can have important implications for the improvement of cancer diagnosis and the identification of new drug targets. Individual-gene-ranking methods ignore interactions between genes. Furthermore, popular pair-wise gene evaluation methods, e.g. TSP and TSG, are helpless for discovering pair-wise interactions. Several efforts to discover pair-wise synergy have been made based on the information approach, such as EMBP and FeatKNN. However, the methods which are employed to estimate mutual information, e.g. binarization, histogram-based and KNN estimators, depend on known data or domain characteristics. Recently, Reshef et al. proposed a novel maximal information coefficient (MIC) measure to capture a wide range of associations between two variables that has the property of generality. An extension from MIC(X; Y) to MIC(X1; X2; Y) is therefore desired. We developed an approximation algorithm for estimating MIC(X1; X2; Y) where Y is a discrete variable. MIC(X1; X2; Y) is employed to detect pair-wise synergy in simulation and cancer microarray data. The results indicate that MIC(X1; X2; Y) also has the property of generality. It can discover synergic genes that are undetectable by reference feature selection methods such as MIC(X; Y) and TSG. Synergic genes can distinguish different phenotypes. Finally, the biological relevance of these synergic genes is validated with GO annotation and OUgene database.

Figure 1. Synergic pairs conducted by function.

Y = |X1 – X2|(n = 200). Y is binarized with a median. Red point: positive sample. Green point: negative sample.

Figure 2. Examples of scatter plots of discretization for gene expression.

(A,B) are real-word gene expression values for prostate dataset and yeast dataset; the values of HTB1 gene are binarized with 0. C and D are simulation datasets from Y = 4·X² and Y = sin (4·π·X), Y is binarized with 0.5 and 0, respectively. Red point: positive sample. Green point: negative sample.

Figure 3. Schematic of getting superclumps partition for three variables.

The points with the same color belong to the same superclump.

Figure 4. Y completely determined by the synergy between X₁ and X₂.

X₁ and X₂∈[10, 30], and result from binarization vector of X₁ and X₂, respectively. Y = (n = 1000). Green and red dots represent Y = 1 and Y = 0, respectively.

Figure 5. Ten noiseless functions with Y = f (X₁, X₂).

Y is binarized with median, green and red dots represent Y=1 and Y=0, respectively.

Figure 6. Overlaps among the Top200s selected by MIC(X; Y), MRMR, SVM-RFE and TSG in the Prostate dataset.

Figure 7. Overlaps among the Top200s selected by MIC(X; Y), MRMR, SVM-RFE and TSG in the DLBCL dataset.

Figure 8. Overlaps among the Top200s selected by MIC(X; Y), MRMR, SVM-RFE and TSG in the Lung dataset.

Figure 9. Overlaps between the Top200 selected by MIC(X₁; X₂; Y) and the Top200s selected by MIC(X; Y), MRMR, SVM-RFE and TSG in the Prostate dataset.

Figure 10. Overlaps between the Top200 selected by MIC(X₁; X₂; Y) and the Top200s selected by MIC(X; Y), MRMR, SVM-RFE and TSG in the DLBCL dataset.

Figure 11. Overlaps between the Top200 selected by MIC(X₁; X₂; Y) and the Top200s selected by MIC(X; Y), MRMR, SVM-RFE and TSG in the Lung dataset.

Figure 12. Prediction accuracy of five feature selection methods combined with SVC Classifier over three datasets.

Figure 13. GO annotations for the Top200s selected by different methods in the Prostate dataset.

Deeper colors of one point in the figure means the terms covered with more genes. We have removed the terms in which the sum of genes number is less than 25 across all methods.

Figure 14. Three representative patterns of pair-wise synergy identified by MIC(X₁, X₂: Y) method.

(A–E) are from real-world datasets, (F–H) are the corresponding hypothetical extreme examples.