Selecting Informative Geneswith Parallel Genetic

Algorithms

Deodatta BhoitePrashant Jain

Terminology

GenesDNA, mRNAGene expressionMicroarrays

Microarray output

Gene SelectionLarge number of irrelevant genes

introduce “biological noise”Analysis of results can be simplified

by selecting only relevant genes for study

Two categories of gene selection– Filter approach selection– Wrapper approach selection

Gene Selection

Classifier

What is a classifier used for?Mapping of label pairs <xi, li> to

{0,1,?}Golub-Slonim classifier

Positive value = class 1, negative value = class 2

classifieringgene

ggg

gggg xsignxclass ]}2/)()][/()[({)( 212121

Ranking based gene selection methods

GS-correlation

Genes with most positive and negative correlation values are selected.

Tends to not select genes for which class values have large standard deviations with respect to training data (some of them may be most relevant and informative).

Ranking with disorder

This method doesn’t use the actual expression levels.

Ng_I represents the set of indices that belong to class I and h(x) is the indicator function.

Need for subset ranking

Individual ranking may not always result in selection of informative genes.

They ignore the relationships between genes by solely relying on individual scores.

Thus we need to explore subsets of genes to find the optimal subset for classification.

Genetic AlgorithmWhat is a genetic algorithm?

– “Genetic Algorithms are defined as global optimization procedures that use an analogy of genetic evolution of biological organisms.”

– Basically genetic algorithms tend to find the best solution to a problem by following an evolutionary process.

Basic Genetic Algorithm

Parallel Genetic Algorithm

For large population sizes, G.A. is computationally infeasible.

Hence the use of Parallel Genetic Algorithms.

Parallel Genetic Algorithm

Model and Encoding

Island Model -: Each processor runs a G.A. on a subset of the population and there is periodic migration.

Fixed Length Binary String Encoding-: Here if gene is included in the subset then value is 1 else 0.

Fitness EvaluationTwo Different Criteria

– Classification Accuracy– Size of the subset

fitness(x) = w1 * accuracy(x) + w2 *(1 – dimensionality(x))

Here,– accuracy(x) = test accuracy of the classifier

built with the gene subset represented by x – dimensionality(x) [0,1] = the dimension

of the subset

Fitness Evaluation

– w1 = weight assigned to accuracy– w2 = weight assigned to dimensionality

High classification accuracy and low dimension has high fitness.

Data Sets Used

Test Parameters

The tests were run on two processors.

The parameters of G.A. in each processor were set as -:– Population Size : 1000– Trials : 400000– Crossover probability: 0.6– Mutation probability: 0.001

Test Parameters

– Selection Strategy: Elitist– Migration Probability: 0.002

Crossover probability of average level to get different subpopulation with good traits of the parents.

Mutation Probability low to avoid randomness of selection.

Selection Strategy is Elitist which ensures that the best individuals are kept and hence leads to more accurate subsets of genes.

Results

Results

Leukemia Data Set– Subset with 29 Genes found– Classifies 36/38 training instances

correctly– Classifies 30/34 test instances correctly

Colon Data Set– Subset with 30 genes found– 92% accuracy on the training data set

Results Comparison

Results better than other algorithms such as G-S and NB algorithms which have accuracies less than 90% and gene numbers varying from 10 to 500.

Average Performance Graphs

Conclusion

Method does well in finding smaller gene subsets and better accuracies.

Fitness function needs to be something more sophisticated than the simple one used right now to ensure a final compact subset every time.

Questions

Thank You.