Kernel Learning Framework for Cancer Subtype Analysis with Multi-omics Data IntegrationWilliam Bradbury1, Thomas Lau2, Shivaal Roy1

1Department of Computer Science, 2Department of Bioengineering

• Supervised multiple kernel learning has been implemented in Gevaert et al. to classifyrectal cancer microarray data. The resulting Support Vector Machine accurately classi�ed di�erent outcomes, often reaching above 0.90. The model also performed better whenusing more than one genome-widedata set, suggesting that integrating multiplegenome-wide data sources allows models to reach higher accuracy.

• The iCluster algorithm developed by Shen et al. was used to accurately group canceroutcomes based on multi-omic considerations found in TCGA data on breast cancer. Thealgorithm clusters di�erent cancer subtypes using multiple genomic features such asDNA copy number changes and gene expression. iCluster does not however implementany kernel methods.

• Doctors have independently identified cancer subtypes in patients throughmeasuring the progression of their cancers. However, these subtype classi�cations areslow to perform and can only be made after the cancer has already progressed a fairamount, thereby not proving e�ective in determining the best method of treatment.

Background

[1] Anneleen Daemen et al. “A kernel-based integration of genome-wide data forclinical decision support.” In:Genome medicine1.4 (2009),p. 39.

[2] Anneleen Daemen et al. “Improved microarray-based decision support with graph encoded interactome data.” In:PloS one5.4 (2010),e10225.

[3] GRG Lanckriet and Nello Cristianini. “ Learning the kernel matrix with semidef-inite programming”. In:Journal of MachineLearning Research5 (2004),pp. 27–72.

[4] Cheng Li and Ariel Rabinovic. “Adjusting batch e�ects in microarray ex-pression data using empirical Bayes methods”.In:Biostatistics8.1 (2007),pp. 118–127.

[5] R. Shen, A. B. Olshen, and M. Ladanyi. “Integrative clustering of multiplegenomic data types using a joint latent variable model with application tobreast and lung cancer subtype analysis”. In:Bioinformatics25.22 (2009),pp. 2906–2912.

[6] Ronglai Shen et al. “Integrative Subtype Discovery in Glioblastoma UsingiCluster”. In:PLoS ONE7.4 (2012), e35236.

[7] Emily a. Vucic et al. “Translating cancer ’omics’ to improved outcomes”. In:Genome Research22.2 (2012), pp. 188–195.

[8] Jinfeng Zhuang et al. “Unsupervised multiple kernel learning”. In:Proceed-ings of the Third Asian Conference on Machine Learning20(2011), pp. 129–144.

Literature Cited

• Extend existing unsupervised multiple kernel learning technique in Zhuang et al. toleverage sparse labeling for speci�c use with clinical and multi-omic data from TCGA.

• Characterize genomic and multi-omic features of known cancer subtypes and identifypreviously unknown subtypes.

Objective

• Multiple Kernel Learning is the use of a linear combination of kernels to map points to ahigher-dimensional feature space where they can be more easily separated by an SVM.We write this as

where ut is the weight assigned to each kernel. In MKL, we try to learn the kernelcombination that linearly separates the data best.

Problem Formulation

• Unsupervised Multiple Kernel Learning also implements a linear combination of kernelsto create a distance metric in a higher-dimensional space. The distance metric is used todetermine groupings using a k-means or alternate clustering algorithm.

Unsupervised Multiple Kernel Learning

• We take advantage of various labels, although sparse, to constrain our data and aid in the clusteringprocess. We incorporate the clinical data mentioned above into our cost function to have the resultantcombination of kernels re�ect this added restriction. An additional constraint we impose uses ourknowledge of non-cancer patients in TCGA. Our algorithm should not cluster cancer and non-cancerpatients into the same group and thus we can incorporate this knowledge into our choice of kernels.

Sparse Labels

• Cluster-label alignment metric

Optimization Problem

• TCGAThe Cancer Genome Atlas is the world's largest collection of multi-omic cancer data, collection fromUS patients by hospitals around the world.

• Clinical DataTCGA contains sparse clinical data including eventual patient outcomes, optimal treatment plans,and clinicial established subtypes.

• Multi-omic DataMulti-omic data available in TCGA includes: • Copy Number Variation • Methylation Data • miRNA • mRNA • RPPA

• Patient Class DataEach patient is tagged with patient information, speci�cally which hospital they were treated atand whether or not they had cancer. This can be used as another source of sparsely labeled datain the clustering process above.

Data sources

The iCluster paper by Shen et al. is a source of reproducible and standard automated subtypeanalyses. These can be used both as validation and as seed labels for our algorithm. In the �rst caseit can be used to demonstrate demonstrate robustness of this algorithm while in the second case itcan be used to jump start the process of discovering subtypes.

iCluster

We thank Prof. Olivier Gevaert for his help in formulating and guiding this project and for his help in using TCGA and MKL.We thank Prof. Sera�m Batzoglou for his suggestions which led us to cancer subtype analysis in the�rst place.

Acknowledgements

Figure 1. Results from seperate clustering (left) and integrative clustering (right)

Figure 2. Integrative Multi-omics Framework