Integration II
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Transcript of Integration II
Integration II
Prediction
Kernel-based data integration
• SVMs and the kernel “trick”• Multiple-kernel learning• Applications– Protein function prediction– Clinical prognosis
SVMs
These are expression measurements from two genes for two populations(cancer types)
The goal is to define a cancer type classifier...
[Noble, Nat. Biotechnology, 2006]
SVMs
These are expression measurements from two genes for two populations(cancer types)
The goal is to define a cancer type classifier...
One type of classifier is a “hyper-plane”that separates measurements fromtwo cancer types
[Noble, Nat. Biotechnology, 2006]
SVMs
These are expression measurements from two genes for two populations(cancer types)
The goal is to define a cancer type classifier...
One type of classifier is a “hyper-plane”that separates measurements fromtwo cancer types
E.g.: a one-dimensional hyper-plane
[Noble, Nat. Biotechnology, 2006]
SVMs
These are expression measurements from two genes for two populations(cancer types)
The goal is to define a cancer type classifier...
One type of classifier is a “hyper-plane”that separates measurements fromtwo cancer types
E.g.: a two-dimensional hyper-plane
[Noble, Nat. Biotechnology, 2006]
SVMs
Suppose that measurements are separable:there exists a hyperplane thatseparates two types
Then there are an infinite number ofseparating hyperplanes
Which to use?
[Noble, Nat. Biotechnology, 2006]
SVMs
Suppose that measurements are separable:there exists a hyperplane thatseparates two types
Then there are an infinite number ofseparating hyperplanes
Which to use?
The maximum-margin hyperplane
Equivalently: minimizer of
[Noble, Nat. Biotechnology, 2006]
SVMs
Which hyper-plane to use?
In reality: minimizer of trade-off between1. classification error, and2. margin size
loss penalty
SVMs
This is the primal problem
This is the dual problem
SVMs
What is K?
The kernel matrix:each entry is sample inner productone interpretation: sample similaritymeasurements completely described by K
SVMs
Implication:Non-linearity is obtained byappropriately defining kernelmatrix K
E.g. quadratic kernel:
SVMs
Another implication:No need for measurement vectorsall that is required is similarity between samples
E.g. string kernels
Protein Structure PredictionProtein structure
Protein sequence
Sequence similarity
Protein Structure Prediction
Kernel-based data fusion
Core idea: use different kernels for different genomic data sources a linear combination of kernel matrices is a kernel (under certain conditions)
Kernel-based data fusion
Kernel to use in prediction:
Kernel-based data fusion
In general, the task is to estimateSVM function along withcoefficients of the kernelmatrix combination
This is a type of well-studiedoptimization problem(semi-definite program)
Kernel-based data fusion
Kernel-based data fusion
Kernel-based data fusion
Same idea applied to cancer classification from expression and proteomic data
Kernel-based data fusion
• Prostate cancer dataset– 55 samples– Expression from microarray– Copy number variants
• Outcomes predicted:– Grade, stage, metastasis, recurrence
Kernel-based data fusion