Applying Support Vector Learning to Stem Cells Classification

IntroductionOnline Machine Learning

The ApplicationDiscussion

Applying Support Vector Learningto Stem Cells Classification

Ofer M. [email protected]

Natural Computing GroupLeiden University

LUMC, MCB Seminar, 25-09-2006

Ofer M. Shir SVM to Stem-Cells Classification



Outline1 Introduction

The Problem: Stem Cells ClassificationNucleus Imaging

2 Online Machine LearningThe Teacher-Learner ModelSimple PerceptronThe SVM AlgorithmImages as Instances

3 The ApplicationApplying PerceptronApplying SVM

4 DiscussionConclusionsProspectsTake-Home Message














Biological Motivation

The nuclear lamina envelops the nucleus. Intact lamina isvital for cell survival, knowckdown of lamin B results inlethal embryos in mice, and mutations in Lamin A causepremature aging syndromes in human.In human mesenchemyal stem cells (hMSCs) the laminashows a round and flat shape after 3D reconstruction. InhMSCs undergoing cell death the lamina shapedramatically changed and precedes the wholemarks ofapoptosis, such as nuclear breakdown and chromatinfragmentation.Soon after caspase-8 activation, which ultimately leads tocell death, intranuclear organization of the lamina areformed and the depth of the nucleus increased. Similarchanges in lamina organization are found in hMSCsundergoing replicative senescence.





Biological Motivation

Thus, it is possible that changes in the spatial organizationof the lamina are correlated with the functional state of thecell. The spatial organization of the lamina can be used asan early marker to sort between healthy and not-healthycells, as changes in lamina organization are visible beforechanges in cell morphology are detected.Here we tested this hypothesis using a machine learningapproach.





Nucleus Imaging

The lamina of hMSCs was detected after transduction ofthe Lamin B-GFP lentivirus vector.Image stacks of the lamin B-GFP were aquired with aconfocal microscope, and 3D reconstruction was obtainedwith TeloView.In control cells the XY and the XZ orientations revealed around and flat shape of the lamina.After activation of caspase-8, the shape of the lamina issignificantly changed.





Control vs. Apoptotic





Nucleus Imaging

Serial slicing along the XZ axis taken from an individualnucleus with DIPimage toolbox revealed little changes inthe spatial organization of the lamina in a control cell.High variations were found in serial slicing taken from anapoptotic cell.




The Teacher-Learner ModelSimple PerceptronThe SVM AlgorithmImages as Instances










Machine Learning: TRAINING

Online learning considers a situation in which instancesare presented one at a time, where the learner’s task is tolearn a hypothesis which classifies the data correctly.Training phase: instances {xi}l

i=1 in Rn, and their labelsset Y = {−1,+1} are presented to the machine. Thealgorithm aims to update its hypothesis h : Rn → {±1} inorder to minimize the prediction error.Various algorithms have different update rules.Analogy: teacher, learner, corrections.





Machine Learning: TESTING

This training phase is followed by the testing phase, wheremore data is given to the learned hypothesis.Ideally unseen data. (Why...?)The correct labels are not presented to the machine!The accuracy rate is considered - how did the machineperform?





Simple Perceptron

The Perceptron algorithm (Rosenblatt, 1957) is an onlinelearning algorithm for finding a consistent hypothesis within theclass of hyperplanes:

C ={h(~x) = sign

(~wT · ~x + b

)~wt ∈ Rn, b ∈ R

}The optimal hyperplane is defined as the one with the maximalmargin of separation between the two instances classes.





Perceptron: Optimal Hyperplane





Non-Realizable for Hyperplanes Separation

But what if the data is not linearly-separable...?There is no hyperplane separator hypothesis for the problem!





Mapping...

We would like then to map the instances to a higherdimensional space, where linear separation is feasible:





Desirable Mapping





The Algorithm

The Support Vector Machines (SVM) algorithm (Boser, Guyonand Vapnik, 1992) is a linear method in a high-dimensionalfeature space, which is non-linearly interlinked to the instancespace. It allows learning a hypothesis for data which is notlinearly-separable.





The Kernel Function

The function φ : Rn → F maps the instance vectors onto a

higher dimensional space F, and then the SVM aims to find a

hyperplane separator with the maximal margin in this space.

k (~xi, ~xj) ≡ φ(~xi)Tφ(~xj)





Kernels

In particular, we consider the following kernel functions:The polynomial kernel:

k (~xi, ~xj) =(γ

(~xT

i · ~xj

)+ r

)d(1)

Radial basis function (RBF) kernel:

k (~xi, ~xj) = exp{− 1

2σ2‖~xi − ~xj‖2

}(2)

The sigmoid kernel:

k (~xi, ~xj) = tanh(κ

(~xT

i · ~xj

)+ Θ

)(3)





Images as Instances





Grayscale Images





Intermediate Conclusions

Grayscale images are simply matrices with normalizedelements in [0, 1].In particular, as instance vectors in Rn!Essentially, an image could be introduced directly tothe learning algorithm, without further processing.




Applying PerceptronApplying SVM










Experimental Procedure: Modus Operandi

Training phase: provide the machine with shuffled 2000slices and their correct labels.Testing phase: test the machine with shuffled 1040 sliceswithout their labels - and check its accuracy.Correct classification means that the output of the machineper given instance is its correct label as in our database.Wrong classification (error rate) - vice versa.





Applying Perceptron

Applying the Perceptron was straightforward, with respectto parameter settings, and did not require any preliminarytuning.However, the algorithm obtained, after training, a testaccuracy of 70.38% (732/1040 images were classifiedcorrectly).This result led us to the conclusion that the data was notlinearly-separable, and a stronger approach was muchneeded.





Applying SVM - Preliminary

Applying SVM (libsvm package) to the classificationproblem with default settings yielded test accuracy of 55%on average.Thus, tuning the kernel parameters was essential - severalparameters as well as the profile of the kernel (Eq. 1, 2, 3)and its various appropriate parameters ({γ, r, d}, {σ} and{κ, Θ}).The Covariance Matrix Adaptation Evolution Strategy(CMA-ES) [Hansen et al., 2001] was selected as theoptimization tool: the cross-validation accuracy rate wasthe objective function to be optimized.Each objective function evaluation takes 11 minutes on asingle processor: runs were limited.





SVM - Numerical Results

CMA-ES found an RBF kernel with 98.90%cross-validation.Testing phase:Accuracy of 97.02% - 1009/1040 images were classifiedcorrectly!Highly satisfying! Beyond any expectation!




ConclusionsProspectsTake-Home Message










Conclusions

Machine learning as a way of life.Machine classification of stem cells is feasible!Numerical results are remarkably excellent.No further image analysis, after the image acquisition, isrequired.Behind everything in life there is a matrix...





Prospects

Classification of other ”colors”.Classification of 3D images!Analysis of time-dependent 3D movies.





Take-Home Message

Natural computing, machine learning and data mining arerich fields with a lot to offer!Find yourself a nice computer-scientist, and invest in yourrelationship.You may prefer to consider those tools as a black-boxes.BUT then apply and boost medicine...


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Applying Support Vector Learning to Stem Cells Classification