Applying Support Vector Learning to Stem Cells Classification

Introduction
Online Machine Learning
The Application
Discussion

Applying Support Vector Learning
to Stem Cells Classiﬁcation

Ofer M. Shir
oshir@liacs.nl
Natural Computing Group
Leiden University

LUMC, MCB Seminar, 25-09-2006

Ofer M. Shir SVM to Stem-Cells Classiﬁcation

Introduction
The Application
Discussion

Outline
1 Introduction
The Problem: Stem Cells Classiﬁcation
Nucleus Imaging
2 Online Machine Learning
The Teacher-Learner Model
Simple Perceptron
The SVM Algorithm
Images as Instances
3 The Application
Applying Perceptron
Applying SVM
4 Discussion
Conclusions
Prospects
Take-Home Message

Introduction
Online Machine Learning The Problem: Stem Cells Classiﬁcation
The Application Nucleus Imaging
Discussion

Outline
1 Introduction
Nucleus Imaging
Simple Perceptron
The SVM Algorithm
Images as Instances
3 The Application
Applying Perceptron
Applying SVM
4 Discussion
Conclusions
Prospects
Take-Home Message

Introduction
Discussion

Biological Motivation
The nuclear lamina envelops the nucleus. Intact lamina is
vital for cell survival, knowckdown of lamin B results in
lethal embryos in mice, and mutations in Lamin A cause
premature aging syndromes in human.
In human mesenchemyal stem cells (hMSCs) the lamina
shows a round and ﬂat shape after 3D reconstruction. In
hMSCs undergoing cell death the lamina shape
dramatically changed and precedes the wholemarks of
apoptosis, such as nuclear breakdown and chromatin
fragmentation.
Soon after caspase-8 activation, which ultimately leads to
cell death, intranuclear organization of the lamina are
formed and the depth of the nucleus increased. Similar
changes in lamina organization are found in hMSCs
undergoing replicative senescence.

Introduction
Discussion

Biological Motivation

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


Introduction
Discussion

Nucleus Imaging

The lamina of hMSCs was detected after transduction of
the Lamin B-GFP lentivirus vector.
Image stacks of the lamin B-GFP were aquired with a
confocal microscope, and 3D reconstruction was obtained
with TeloView.
In control cells the XY and the XZ orientations revealed a
round and ﬂat shape of the lamina.
After activation of caspase-8, the shape of the lamina is
signiﬁcantly changed.


Introduction
Discussion

Control vs. Apoptotic


Introduction
Discussion

Nucleus Imaging
Serial slicing along the XZ axis taken from an individual
nucleus with DIPimage toolbox revealed little changes in
the spatial organization of the lamina in a control cell.
High variations were found in serial slicing taken from an
apoptotic cell.


Introduction The Teacher-Learner Model
Online Machine Learning Simple Perceptron
The Application The SVM Algorithm
Discussion Images as Instances

Outline
1 Introduction
Nucleus Imaging
Simple Perceptron
The SVM Algorithm
Images as Instances
3 The Application
Applying Perceptron
Applying SVM
4 Discussion
Conclusions
Prospects
Take-Home Message


Machine Learning: TRAINING

Online learning considers a situation in which instances
are presented one at a time, where the learner’s task is to
learn a hypothesis which classiﬁes the data correctly.
Training phase: instances {xi }l in Rn , and their labels
i=1
set Y = {−1, +1} are presented to the machine. The
algorithm aims to update its hypothesis h : Rn → {±1} in
order 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, where
more 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 machine
perform?



Simple Perceptron

The Perceptron algorithm (Rosenblatt, 1957) is an online
learning algorithm for ﬁnding a consistent hypothesis within the
class of hyperplanes:

C = h(x) = sign wT · x + b w t ∈ Rn , b ∈ R

The optimal hyperplane is deﬁned as the one with the maximal
margin 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 higher
dimensional space, where linear separation is feasible:



Desirable Mapping



The Algorithm

The Support Vector Machines (SVM) algorithm (Boser, Guyon
and Vapnik, 1992) is a linear method in a high-dimensional
feature space, which is non-linearly interlinked to the instance
space. It allows learning a hypothesis for data which is not
linearly-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 )T φ(xj )



Kernels

In particular, we consider the following kernel functions:
The polynomial kernel:
d
k (xi , xj ) = γ xT · xj + r
i (1)

Radial basis function (RBF) kernel:

1 2
k (xi , xj ) = exp − xi − xj (2)
2σ 2

The sigmoid kernel:

k (xi , xj ) = tanh κ xT · xj + Θ
i (3)



Images as Instances



Grayscale Images



Intermediate Conclusions

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


Introduction
Online Machine Learning Applying Perceptron
The Application Applying SVM
Discussion

Outline
1 Introduction
Nucleus Imaging
Simple Perceptron
The SVM Algorithm
Images as Instances
3 The Application
Applying Perceptron
Applying SVM
4 Discussion
Conclusions
Prospects
Take-Home Message

Introduction
Discussion

Experimental Procedure: Modus Operandi

Training phase: provide the machine with shuffled 2000
slices and their correct labels.
Testing phase: test the machine with shuffled 1040 slices
without their labels - and check its accuracy.
Correct classification means that the output of the machine
per given instance is its correct label as in our database.
Wrong classification (error rate) - vice versa.


Introduction
Discussion

Applying Perceptron

Applying the Perceptron was straightforward, with respect
to parameter settings, and did not require any preliminary
tuning.
However, the algorithm obtained, after training, a test
accuracy of 70.38% (732/1040 images were classiﬁed
correctly).
This result led us to the conclusion that the data was not
linearly-separable, and a stronger approach was much
needed.


Introduction
Discussion

Applying SVM - Preliminary

Applying SVM (libsvm package) to the classiﬁcation
problem with default settings yielded test accuracy of 55%
on average.
Thus, tuning the kernel parameters was essential - several
parameters 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 the
optimization tool: the cross-validation accuracy rate was
the objective function to be optimized.
Each objective function evaluation takes 11 minutes on a
single processor: runs were limited.

Introduction
Discussion

SVM - Numerical Results

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


Introduction
Conclusions
Prospects
The Application
Take-Home Message
Discussion

Outline
1 Introduction
Nucleus Imaging
Simple Perceptron
The SVM Algorithm
Images as Instances
3 The Application
Applying Perceptron
Applying SVM
4 Discussion
Conclusions
Prospects
Take-Home Message

Introduction
Conclusions
Prospects
The Application
Take-Home Message
Discussion

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, is
required.
Behind everything in life there is a matrix...


Introduction
Conclusions
Prospects
The Application
Take-Home Message
Discussion

Prospects

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


Introduction
Conclusions
Prospects
The Application
Take-Home Message
Discussion

Take-Home Message

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


Applying Support Vector Learning to Stem Cells Classification

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