Prediction of Malignancy of Ovarian Tumors Using Least Squares Support Vector Machines

(1)

Prediction of Malignancy of Ovarian Tumors Using Least Squares Support Vector Machines

C. Lu ¹ , T. Van Gestel ¹ ^, J. A. K. Suykens ¹ , S. Van Huffel ¹ , I. Vergote ² , D. Timmerman ²

1 Department of Electrical Engineering, Katholieke Universiteit Leuven, Leuven, Belgium,

2 Department of Obstetrics and Gynecology, University Hospitals Leuven, Leuven, Belgium Email address: chuan.lu@esat.kuleuven.ac.be

Variable (symbol) Benign Malignant Demographic Age (age)

Postmenopausal (meno) 45.6  15.2 31.0 %

56.9  14.6 66.0 % Serum marker CA 125 (log) (l_ca125) 3.0  1.2 5.2  1.5

CDI High color score (colsc3,4) 19.0% 77.3 %

Morphologic Abdominal fluid (asc) Bilateral mass (bilat) Unilocular cyst (un)

Multiloc/solid cyst (mulsol) Solid (sol)

Smooth wall (smooth) Irregular wall (irreg) Papillations (pap)

32.7 % 13.3 % 45.8 % 10.7 % 8.3 % 56.8 % 33.8 % 12.5 %

67.3 % 39.0 % 5.0 % 36.2 % 37.6 % 5.7 % 73.2 % 53.2 %

Demographic, serum marker, color Doppler imaging and morphologic variables

1. Introduction

Ovarian masses is a common problem in gynecology. A reliable test for preoperative discrimination between benign and malignant

ovarian tumors is of considerable help for clinicians in choosing appropriate treatments for patients.

In this work, we develop and evaluate several LS-SVM models within Bayesian evidence

framework, to preoperatively predict malignancy of ovarian tumors. The analysis includes exploratory data analysis, optimal input variable selection,

parameter estimation, performance evaluation via Receiver Operating Characteristic (ROC) curve analysis.

2. Methods

o: benign case x: malignant case

Visualizing the correlation between the

variables and the relations between the variables and

clusters.

Biplot of Ovarian Tumor Data

Patient Data

Unv. Hospitals Leuven

1994~1999

425 records, 25 features 32% malignant

Univariate Analysis

Preprocessing

Multivariate Analysis

PCA, Factor analysis Stepwise logistic regression

Model Building

Bayesian LS-SVM Classifier (RBF, Linear)

Logistic Regression

Model Evaluation

ROC analysis: AUC

Cross validation (Hold out, K-fold CV)

Descriptive statistics Histograms

Input Selection

Data Exploration

Model Development

Procedure of developing models to predict the malignancy of ovarian tumors

Bayesian LS-SVM (RBF, Linear) Forward Selection (Max Evidence)

LS-SVM Classifier within Bayesian Evidence Framework

 

1,...,

2

, , 1

Given {( , )} , where , 1,1

The following model is taken:

min ( , , )

2 2

S.T. [ ( ) ] 1 1,..., with regul

(

arizer .

) ( )

i

p

i i i N i i

T N

i i

w b e

i

i i

T

T i

D x y x R y

J w b e w w e

y w x b e i N

f b







 





   



 





  



x w x

1 1

1

0 1 0

1 [ ,..., ]',1 [1,...,1], [ ,..., ], [ ,..., ]'

( ) ( ) ( , )

The result

( ) [ ( ,

ing LS-SVM classifier )

is ]

T v

v N

N v

N N

N

i i i

T

ij i j i j

i

y x sign y K b I Y

Y y y

e e e

x x K x x

x x b



  













     

            

 

 

 

 

  



 

( , , )

2

for rbf kernels ,

exp( ( , )) Given model (kernel parameter, e.g. )

, , ,

( , , , , ) ( , , , )

=> the Maximum A Posteriori Estimation for an w d b will be the solution of basi

p D H

p D w b H p w b H H

w b

P D J w b

H



 



 

  

 



c LS-SVM classifier

Level 1: infer w,b

1

( , , ) ( , , ) with is the prior clas

( ) ( )

s probabil ( , , )

ity

( ) .

y

p y p y p

p x y D H p y x D H p x

H y



y D

 

( , , ) ( , )

( , ) =

(Assume ( ,

, ) separable uniform distribute (

d.) ( , , ) )

p D H p p D H p D H H

p H

p D H

   

 



 

 

( ) ( )

( )

(Assume prior ( ) is uniform distributed choose the which maximize

( )

.) the

j

j j

j

p D H p D H p H

p D

H p

H

H p D

 

Level 2: Infer hyperparameter

Level 3: Compare models

} / exp{

) ,

( x z   x  z

²



²

K

x z z

x

^T

K ( , ) 

Positive definite kernel K(.,.)

RBF:

Linear:

Mercer’s theorem

Posterior class probability

Model evidence

Input variable selection

Given a certain type of kernel, Performs forward selection

 Initial: 0 variables,

 Add: variable which gives the greatest increase in the current model evidence at each iteration.

 Stop: when the adding of any remaining variable can no longer increase the model evidence.

solved in dual space

y(x)

_,

p(y=1|x,D,H)

D

_train

Bayesian LS-SVM Classifier

kernel type (rbf/linear)

model evidence

x

,,,, , b

initial set of {

_j

} for rbf kernels

training test

10 variables were selected using an RBF kernel.

l_ca125, pap, sol, colsc3, bilat, meno, asc, shadows, colsc4, irreg

Blackbox of Bayesian LS-SVM Classifier

3. Experimental Results

RMI: risk of malignancy index = score_morph× score_meno× CA125

2) Results from randomized cross-validation (30 runs)



Training set : data from the first treated 265 patients

 Test set : data from the latest treated 160 patients

1) Results from Temporal validation

--

LSSVMrbf

--

LSSVMlin

--

LR

--

RMI

ROC curve on test set

MODEL TYPE

AUC cut off

Accur acy

Sensi tivity

Speci ficity RMI 0.8733 0.4 78.13 74.07 80.19

0.3 76.88 81.48 74.53 LR1 0.9111 0.4 80.63 75.96 83.02 0.3 80.63 77.78 82.08 LS-SVM1 0.9141 0.4 81.25 77.78 83.02 (LIN) 0.3 81.88 83.33 81.13 LS-SVM1 0.9184 0.4 83.13 81.48 83.96 (RBF) 0.3 84.38 85.19 83.96

Performance on Test set Averaged Performance on 30 runs of validations

MODEL TYPE

AUC (SD)

cut off

Accu racy

Sensi tivity

Speci ficity RMI 0.8882 0.5 82.6 81.73 83.06

0.0318 0.4 81.1 83.87 79.85 LR1 0.9397 0.5 83.3 89.33 80.55 0.0238 0.4 81.9 91.6 77.55 LS-SVM1 0.9405 0.5 84.3 87.4 82.91 (LIN) 0.0236 0.4 82.8 90.47 79.27 LS-SVM1 0.9424 0.5 84.9 86.53 84.09 (RBF) 0.0232 0.4 83.5 90 80.58

randomly separating training set (n=265) and test set (n=160)

Stratified, #malignant : #benign ~ 2:1 for each training and test set.

Repeat 30 times

Prediction of Malignancy of Ovarian Tumors Using Least Squares Support Vector Machines