Data Analysis Machine Learning and Applications Episode 1 Part 3 docx

Computer Assisted Classification of Brain Tumors

Norbert Röhrl1, José R. Iglesias-Rozas2 and Galia Weidl1

1 Institut für Analysis, Dynamik und Modellierung, Universität Stuttgart

Pfaffenwaldring 57, 70569 Stuttgart, Germany

[email protected]

2 Katharinenhospital, Institut für Pathologie, Neuropathologie

Kriegsbergstr. 60, 70174 Stuttgart, Germany

[email protected]

Abstract. The histological grade of a brain tumor is an important indicator for choosing the

treatment after resection. To facilitate objectivity and reproducibility, Iglesias et al. (1986)

proposed to use a standardized protocol of 50 histological features in the grading process.

We tested the ability of Support Vector Machines (SVM), Learning Vector Quantization

(LVQ) and Supervised Relevance Neural Gas (SRNG) to predict the correct grades of the

794 astrocytomas in our database. Furthermore, we discuss the stability of the procedure with

respect to errors and propose a different parametrization of the metric in the SRNG algorithm

to avoid the introduction of unnecessary boundaries in the parameter space.

1 Introduction

Although the histological grade has been recognized as one of the most powerful

predictors of the biological behavior of tumors and significantly affects the manage￾ment of patients, it suffers from low inter- and intraobserver reproducibility due to

the subjectivity inherent to visual observation. The common procedure for grading

is that a pathologist looks at the biopsy under a microscope and then classifies the

tumor on a scale of 4 grades from I to IV (see Fig. 1). The grades roughly correspond

to survival times: a patient with a grade I tumor can survive 10 or more years, while

a patient with a grade IV tumor dies with high probability within 15 month. Iglesias

et al. (1986) proposed to use a standardized protocol of 50 histological features in

addition to make grading of tumors reproducible and to provide data for statistical

analysis and classification.

The presence of these 50 histological features (Fig. 2) was rated in 4 categories

from 0 (not present) to 3 (abundant) by visual inspection of the sections under a

microscope. The type of astrocytoma was then determined by an expert and the cor￾responding histological grade between I and IV is assigned.

56 Norbert Röhrl, José R. Iglesias-Rozas and Galia Weidl

Fig. 1. Pictures of biopsies under a microscope. The larger picture is healthy brain tissue

with visible neurons. The small pictures are tumors of increasing grade from left top to right

bottom. Note the increasing number of cell nuclei and increasing disorder.

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Fig. 2. One the 50 histological features: Concentric arrangement. The tumor cells build con￾centric formations with different diameters.

2 Algorithms

We chose LVQ (Kohonen (1995)), SRNG (Villmann et al. (2002)) and SVM (Vap￾nik (1995)) to classify this high dimensional data set, because the generalization

error (expectation value of misclassification) of these algorithms does not depend on

the dimension of the feature space (Barlett and Mendelson (2002), Crammer et al.

(2003), Hammer et al. (2005)).

For the computations we used the original LVQ-PAK (Kohonen et al. (1992)),

LIBSVM (Chan and Lin (2001)) and our own implementation of SRNG, since to our

knowledge there exists no freely available package. Moreover for obtaining our best

results, we had to deviate in some respects from the description given in the original

article (Villmann et al. (2002)). In order to be able to discuss our modification we

briefly formulate the original algorithm.

2.1 SRNG

Let the feature space be Rn and fix a discrete set of labels Y , a training set T ⊆

Rn ×Y and a prototype set C ⊆ Rn ×Y .

The distance in feature space is defined to be