W. Z. YAN, L. BAI

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and robustness of an ANN used in chromosome classifi-

cation [4].

In order to improve the performance of traditional

multilayer ANNs, a number of other more sophisticated

neural networks have been proposed and tested in this

area.

A hierarchical multi-layer neural network with an error

back-propagation training algorithm has been adopted for

the automatic classification of Giemsa-stained human

chromosomes. Firstly, chro mosomes data is classified into

7 major groups based on their morphological features

such as relative length, relative area, centromeric index,

and 80 density profiles. Then each 7 major groups are

classified into 24 subgroups using each group classifier.

Figure 2 shows the two steps of chromosome classifica-

tion. The classification error decreased by using two

steps of classification and the classification error was

5.9% [5].

A fuzzy Hopfield neural network is a combination

model of neuro and fuzzy computing. Its main difference

from the traditiona l ANN is that it holds fuzzy clustering

capability and learning mechanism of acquiring know-

ledge about the targets (human chromosomes) from the

noisy training samples. It develops a Classifier with the

Fuzzy Hopfield Network (CFHN) to identify each ob-

served human chromosome and assign it to one of the 24

human chromosome classes. In a test involving 100 hu-

man chromosomes, the fuzzy Hopfield neural network

produces a very low u nidenti f ication rate of 3. 33 % [6].

3. Wavelet Transforms Based Algorithms

Some researchers have set out to explore the use of

wavelet-based band pattern descriptors for chromosome

classification. Compared with other methods, wavelet

transforms use different basis functions that lead to the

desirable property of characterizing and localizing signal

Figure 2. Architecture of the hierarchical multi-layer neural

network.

features simultaneously in both the space and transform

domains. Furthermore, they offer a means of signal re-

presentation that facilitates multi-resolution analysis [7].

An expanded basis function system that allows high

resolution decomposition of a signal is called the wavelet

packet transform. These are computed by iterating not

only down the lowpass scaling function branch of Mal-

lat’s Discrete Wavelet Transform (DWT ) algorithm tree,

but also down the highpass wavelet branch [7]. Thus, the

wavelet packet transform offers more basis functions for

signal analysis than the wavelet transform. Compared

with the wavelet transform, the wavelet packet transform

uses only full-width basis functions. They are all ortho-

gonal, and all but the first have zero area. These are in-

tuitively more satisfying weighting functions than the

ever-narrowing wavele t basis f unc t ions.

In one study, researchers describe their recent study to

employ wavelet packets as basis function sets to compute

chromosome band pattern features. During the study, they

evaluated a total of 28 wavelet packet basis function sets,

including the well known Haar and Daubechies’4 and

Daubechies’6 wavelet packets. They conducted experi-

ments on two benchmark chromosome datasets and com-

pare the experimental results with the results of the cur-

rently best performing Weighted Density Distribution

(WDD) method. Table 1 summarizes the experimental

results. For the sake of clarity and page limit, this table

includes only those of the well-known Haar, Daubechies’4

(D4), Daubechies’6 (D6), and the best-performing wave-

let packet (BPWP), in comparison to the WDD results

[8].

Another research proposes a method for chromosome

classification based on the chromosome shape analysis.

This approach is based on wavelet packet transform (WPT)

and best basis algorithm (BBA). First, the chromosome

image is preprocessed and binarized. Second, the contour

of the chromosome is detected and the signature of the

contour is produced. Figure 3 shows a binarized chro-

mosome, its contour and its signature of the contour.

Third, the signature is decomposed by the wavelet packet

transform and its best basis is found. Finally, the coeffi-

cients of the best tree of wavelet packet transform cor-

respondent to the signature of chromosomes are com-

pared in order to classify the chromosomes. The results

obtained show that the proposed method provides an

effective chromosome classification based on WPT and

BBA of the shape signature of the chromosomes [9].

Table 1. Summary of the chromosome classification expe-

rimental results based on the two data sets

WDD BPWP Haar D4 D6

Copenhagen set 96.8% 96.2% 95.7% 95.2% 94.0%

Genzyme set 85.3% 84.6% 83.8% 79.9% 80.0%