A novel method is proposed to establish the classifier which can classify the pancreatic images into normal or abnormal. Firstly, the brightness feature is used to construct high-order tensors, then using multilinear principal component analysis (MPCA) extracts the eigentensors, and finally, the classifier is constructed based on support vector machine (SVM) and the classifier parameters are optimized with quantum simulated annealing algorithm (QSA). In order to verify the effectiveness of the proposed algorithm, the normal SVM method has been chosen as comparing algorithm. The experimental results show that the proposed method can effectively extract the eigenfeatures and improve the classification accuracy of pancreatic images.
Pancreatic carcinoma is a frequent digestive tract tumor. The malignant degree of this kind of cancer is always very high, and it is difficult to be early diagnosed and treated. Due to the fact that pancreatic carcinoma is often diagnosed when it is advanced, very few pancreatic tumors can be removed by operation. As we know, many famous people died of this disease. So, it is necessary to diagnose pancreatic carcinoma as early as possible. Computer-aided diagnosis (CAD) [
Tensors are geometrical quantity that is used to describe linear relations among vectors, scalars, and other tensors. In this paper, the pancreas CT images can be treated as several third-order tensors, and then we extract the feature to gain the eigentensors for classification.
Principal component analysis (PCA) [ Basic using of PCA to transfer tensor objects to high-dimension vector (vectorization) obviously results in high cost of processing and memory in next step [ In using PCA, reshaping breaks the natural structure and correlation in the original data [
In order to solve these problems, this paper uses multilinear principal component analysis (MPCA) referred to in [
Support vector machine (SVM) [ The objective function can be nonlinear, discontinuous, and random. The objective function can have any boundary conditions and constraints. The programming workload of SA is low, so that it is easy to be implemented. In statistics, we can find the optimal solutions.
But there are also some problems of SA. For example, rapid cooling can lead to simulation hardening which cannot be ensured to find the optimal solution. Quantum evolution algorithm (QEA) [
In this section, firstly we will introduce the whole procedure of the proposed method, which is shown in Figure
The main flow of the proposed method.
The process of the proposed method is as follows. Image preprocessing: first, we segment the CT images of abdomen to gain the pancreas region of image, and then we normalized the images after segmentation. High-order tensors construction: at first, we collect a group of pancreatic images and then combine them into a new dataset. The feature extraction: in this paper, we use the method of MPCA to extract the eigentensors for classification. Pancreas diseases classification based on QSA-SVM: after we obtain the eigentensors by MPCA, we can treat the eigentensors as samples, and then we use the approach of SVM optimized by QSA to classify pancreas diseases.
We treat the segmented pancreatic CT images as several third-order tensors with the column, row, and thickness modes. In this paper, we treat each CT image as one data sample. Hence, the input is several third-order tensors and the spatial column space, row space, and the thickness space were regarded as its three modes, as shown in Figure
Illustration of the pancreatic CT image as a third-order tensor.
The size of each image is standard
In this paper, an MPCA [
The flow of MPCA algorithm.
In the preprocessing phase, we center the input original tensors
In the initialization phase, we calculate the eigendecomposition of
In the local optimization phase, we will focus on doing the local optimization to obtain the new
Local optimization (i) Calculate (ii) Calculate (iii) For For corresponding to the largest Calculate If
In the projection phase, we project the centralized eigentensors
We used the eigenvector
The term quantum comes from quantum mechanics. Quantum, which is the general name of all microscopic particles in the microscopic world, is different from the macroscopic object. Its movements obey the statistical law, not the deterministic law. Compared with the classical computing using 0 and 1 to represent information, the quantum computing uses
The measurement of quantum state can cause the collapse of quantum state, so that the final state can be confirmed. The relationship of quantum state, superposition state, and the collapse caused by measurement is shown in Figure
The relationship of the three states.
In the quantum computing, the quantum state changes when we have a series of unitary transformations on it. The equipment (a unitary matrix) is called quantum gate which is as follows:
We exchange two probability amplitudes of a quantum bit by the quantum gate as follows
We use SVM to train the classifier. SVM can be used to solve some problems, such as the small number of samples, nonlinear, high dimension pattern recognition, and local minimum point, but if the selection of the kernel function parameters, penalty factor
In this paper, QSA is used for optimizing the SVM parameters, penalty factor
We assume that there are
In the following description, we set that
The main flow of QSA-SVM is shown in Figure
The flow of QSA-SVM.
Initialization of parameters.
Coding the chromosome using phase,
Solution space transformation for chromosomes and computing fitness. For the quantum bit,
We use the SVM prediction accuracy as the fitness of chromosomes and leave one out (LOO) to evaluate. Then, we keep all information of the optimal individual.
Computing the annealing temperature
The position update of new individual. We divide the neighborhood space for phase and then generate a random update vector
According to the Metropolis criterion, we update the chromosomes. The probability of new chromosomes acceptation obeys the Boltzmann probability distribution. In (
Implement quantum variation operation using the following:
Update the current individuals and execute Step
Determine if it has met the end conditions true is the end to return the optimal parameters and false goes to Step
Use the optimal parameters to train an SVM classifier.
After we obtain the classifier using optimal parameters, we will use it to classify the testing samples. Then, we compare the classification labels with the known labels, so that we can get the classification accuracy for evaluating the performance of classifier. It is shown as (
We select 114 groups of pancreas images; among them 81 groups are normal and 33 groups are abnormal. The resolution of each image is
Figure
Illustration of samples. (a) Normal pancreas. (b) Abnormal pancreas.
We can see the mean of the samples of each 81 normal pancreas and 33 abnormal pancreas in Figure
Illustration of the mean figure of the samples. (a) The mean of the normal samples. (b) The mean of the abnormal samples.
In this paper, we use the SVM method to classify the pancreas data. We can see several results in Table
Accuracy of centered data and not centered data using SVM.
|
|
Centered data | Not centered data |
---|---|---|---|
0.375 | 145 | 71.43% | 46.33% |
0.165 | 120 | 71.42% | 43.66% |
0.100 | 200 | 68.29% | 38.54% |
0.325 | 350 | 65.63% | 37.53% |
The experimental result of 5 groups of QSA-SVM is shown in Table
Experiments result of QSA-SVM.
|
|
Accuracy | Time |
---|---|---|---|
412.3415 | 20.0268 | 92.8571% | 134.33 s |
459.1865 | 127.9188 | 94.6429% | 134.83 s |
357.8127 | 95.1239 | 91.0714% | 114.28 s |
465.7957 | 30.7913 | 96.4286% | 111.06 s |
1020.5 | 267.1588 | 98.2143% | 152.23 s |
Compared with other classifiers, the accuracy of QSA-SVM is better which is shown in Figure
Classification accuracy of pancreas images using 5 classifiers.
Classification time of pancreas images using 5 classifiers.
Classifier BPNN is BP neural network, the accuracy is 25% and the running time is 6.76 s; classifier Fisher is fisher linear classifier, the accuracy and running time are 35% and 0.98 s; classifier SVM is the common SVM, the accuracy is 71.4286% and the running time is only 0.13 s; classifier ACO-SVM [
At present, radiologists usually diagnose pancreatic diseases with their own experience and the morphology information of image. But missed diagnosis sometimes inevitably happened due to individual differences of patients or limitation of doctor’s knowledge of image information. Hence, the proposed method can be used in CAD technology and give early diagnosis of pancreatic diseases in the acceptable time of doctor, so that the classifier can help doctors to diagnose the disease of patient and improve diagnosis rate of disease.
In this paper, tensors have been used to represent the image and MPCA extended linear PCA to multilinear subspace learning for the tensor object analysis, and QSA-SVM method has been proposed to classify images. As an application for classifying pancreatic images, the method combining MPCA and QSA-SVM achieved the better classification accuracy, because MPCA method can preserve the relationship of features in the original tensor and the structure of the original image as much as possible; in the acceptable time, QSA which was used for optimizing SVM classified model is able to find the optimal model parameters. Therefore, the proposed method can improve the classification accuracy of pancreatic images and then assist doctors to diagnose diseases.
The research is supported by the National Natural Science Foundation of China (no. 61272176, no. 60973071) and the Fundamental Research Funds for the Central Universities (no. 110718001).