Dual-Tree Complex Wavelet Transform and Twin Support Vector Machine for Pathological Brain Detection
Abstract
:1. Introduction
2. Materials
3. Methodology
3.1. Discrete Wavelet Transform
3.2. Dual-Tree Complex Wavelet Transform
3.3. Comparison between DWT and DTCWT
3.4. Variance and Entropy (VE)
3.5. Generalized Eigenvalue Proximal SVM
3.6. Twin Support Vector Machine
3.7. Pseudocode of the Whole System
4. Experiment Design
4.1. Statistical Setting
4.2. Parameter Estimation for s
4.3. Evaluation
5. Results and Discussions
5.1. Classifier Comparison
5.2. Optimal Decomposition Level Selection
5.3. Comparison to State-of-the-Art Approaches
5.4. Results of Different Runs
5.5. Computation Time
5.6. Comparison to Human Reported Results
6. Conclusions and Future Research
Acknowledgment
Author Contributions
Conflicts of interest
Abbreviations
(A)(BP)(F)(PC)NN | (Artificial) (Back-propagation) (Feed-forward) (Pulse-coupled) neural network |
(B)PSO(-MT) | (Binary) Particle Swarm Optimization (-Mutation and TVAC) |
(D)(S)W(P)T | (Discrete) (Stationary) wavelet (packet) transform |
(k)(F)(LS)(GEP)SVM | (kernel) (Fuzzy) (Least-Squares) (Generalized eigenvalue proximal) Support vector machine |
(W)(P)(T)E | (Wavelet) (Packet) (Tsallis) entropy |
CAD | Computer-aided diagnosis |
CS | Cost-sensitivity |
FRFE | Fractional Fourier entropy |
HMI | Hu moment invariant |
KNN | K-nearest neighbors |
MR(I) | Magnetic resonance (imaging) |
PCA | Principal Component Analysis |
RBF | Radial Basis Function |
TVAC | Time-varying Acceleration Coefficients |
WTT | Welch’s t-test |
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Phase I: Offline learning | ||
Step A | Wavelet Analysis | Perform s-level dual-tree complex wavelet transform (DTCWT) on every image in the ground-truth dataset |
Step B | Feature Extraction | Obtain 12 × s features (6 × s Variances and 6s Entropies, and s represents the decomposition level) from the subbands of DTCWT |
Step C | Training | Submit the set of features together with the class labels to the classifier, in order to train its weights/biases. |
Step D | Evaluation | Record the classification performance based on a 10 × K - fold stratified cross validation. |
Phase II: Online prediction | ||
Step A | Wavelet Analysis | Perform s-level DTCWT on the real query image (independent from training images) |
Step B | Feature Extraction | Obtain VE feature set |
Step C | Prediction | Feed the VE feature set into the trained classifier, and obtain the output. |
Dataset | No. of Fold | Training | Validation | Total | |||
---|---|---|---|---|---|---|---|
H | P | H | P | H | P | ||
Dataset66 | 6 | 15 | 40 | 3 | 8 | 18 | 48 |
Dataset160 | 5 | 16 | 112 | 4 | 28 | 20 | 140 |
Dataset255 | 5 | 28 | 176 | 7 | 44 | 35 | 220 |
Our Methods | Dataset66 | Dataset160 | Dataset255 |
---|---|---|---|
DTCWT + VE + SVM | 100.00 | 99.69 | 98.43 |
DTCWT + VE + GEPSVM | 100.00 | 99.75 | 99.25 |
DTCWT + VE + TSVM | 100.00 | 100.00 | 99.57 |
Algorithms | Feature # | Run # | Acc | ||
---|---|---|---|---|---|
Dataset66 | Dataset160 | Dataset255 | |||
DWT + PCA + KNN [4] | 7 | 5 | 98.00 | 97.54 | 96.79 |
DWT + SVM + RBF [5] | 4761 | 5 | 98.00 | 97.33 | 96.18 |
DWT + PCA + SCG-FNN [6] | 19 | 5 | 100.00 | 99.27 | 98.82 |
DWT + PCA + SVM + RBF [7] | 19 | 5 | 100.00 | 99.38 | 98.82 |
RT + PCA + LS-SVM [8] | 9 | 5 | 100.00 | 100.00 | 99.39 |
PCNN + DWT + PCA + BPNN [9] | 7 | 10 | 100.00 | 98.88 | 98.24 |
DWPT + TE + GEPSVM [10] | 16 | 10 | 100.00 | 100.00 | 99.33 |
SWT + PCA + HPA-FNN [11] | 7 | 10 | 100.00 | 100.00 | 99.45 |
WE + HMI + GEPSVM [13] | 14 | 10 | 100.00 | 99.56 | 98.63 |
SWT + PCA + GEPSVM [53] | 7 | 10 | 100.00 | 99.62 | 99.02 |
FRFE + WTT + SVM [54] | 12 | 10 | 100.00 | 99.69 | 98.98 |
SWT + PCA + SVM + RBF [55] | 7 | 10 | 100.00 | 99.69 | 99.06 |
DTCWT + VE + TSVM (Proposed) | 12 | 10 | 100.00 | 100.00 | 99.57 |
Run | F1 | F2 | F3 | F4 | F5 | Total |
---|---|---|---|---|---|---|
1 | 51(100.00%) | 51(100.00%) | 51(100.00%) | 51(100.00%) | 51(100.00%) | 255(100.00%) |
2 | 51(100.00%) | 50(98.04%) | 51(100.00%) | 51(100.00%) | 51(100.00%) | 254(99.61%) |
3 | 50(98.04%) | 51(100.00%) | 51(100.00%) | 51(100.00%) | 50(98.04%) | 253(99.22%) |
4 | 50(98.04%) | 50(98.04%) | 51(100.00%) | 51(100.00%) | 51(100.00%) | 253(99.22%) |
5 | 51(100.00%) | 51(100.00%) | 51(100.00%) | 51(100.00%) | 50(98.04%) | 254(99.61%) |
6 | 51(100.00%) | 51(100.00%) | 51(100.00%) | 50(98.04%) | 50(98.04%) | 253(99.22%) |
7 | 51(100.00%) | 51(100.00%) | 51(100.00%) | 51(100.00%) | 50(98.04%) | 254(99.61%) |
8 | 51(100.00%) | 50(98.04%) | 51(100.00%) | 51(100.00%) | 51(100.00%) | 254(99.61%) |
9 | 51(100.00%) | 51(100.00%) | 51(100.00%) | 51(100.00%) | 51(100.00%) | 255(100.00%) |
10 | 51(100.00%) | 50(98.04%) | 51(100.00%) | 51(100.00%) | 51(100.00%) | 254(99.61%) |
Average | 253.9 (99.57%) |
Process | Time (second) |
---|---|
DTCWT | 8.41 |
VE | 1.81 |
TSVM Training | 0.29 |
Process | Time (second) |
---|---|
DTCWT | 0.037 |
VE | 0.009 |
TSVM Test | 0.003 |
Neuroradiologist | Accuracy |
---|---|
O1 | 74% |
O2 | 78% |
O3 | 77% |
O4 | 79% |
Our method | 96% |
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Share and Cite
Wang, S.; Lu, S.; Dong, Z.; Yang, J.; Yang, M.; Zhang, Y. Dual-Tree Complex Wavelet Transform and Twin Support Vector Machine for Pathological Brain Detection. Appl. Sci. 2016, 6, 169. https://doi.org/10.3390/app6060169
Wang S, Lu S, Dong Z, Yang J, Yang M, Zhang Y. Dual-Tree Complex Wavelet Transform and Twin Support Vector Machine for Pathological Brain Detection. Applied Sciences. 2016; 6(6):169. https://doi.org/10.3390/app6060169
Chicago/Turabian StyleWang, Shuihua, Siyuan Lu, Zhengchao Dong, Jiquan Yang, Ming Yang, and Yudong Zhang. 2016. "Dual-Tree Complex Wavelet Transform and Twin Support Vector Machine for Pathological Brain Detection" Applied Sciences 6, no. 6: 169. https://doi.org/10.3390/app6060169