A Clinical Decision Support Framework for Incremental Polyps Classification in Virtual Colonoscopy
Abstract
:1. Introduction
2. MultiClassification LSSVM Survey
3. Proposed multiclassification WPSVM
3.1. Proposed MultiClassification
Matrix Symbol  Matrix Element 
C  Diagonal matrix of size (f*c) by (f*c), the diagonal elements are composed of the square matrix c_{n} which is of size f: ${c}_{n}=\frac{c.I}{\lambda}+{\displaystyle \sum _{i=1}^{N}{x}_{i}{x}_{i}^{T}}+c{\displaystyle \sum _{p=1}^{q(n)}{\zeta}^{ip}{x}_{ip}{x}_{{i}_{p}}^{T}}$ 
D  Diagonal matrix of size (f*c) by c, the diagonal elements are the column vector d_{n} of length f ${d}_{n}={\displaystyle \sum _{i=1}^{N}{x}_{i}+}c{\displaystyle \sum _{p=1}^{q(n)}{\zeta}^{ip}{x}_{{i}_{p}}}$ 
E  Column vector of size c made from ${e}_{n}=2{\displaystyle \sum _{i=1}^{N}{x}_{i}}2(1+c){\displaystyle \sum _{p=1}^{q(n)}{\zeta}^{{i}_{p}}{x}_{{i}_{p}}}$ 
H  Matrix of size (f*c) by c. The row vector is h_{n} of length c and of the form ${h}_{n}=\left[{\displaystyle \sum _{p=1}^{q(1)}{\zeta}^{1}{x}_{{i}_{p}}+{\displaystyle \sum _{p=1}^{q(n)}{\zeta}^{{i}_{p}}{x}_{{i}_{p}}\text{\hspace{1em}}\begin{array}{ccc}{\displaystyle \sum _{p=1}^{q(2)}{\zeta}^{2}{x}_{{i}_{p}}+{\displaystyle \sum _{p=1}^{q(n)}{\zeta}^{{i}_{p}}{x}_{{i}_{p}}}}& \text{}\dots \text{}& {\displaystyle \sum _{p=1}^{q(c)}{\zeta}^{c}{x}_{{i}_{p}}+{\displaystyle \sum _{p=1}^{q(n)}{\zeta}^{{i}_{p}}{x}_{{i}_{p}}}}\end{array}}}\right]$ 
G  Square matrix of size (f*c) by (f*c), composed of matrix g_{n} of size f by c such that ${g}_{n}=\left[({\displaystyle \sum _{p=1}^{q(1)}{\zeta}^{1}{x}_{{i}_{p}}{x}_{{i}_{p}}^{T}+{\displaystyle \sum _{p=1}^{q(n)}{\zeta}^{{i}_{p}}{x}_{{i}_{p}}{x}_{{i}_{p}}^{T})\text{\hspace{1em}}\begin{array}{cc}\dots \text{}& ({\displaystyle \sum _{p=1}^{q(c)}{\zeta}^{c}{x}_{{i}_{p}}{x}_{{i}_{p}}^{T}+{\displaystyle \sum _{p=1}^{q(n)}{\zeta}^{{i}_{p}}{x}_{{i}_{p}}{x}_{{i}_{p}}^{T})}}\end{array}}}\right]$ 
Q  Square matrix of size c, made from the row vector q_{n} of length c q_{n} = [(q(1)+q(n)) ... (q(c)+q(n))] 
U  Column vector of size c, made from u_{n} such that u_{n} = −2(N −cq(n)) 
R  Square diagonal matrix of size c, the diagonal elements r_{n} are as follows ${r}_{n}=\frac{1}{\lambda}+N+cq(n)$ 
3.2. Proposed WPSVM
Step #  Algorithm 
Step 1  Train initial model using TrainSet which consists of N patient data each having f features. $\left[\begin{array}{c}W\\ B\end{array}\right]={A}^{1}L;A=\left[\begin{array}{cc}(CG)& (DH)\\ {(DH)}^{T}& (RQ)\end{array}\right];\text{}L=\left[\begin{array}{c}E\\ U\end{array}\right]$ Store only W and B as Initial_Model. Discard TrainSet 
Step 2  Acquire incremental data IncSet. 
Step 3  Validate the generalization performance using decision function of Initial_Model with the independant TestSet $f(x)=\mathrm{arg}\underset{m}{\mathrm{max}}(({w}_{m}^{T}.x)+{b}_{m}),m=\mathrm{1...}c$

4. Experimental Results
4.1. Data Set Details and Feature Selection
Symbol  Name  Count 
DB1  Database 1  Class 1 (FP) = 8008 Class 2 (TP1) = 43 Class 3 (TP2) = 84 
VOI=16*16*16=4096 Features 
4.2. Performance and validation criteria for WPSVM
4.3. WPSVM Performance in Processing Chunk versus Sequential Data
Inc_Model  INC_SEQ_MODEL  Incremental SVM  
Confusion Rate  1.2  1.07  1.24 
CPU Time  0.62  0.675  0.687 
4.4. WPSVM Specificity and Storage Requirements
Reference  Results  Settings 
[33]  95%, average of 1.5 false positive per patient  72 patients, 144 data sets, 21 polyps >=5 mm in 14 patients 
[34]  90.5%, average of 2.4 false positive per patient  121 patients, 242 data sets, 42 polyps >=5 mm in 28 patients 
[35]  80%, average of 8.2 false positive per patient  18 patients, 15 polyps >= 5mm in 9 patients 
[36]  100%, average of 7 false positive per patient  8 patients, 7 polyps>=10 mm in 4 patients 
50%, average of 7 false positive per patient  8 patients, 11 polyps measuring between 5 – 9 mm in 3 patients  
[37]  90%, average of 15.7 false positive per patient  40 patients, 80 data sets,39 polyps>=3 mm in 20 patients 
WPSVM  93.4% average of 3.2 false positive per patient  169 patients, 28 polyps measuring between 69 mm and 33 polyps >10mm 
Classifier Type  Data Structure Size 
Retrain_Model  1 a permanent storage of size (N+incnum)*f that is always increasing. 
Inc_Model  1 f by c for classifier parameters 2temporary memory of size incnum*f for dynamic data if classifier is not updated. 
5. Conclusions
Acknowledgements
References and Notes
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Awad, M.; Motai, Y.; Näppi, J.; Yoshida, H. A Clinical Decision Support Framework for Incremental Polyps Classification in Virtual Colonoscopy. Algorithms 2010, 3, 120. https://doi.org/10.3390/a3010001
Awad M, Motai Y, Näppi J, Yoshida H. A Clinical Decision Support Framework for Incremental Polyps Classification in Virtual Colonoscopy. Algorithms. 2010; 3(1):120. https://doi.org/10.3390/a3010001
Chicago/Turabian StyleAwad, Mariette, Yuichi Motai, Janne Näppi, and Hiroyuki Yoshida. 2010. "A Clinical Decision Support Framework for Incremental Polyps Classification in Virtual Colonoscopy" Algorithms 3, no. 1: 120. https://doi.org/10.3390/a3010001