Enhanced neural gas network for prototype-based clustering

1. Enhanced neural gas network for prototype-based clustering Presenter : Shao-Wei Cheng Authors : A.K. Qin, P.N. Suganthan PR 2005

2. Outline • Motivation • Objective • Methodology • Experiments and Results • Conclusion • Personal Comments

3. Motivation • There are several problems about PBC and NG algorithm. • Sensitivity to initialization. • Sensitivity to input sequence ordering • The adverse influence from outliers. . . . . .

4. Objectives • Present an improved PBC algorithm based on the enhanced NG network framework, called the ENG. • Tackle several problems about PBC. . . . . .

5. . 4 Methodology - original . 3 . . 1 2 • PBC algorithms：k-means, fuzzy k-means • NG network algorithms：single-layered neural network • Faster convergence to low distortion errors. • Lower distortion error than other methods. • Obeying a stochastic gradient descent. • The original NG algorithm • The original NG algorithm with concept of fuzzy . 0 V.

6. Methodology - enhanced • Enhanced NG network framework • (3) – Explain the influence of outlier, updating from Eq. (1) • (4) – The new formula updating from Eq. (3) • (5)、(6)、(7) – Explain the parameters in Eq. (4)

7. Methodology – MDL framework • MDL principle is employed as the performance measure. • Original MDL • MDL in this approach as

8. c synaptic weights W = {w1,w2, . . . ,wc} randomly is the middle value for to control the acceleration of ’s changing κ and η are the parameters used to calculate the MDL value The initial training epoch number: m = 0 The initial iteration step number t in training epoch m : t = 1 Total iteration step number iter is：iter = m · N + t The maximum training epoch is set as Max_epoch The dislocated prototypes’ relocation is defined as RP_epoch The dataset for training is V = {v1, v2, . . . , vN} Methodology - processes Initialize N Draw data in training set and compute (c) If training stage is at RP_epoch (d) For j = 1 to size(V) (a) If m < Max_epoch (b) If trainingset is not empty Y Y Y N N (e) For j = 1 to size(Torelocate) change Y Training epoch += 1 End restore N (f) If current utifactor value < previous utifactor value

9. Methodology - processes

10. Methodology - processes

11. Methodology - processes

12. Experiments • Compared to 9 algorithms：HCM, FCM, NG, FPCM, CFCM-F1, CFCM-F2, HRC-FRC, AHCM, and AFCM. • Data set： • Artificial – D1, D2 • UCI datasets • Run each clustering algorithms 10 times. • Parameter settings： • εi=0.8, εf=0.05；λi=10, λf=0.01；βi=50, βm= 10, βf= 0.01 • κ= 2, η= 1e− 4 • Max_epoch = 10, RP_epoch = 5.

13. Experiments

14. Experiments

15. Experiments

16. Conclusion • Tackle several problems about PBC • Sensitivity to initialization. • Sensitivity to input sequence ordering • The adverse influence from outliers. • Experimental results have shown the superior performance of the proposed method over several existing PBC algorithms. • MDL framework can tackle the problem of compact clusters and sparse clusters simultaneously existed.

17. Personal Comments • Advantage • A heuristic way to tackle outlier problem. • Drawback • Application • clustering • classification