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研究生:黃邦瑄
研究生(外文):Huang, Pang-Hsuan
論文名稱:基於鑑別度最佳化之TS型模糊類神經網路應用於分類問題
論文名稱(外文):Discriminability-Optimization-Based TS-Type Fuzzy Neural Networks for Classification Problems
指導教授:Wu, Gin-Der
指導教授(外文):吳俊德
口試委員:莊家峰梁勝富黃聖傑林基源洪志偉吳俊德
口試委員(外文):Juang, Chia-FengLiang, Sheng-FuHuang, Sheng-ChiehLin, Chi-YuanHung, Jeih-weihWu, Gin-Der
口試日期:2012-06-26
學位類別:博士
校院名稱:國立暨南國際大學
系所名稱:電機工程學系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:英文
論文頁數:101
中文關鍵詞:鑑別度模糊分類器模糊類神經網路第二型模糊集合不確定性
外文關鍵詞:DiscriminabilityFuzzy classifierFuzzy neural networkType-2 fuzzy setUncertainty
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對於分類器而言,鑑別度扮演了一個關鍵的角色。傳統的模糊分類器因為未充分考量鑑別度的緣故,往往導致系統參數過多並且效率不佳。有鑑於此,本論文提出了兩種基於鑑別度最佳化之模糊類神經網路。對於第一型模糊分類器,本論文提出了基於最大化鑑別度之自我佈建式模糊網路(MDSOFN)。MDSOFN將模糊法則分為線性鑑別分析(LDA)與高斯機率模型(GMM)兩個區塊。在LDA區塊中,後鑑部參數將根據有利於鑑別度的方向來更新。在GMM區塊中,參數學習採用梯度下降法來調整高斯模型。相較於其他的模糊網路,MDSOFN能在較小的網路架構下擁有較佳的鑑別力。對於第二型的模糊分類器,本論文提出了基於向量式最佳化之第二型模糊類神經網路(VOM2FNN)。VOM2FNN在前鑑部採用區間式第二型模糊集合來處理不確定性(uncertainty)。在後鑑部方面,VOM2FNN採用向量式最佳化(VOM)來加強鑑別力並減少參數的數量。因此,VOM2FNN擁有高效能的關鍵點在於同時考量不確定性與鑑別度。相較於其他的模糊分類器,VOM2FNN能在較小的網路架構下分類雜訊干擾的資料。為了驗證MDSOFN與VOM2FNN的效能,本論文採用噪音環境下的語音偵測與噪音環境下的語音辨識作為實驗環境。實驗結果指出,MDSOFN與VOM2FNN的效能都凌駕於其他的模糊分類器。
Discriminability plays a critical role in classifiers. This thesis proposes two discriminability optimization based fuzzy neural networks (FNNs) for classification problems. For type-1 fuzzy classifiers, a maximizing-discriminability-based self-organizing fuzzy network (MDSOFN) is proposed. MDSOFN divides the generation of fuzzy rules into linear discriminant analysis (LDA) part and Gaussian mixture model (GMM) part. In LDA part, the weights are updated by seeking directions which are efficient for discrimination. In GMM part, parameter learning adopts the gradient-descent method to adjust the shapes of Gaussian functions. In contrast to other FNNs, MDSOFN has better discriminability while preserving a small network size. For type-2 fuzzy classifiers, a vectorization-optimization-method based type-2 fuzzy neural network (VOM2FNN) is proposed. In antecedent parts, VOM2FNN adopts interval type-2 fuzzy sets to model and minimize the effects of uncertainty. In consequent parts, VOM2FNN adopts a vectorization-optimization-method (VOM) to enhance discriminability and reduce the number of parameters. The key of VOM2FNN is its consideration of both the uncertainty and discrimination. In contrast to other type-2 FNNs, VOM2FNN can efficiently classify noisy patterns while preserving a small network size. To evaluate the performance of MDSOFN and VOM2FNN, noisy speech recognition and noisy speech detection are adopted in experiments. Experimental results indicate that MDSOFN and VOM2FNN outperform other FNNs.
CONTENTS

1 INTRODUCTION 1
2 DISCRIMINABILITY-OPTIMIZATION-BASED FUZZY RULES 6
2.1 Type-1 Fuzzy Logic Systems . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Type-2 Fuzzy Logic Systems . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Discriminability-Optimization-Based Fuzzy Rules . . . . . . . . . . . 14
2.3.1 PCA-based Type-1 Fuzzy Rules . . . . . . . . . . . . . . . . . . . 14
2.3.2 LDA-based Type-1 Fuzzy Rules . . . . . . . . . . . . . . . . . . . 15
2.3.3 VOM-based Type-2 Fuzzy Rules . . . . . . . . . . . . . . . . . . . 20
3 MAXIMIZING-DISCRIMINABILITY-BASED SELF-ORGANIZING FUZZY NETWORK 25
3.1 Structure of MDSOFN . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 Structure Learning of MDSOFN . . . . . . . . . . . . . . . . . . . . 30
3.3 Parameter Learning of MDSOFN . . . . . . . . . . . . . . . . . . . 32
3.4 Experiments and Theoretical Analysis . . . . . . . . . . . . . . . . . 37
3.4.1 Experiment 1 : Speech Detection in Noisy Environments . . . . . . 37
3.4.2 Experiment 2 : Speech Recognition in Noisy Environments . . . . . 40
3.4.3 Theoretical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 43
4 VECTORIZATION-OPTIMIZATION-METHOD BASED TYPE-2 FUZZY NEURAL NETWORK 48
4.1 Structure of VOM2FNN . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2 Structure Learning of VOM2FNN . . . . . . . . . . . . . . . . . . . 55
4.3 Parameter Learning of VOM2FNN . . . . . . . . . . . . . . . . . . 59
4.4 Experiments and Theoretical Analysis . . . . . . . . . . . . . . . . . 67
4.4.1 Experiment 1 : Small Dataset Classification . . . . . . . . . . . . 69
4.4.2 Experiment 2 : Speech Detection in Noisy Environments . . . . . . 69
4.4.3 Experiment 3 : Speech Recognition in Noisy Environments . . . . . 75
4.4.4 Theoretical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 77
5 CONCLUSIONS 81
REFERENCES 82
A DERIVATIONS OF VOM 87
a.1 Matrix Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
a.1.1 Basic Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
a.1.2 Useful Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 89
a.1.3 Useful Operations . . . . . . . . . . . . . . . . . . . . . . . . . . 91
a.2 Derivation of VOM . . . . . . . . . . . . . . . . . . . . . . . . . . 95

LIST OF FIGURES

Figure 2.1 Type-1 FLS. . . . . . . . . . . . . . . . . . . . . . . . 7
Figure 2.2 Interval type-2 fuzzy set . . . . . . . . . . . . . . . . . 10
Figure 2.3 Type-2 FLS . . . . . . . . . . . . . . . . . . . . . . . . 11
Figure 3.1 Structure of MDSOFN . . . . . . . . . . . . . . . . . . 26
Figure 3.2 Fuzzy classifier for speech detection. . . . . . . . . . . . 38
Figure 3.3 Example of speech detection. (a) Original speech waveform.
(b) Speech waveform recorded in additive white
noise (SNR=0dB). (c) Detected word signal islands. . . 39
Figure 3.4 Flowchart of MTDC. . . . . . . . . . . . . . . . . . . . 42
Figure 3.5 Recognition rates of MDSOFN, SOTFN-SV, SONFINPCA,
and SVM in speech recognition across different
noise conditions. . . . . . . . . . . . . . . . . . . . . . 44
Figure 3.6 Effects of the second mapping functions. (a) Original
highly confused patterns. (b) PCA mapping result. (c)
Linear function mapping result. (d) LDA mapping result. 47
Figure 4.1 Structure of VOM2FNN. . . . . . . . . . . . . . . . . . 49
Figure 4.2 Parameter learning flowchart of VOM2FNN. . . . . . . . 68
Figure 4.3 Small dataset for examining the performance of VOM
and other mapping functions. . . . . . . . . . . . . . . 70
Figure 4.4 Performance of VOM and other mapping functions in the
small dataset.(a) Original distribution of the dataset. (b)
PCA mapping result. (c) LDA mapping result. (d) VOM
mapping result. . . . . . . . . . . . . . . . . . . . . . . 71
Figure 4.5 Clean speech signals. (a) Original speech waveform. (b)
Original speech endpoint locations. . . . . . . . . . . . 73
Figure 4.6 Speech detection result of VOM2FNN and other FNNs in
noisy environment. (a) Speech signal with additive white
noise (SNR=0dB). (b) Detection result by SONFIN-PCA.
(c) Detection result by MDSOFN-LDA. (d) Detection
result by SEIT2FNN. (e) Detection result by VOM2FNN. 74
Figure 4.7 Difference of modeling ability between type-1 and type-2
fuzzy sets in experiment 1. (a) Type-1 MFs in the first
dimension (12 parameters). (b) Type-2 MFs in the first
dimension (9 parameters). . . . . . . . . . . . . . . . . 78

LIST OF TABLES

Table 3.1 Performance of MDSOFN and other classifiers in speech
detection. . . . . . . . . . . . . . . . . . . . . . . . . . 40
Table 3.2 Performance of MDSOFN and other classifiers in speech
recognition. . . . . . . . . . . . . . . . . . . . . . . . 43
Table 3.3 Differences between MDSOFN and other classifiers. . . . 45
Table 4.1 Performance of VOM2FNN and other FNNs in the small
dataset. . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Table 4.2 Performance of VOM2FNN and other FNNs in speech
detection. . . . . . . . . . . . . . . . . . . . . . . . . . 75
Table 4.3 Performance of VOM2FNN and other FNNs in noisy
speech recognition. . . . . . . . . . . . . . . . . . . . . 76
Table 4.4 Differences between VOM2FNN and other FNNs. . . . . 80

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