神經模糊建模是一種高效率的系統建模方法。它主要是整合了類神經網路及模糊系統這兩種著名的方法，因此，具有學習能力、強健性、仿人類的推論模式、及高度可懂性之優點。目前為止，已經有很多神經模糊建模方法被提出來，然而，仍然存在著許多待解決之問題。

在本論文中，我們針對神經模糊建模中的結構辨識及參數辨識這兩個問題，分別提出了兩種自建構式法則產生方法（基於相似度之法則產生方法與基於相似度及合併之法則產生方法）及一種混合式學習演算法。這兩種自建構式法則產生方法皆是利用在輸入及輸出空間上的相似度測試而逐漸地將輸入-輸出訓練資料聚成數個模糊群，而每個模糊群的歸屬函數則是根據其所包含的資料之平均值及標準差來定義。此外，基於相似度及合併之法則產生方法多了一個合併的機制以動態地合併相似的模糊群。之後，從每一個模糊群擷取出一條零階或一階TSK型式的模糊“若-則”法則，以組成一個初步的模糊法則庫，此法則庫可以直接使用於模糊推論或由下一個參數辨識階段來進一步的最佳化。與其他方法比較起來，我們這兩種自建構式法則產生方法具有幾個優點：可快速產生模糊法則、可產生較為接近資料分佈的歸屬函數、及對於有新增加資料的情況，不需重新產生全部的模糊群。此外，基於相似度及合併之法則產生方法提供了一個較為合理且快速的模糊群合併機制，藉此減輕資料輸入順序所造成的影響，並可避免一般遞增式聚類方法容易產生多餘模糊群的問題。

為了優化由結構辨識階段所產生的初步模糊法則，我們根據這些法則來建立一個零階或一階TSK型式的模糊類神經網路。之後，利用我們所發展的混合式學習演算法來對網路進行學習。此演算法結合了基於SVD（奇異值分解；Singular Value Decomposition）之遞迴式最小平方估計值及陂降法，具有可減輕局部最小值問題、學習快速、需要較少記憶體、可達到較小之近似誤差之優點。

為了驗證我們方法的實用性，我們將其應用於函數近似及分類上。在函數近似方面，我們利用所提出的方法來模擬幾個非線性的函數及實際的系統。在分類方面，我們則是利用所提出的方法來解決人體物件偵測的問題。首先，利用一個模糊聚類方法來將訓練之影像畫面分成數個區段，接者再根據一些判斷標準來將這些區段分類成初步的前景或背景。然後，利用我們的混合式學習演算法來訓練一個模糊類神經網路，用以擷取訓練影像畫面及其他影像畫面之人體物件。實驗結果顯示，我們的方法可以改善人體物件擷取的準確度，甚至對於在影像中移動不甚明顯的人體物件，依然能夠有較好的擷取結果。

Neuro-fuzzy modeling is an efficient computing paradigm for system modeling problems. It mainly integrates two well-known approaches, neural networks and fuzzy systems, and therefore possesses advantages of them, i.e., learning capability, robustness, human-like reasoning, and high understandability. Up to now, many approaches have been proposed for neuro-fuzzy modeling. However, it still exists many problems need to be solved.

We propose in this thesis two self-constructing rule generation methods, i.e., similarity-based rule generation (SRG) and similarity-and-merge-based rule generation (SMRG), and one hybrid learning algorithm (HLA) for structure identification and parameter identification, respectively, of neuro-fuzzy modeling. SRG and SMRG group the input-output training data into a set of fuzzy clusters incrementally based on similarity tests on the input and output spaces. Membership functions associated with each cluster are defined according to statistical means and deviations of the data points included in the cluster. Additionally, SMRG employs a merging mechanism to merge similar clusters dynamically. Then a zero-order or first-order TSK-type fuzzy IF-THEN rule is extracted from each cluster to form an initial fuzzy rule-base which can be directly employed for fuzzy reasoning or be further refined in the next phase of parameter identification. Compared with other methods, both our SRG and SMRG have advantages of generating fuzzy rules quickly, matching membership functions closely with the real distribution of the training data points, and avoiding the generation of the whole set of clusters from the scratch when new training data are considered. Besides, SMRG supports a more reasonable and quick mechanism for cluster merging to alleviate the problems of data-input-order bias and redundant clusters, which are encountered in SRG and other incremental clustering approaches.

To refine the fuzzy rules obtained in the structure identification phase, a zero-order or first-order TSK-type fuzzy neural network is constructed accordingly in the parameter identification phase. Then, we develop a HLA composed by a recursive SVD-based least squares estimator and the gradient descent method to train the network. Our HLA has the advantage of alleviating the local minimal problem. Besides, it learns faster, consumes less memory, and produces lower approximation errors than other methods.

To verify the practicability of our approaches, we apply them to the applications of function approximation and classification. For function approximation, we apply our approaches to model several nonlinear functions and real cases from measured input-output datasets. For classification, our approaches are applied to a problem of human object segmentation. A fuzzy self-clustering algorithm is used to divide the base frame of a video stream into a set of segments which are then categorized as foreground or background based on a combination of multiple criteria. Then, human objects in the base frame and the remaining frames of the video stream are precisely located by a fuzzy neural network which is constructed with the fuzzy rules previously obtained and is trained by our proposed HLA. Experimental results show that our approaches can improve the accuracy of human object identification in video streams and work well even when the human object presents no significant motion in an image sequence.

Title Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 Network Architectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.2 Learning Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.3 Backpropagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3 Fuzzy Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3.1 Fuzzy Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3.2 Fuzzy IF-THEN Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3.3 Fuzzy Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3.4 Fuzzy Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.4 Neuro-Fuzzy Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.4.1 Types of Neuro-Fuzzy Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.4.2 Literature Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.5 Human Object Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.5.1 Video Object Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.5.2 Human Object Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
1.5.3 Literature Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.6 Organization of This Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2 Self-Constructing Rule Generation Methods for Structure Identification 34
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.2 Similarity-Based Rule Generation (SRG) . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.3 Similarity-and-Merge-Based Rule Generation (SMRG) . . . . . . . . . . . . . . . . . . 40
2.3.1 Data Partitioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.3.2 ClusterMerge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.4 Fuzzy Rule Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.5 Conclusion and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3 Hybrid Learning Algorithm for Parameter Identification 53
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.2 Zero-Order TSK-Type Fuzzy Neural Networks . . . . . . . . . . . . . . . . . . . . . . 55
3.3 Hybrid Learning Algorithm (HLA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.3.1 Recursive SVD-Based Least Squares Estimator . . . . . . . . . . . . . . . . . . 57
3.3.2 Gradient DescentMethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.4 First-Order TSK-Type Fuzzy Neural Networks . . . . . . . . . . . . . . . . . . . . . . 66
3.5 Conclusion and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4 Performance and Comparison with Experiments 72
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.2 Examples of Function Approximation with Our Systems . . . . . . . . . . . . . . . . . 76
4.2.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.2.2 Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.3 Comparison on Structure Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.3.1 Experiment 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.3.2 Experiment 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.3.3 Experiment 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.4 Comparison on Parameter Identification . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.5 Comparison on SystemLevel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5 Segmentation of Human Objects in Video Streams 94
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.3 Segment Labeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.4 Face and Body Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.4.1 Face Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.4.2 Body Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.5 Human Object Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.5.1 Neural Network Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.5.2 Hybrid Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.5.3 Final Human Object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.6 Experimental Results and Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5.7 Conclusion and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
6 Conclusion and Future Work 128
6.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.2 FutureWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Bibliography 133

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