本文選題：字典學(xué)習(xí) + 稀疏表示��； 參考：《哈爾濱工業(yè)大學(xué)》2017年博士論文

【摘要】：字典學(xué)習(xí)已被廣泛應(yīng)用于圖像處理、模式識別和計算機(jī)視覺等領(lǐng)域。判別字典學(xué)習(xí)是字典學(xué)習(xí)理論中一個重要的研究方向,其核心問題是如何設(shè)計判別式提高字典的判別性能。一般來說,判別式的設(shè)計可以分為兩類。第一類是利用訓(xùn)練樣本的特征結(jié)合編碼系數(shù)構(gòu)造判別式模型。但是,訓(xùn)練樣本易受光照和遮擋等因素的影響,導(dǎo)致訓(xùn)練樣本的特征與實際存在誤差,影響判別式的魯棒性,也降低了字典的判別性能。第二類是利用原子的自相關(guān)性特征設(shè)計判別式模型。雖然原子的自相關(guān)性特征具有一定的自適應(yīng)性,如果數(shù)據(jù)的結(jié)構(gòu)特征非線性的嵌入到高維空間中,基于原子自相關(guān)性特征約束的字典學(xué)習(xí)算法并不能真正地捕獲訓(xùn)練樣本的結(jié)構(gòu)特征,也會降低字典的判別性能。因此,如何設(shè)計魯棒的判別式模型,使字典盡可能地反映訓(xùn)練樣本的特征并具有較強的判別性能,是字典學(xué)習(xí)理論中的一個重要研究方向,也是本文的研究重點。本文利用編碼系數(shù)矩陣的行向量(profiles)和原子特征構(gòu)建基于魯棒判別式約束的字典學(xué)習(xí)模型,增強字典的判別性,提高字典學(xué)習(xí)算法的分類性能。利用原子構(gòu)建拉普拉斯圖表示它們的結(jié)構(gòu)特征,并在此基礎(chǔ)上利用流形學(xué)習(xí)理論構(gòu)建魯棒判別式模型,使其既能繼承訓(xùn)練樣本的結(jié)構(gòu)特征,又能保持原子的結(jié)構(gòu)和自相關(guān)性特征。此外,根據(jù)原子與profiles的一一對應(yīng)關(guān)系,構(gòu)建基于profiles的Fisher判別和局部結(jié)構(gòu)特征約束的判別式模型,增強字典的判別性能。本文提出的基于魯棒判別式約束的字典學(xué)習(xí)模型能在一定程度上解決判別字典學(xué)習(xí)算法中存在著判別式的魯棒性和自適應(yīng)性差以及字典判別性不強等問題。具體地說,本文的主要研究內(nèi)容概括如下:(1)根據(jù)profiles的定義,給出其在理想字典學(xué)習(xí)模型中的描述,使得抽象的profiles更加直觀和易于理解,并建立原子與profiles間的對應(yīng)關(guān)系。利用理想情況下的字典學(xué)習(xí)模型推導(dǎo)出原子與profiles間的相似性關(guān)系。此外,本章還給出訓(xùn)練樣本、編碼系數(shù)、原子和profiles間的類標(biāo)關(guān)系,并在此基礎(chǔ)上提出一種利用profiles自適應(yīng)地構(gòu)造原子類標(biāo)的方法。本章推導(dǎo)出的原子與profiles間的相似性定理以及原子類標(biāo)構(gòu)造方法,為設(shè)計魯棒判別式模型提供一定的理論和算法基礎(chǔ)。(2)提出一個基于自適應(yīng)局部特征約束的字典學(xué)習(xí)算法(Adaptive Locality Constrained Dictionary Learning,ALC-DL)。ALC-DL算法利用字典中的原子構(gòu)造拉普拉斯圖,使其能夠反映原子間的結(jié)構(gòu)特征;然后,利用profiles衡量原子間的相似性,并構(gòu)造基于自適應(yīng)局部特征約束的判別式模型,使其能夠繼承訓(xùn)練樣本的結(jié)構(gòu)特征。由于原子和profiles在字典學(xué)習(xí)中不斷的更新,基于自適應(yīng)局部特征約束的判別式模型具有一定的魯棒性。此外,本章還推導(dǎo)出基于原子局部特征約束的判別式與基于訓(xùn)練樣本局部特征約束的判別式間的關(guān)系。實驗結(jié)果表明ALC-DL算法比直接利用訓(xùn)練樣本的局部特征約束的字典學(xué)習(xí)算法取得更好的分類性能。(3)針對目前字典學(xué)習(xí)算法中沒有同時利用原子的局部特征和類標(biāo)的情況,提出一個基于原子局部特征和類標(biāo)嵌入約束的字典學(xué)習(xí)算法(Locality Constrained and Label Embedding Dictionary Learning,LCLE-DL)。首先,LCLE-DL算法利用特定類字典學(xué)習(xí)算法獲得原子類標(biāo),并利用原子類標(biāo)構(gòu)造原子類標(biāo)嵌入項,促使同類原子對應(yīng)的profiles相似;然后,結(jié)合原子的自適應(yīng)局部特征約束項設(shè)計雙重構(gòu)約束的字典學(xué)習(xí)算法,促使原子的局部特征與判別信息可以相互傳遞,增強判別式的魯棒性。為了使得基于原子局部特征約束的編碼系數(shù)和基于原子類標(biāo)約束的編碼系數(shù)盡可能的一致,利用2l范數(shù)對兩種編碼系數(shù)的差進(jìn)行約束,并能夠減少算法的復(fù)雜度。此外,本章還給出LCLE-DL算法與兩種類標(biāo)約束的字典學(xué)習(xí)算法的關(guān)系。實驗結(jié)果表明LCLE-DL算法比單獨利用類標(biāo)或局部特征約束的字典學(xué)習(xí)算法取得更好的分類性能。(4)提出基于profiles的Fisher判別和局部特征約束的字典學(xué)習(xí)算法(Fisher Discriminative and Locality Constraint Dictionary Learning,FDLC-DL)。在FDLC-DL算法中,利用Fisher判別準(zhǔn)則構(gòu)造基于profiles的判別式模型,使得同類原子對應(yīng)的profiles類內(nèi)散度盡可能的小,不同類原子對應(yīng)的profiles類間散度盡可能的大,增強編碼系數(shù)的判別性能。此外,在FDLC-DL算法中,利用profiles構(gòu)造拉普拉斯圖保持profiles的局部特征,并利用原子衡量profiles間的相似性,在此基礎(chǔ)上構(gòu)造基于profiles局部特征約束的判別式模型。由于profiles矩陣是編碼系數(shù)矩陣的轉(zhuǎn)置矩陣,因此,基于profiles的局部特征約束項也能增強編碼系數(shù)的判別性能。在字典學(xué)習(xí)過程中,profiles隨著字典學(xué)習(xí)不斷地更新,因此,FDLC-DL算法中的判別式也具有一定的魯棒性。為了減少算法的復(fù)雜度,FDLC-DL算法也利用2l范數(shù)對編碼系數(shù)進(jìn)行約束。此外,本章還給出FDLC-DL算法與其它兩種字典學(xué)習(xí)算法的關(guān)系。實驗結(jié)果表明FDLC-DL算法能夠有效地提高基于字典學(xué)習(xí)算法的分類性能。綜上所述,為了提高判別式的魯棒性,本文利用拉普拉斯圖、流形學(xué)習(xí)和Fisher判別準(zhǔn)則等方法,結(jié)合原子和profiles的特征,提出三種判別式模型,并成功的應(yīng)用于判別字典學(xué)習(xí)中。經(jīng)過大量的實驗證明本文提出的三種基于魯棒判別式約束的字典學(xué)習(xí)算法都有效地提高了模式分類的性能。
[Abstract]:Dictionary learning has been widely used in the fields of image processing, pattern recognition and computer vision. Discriminatory dictionary learning is an important research direction in dictionary learning theory. The core problem is how to design discriminant to improve the discriminant performance of dictionaries. Generally speaking, the design of discriminant can be divided into two categories. The first class is to use training. The characteristics of the sample are combined with the coding coefficients to construct a discriminant model. However, the training sample is easily affected by the factors such as illumination and occlusion, which leads to the error of the training sample and the actual existence, affects the robustness of the discriminant and the discriminant performance of the dictionary. The second kind is to design a discriminant model by using the autocorrelation characteristics of the original subunit. The autocorrelation feature of the atom has a certain adaptability. If the structural features of the data are embedded in the high dimensional space, the dictionary learning algorithm based on the autocorrelation characteristic of the atom can not really capture the structural features of the training samples, but also reduces the discriminant performance of the dictionary. Therefore, how to design a robust discriminant? The model, which makes the dictionary as much as possible to reflect the characteristics of the training samples and has strong discriminative performance, is an important research direction in the dictionary learning theory, and is also the focus of this paper. In this paper, the dictionary learning model based on robust discriminant constraint is constructed by using the line vector (Profiles) and the atomic characteristics of the coding coefficient matrix to enhance the character of the word. The discriminability of the dictionary improves the classification performance of the dictionary learning algorithm. Using the atomic construction Laplasse graph to represent their structural features, the robust discriminant model is constructed by the manifold learning theory, so that it can not only inherit the structural features of the training samples, but also maintain the structure and autocorrelation of the atoms. With the one-to-one correspondence between the sub and the profiles, the discriminant model based on the Fisher discrimination and the local structural feature constraint based on profiles is constructed to enhance the discriminant performance of the dictionary. The dictionary learning model based on the robust discriminant constraint can solve the discriminant robustness and self of the discriminant algorithm to a certain extent. In particular, the main contents of this paper are summarized as follows: (1) according to the definition of profiles, the description in the ideal dictionary learning model is given, which makes the abstract profiles more intuitive and easy to understand, and establishes the correspondence between the original and the profiles. The dictionary learning model derives the similarity relation between the atom and the profiles. In addition, this chapter gives the training sample, the coding coefficient, the class relation between the atom and the profiles. On this basis, a method of using profiles to construct the atomic class standard is proposed. The similarity theorem between the atom and the profiles is derived in this chapter. The subclass standard construction method provides a certain theoretical and algorithm basis for the design of robust discriminant model. (2) a dictionary learning algorithm (Adaptive Locality Constrained Dictionary Learning, ALC-DL).ALC-DL algorithm based on adaptive local feature constraints is proposed to use the atomic structure of the Laplasse graph in the dictionary to reflect the atom. The structural characteristics of the interatomic structure; then, using profiles to measure the similarity between atoms, and construct a discriminant model based on adaptive local feature constraints, so that they can inherit the structural features of the training samples. Because of the constant updating of the atom and the profiles in the dictionary learning, the discriminant model based on the adaptive local characteristic constraints has a certain degree. In addition, this chapter also derives the relationship between the discriminant based on the local characteristic constraints of the atom and the discriminant based on the local feature constraint based on the training sample. The experimental results show that the ALC-DL algorithm achieves better classification performance than the dictionary learning algorithm using the local feature constraint directly using the training sample. (3) for the current dictionary learning calculation. In the method, a dictionary learning algorithm (Locality Constrained and Label Embedding Dictionary Learning, LCLE-DL) is proposed, which is based on the local characteristics of the atom and the embedding constraint of the class standard. First, the LCLE-DL algorithm uses a specific class dictionary learning algorithm to obtain the atomic class standard and uses the original method. The subclass standard constructs the embedded term of the atomic class standard to promote the similarity of the profiles of the same atom. Then, the dictionary learning algorithm, which combines the adaptive local characteristic constraint of the atom, is designed to promote the local characteristics of the atom and the discriminant information to communicate with each other and enhance the robustness of the discriminant. In order to make the local feature based on the atom. The coding coefficients of the constraints and the coding coefficients based on the constraints of the atomic class are as consistent as possible. The 2l norm is used to restrain the difference between the two coding coefficients, and the complexity of the algorithm can be reduced. In addition, the relationship between the LCLE-DL algorithm and the dictionary learning algorithm with the two type constraint is also given. The experimental results show that the LCLE-DL algorithm is more than single. Dictionary learning algorithm that uses class or local feature constraints to achieve better classification performance. (4) a dictionary learning algorithm based on Fisher discrimination and local feature constraints (Fisher Discriminative and Locality Constraint Dictionary Learning, FDLC-DL) is proposed. In FDLC-DL algorithm, a Fisher discrimination criterion is used to construct a profiles based algorithm. The discriminant model of Les makes the corresponding profiles class as small as possible, and the divergence of the profiles classes corresponding to different classes of atoms is as large as possible and enhances the discriminant performance of the coding coefficients. In addition, in the FDLC-DL algorithm, the local characteristics of the profiles are preserved by the Laplasse graph, and the profile is used to measure the profile. Based on the similarity between S, a discriminant model based on profiles local feature constraints is constructed. Because the profiles matrix is the transposed matrix of the coding coefficient matrix, the local feature constraint based on the profiles can also enhance the discriminant performance of the coding coefficients. In the dictionary learning process, profiles is constantly updated with the dictionary learning, Therefore, the discriminant in the FDLC-DL algorithm also has a certain robustness. In order to reduce the complexity of the algorithm, the FDLC-DL algorithm also uses the 2l norm to restrain the coding coefficients. In addition, the relationship between the FDLC-DL algorithm and the other two kinds of dictionary learning algorithms is also given. The experimental results show that the FDLC-DL algorithm can effectively improve the lexicography based on the dictionary. In summary, in order to improve the robustness of the discriminant, in order to improve the robustness of the discriminant, this paper uses Laplasse graph, manifold learning and Fisher criterion, combined the characteristics of atomic and profiles, to propose three discriminant models, and successfully applied to discriminant dictionary learning. After a large number of experiments, three kinds of bases proposed in this paper have been proved. The dictionary learning algorithm with robust discriminant constraints effectively improves the performance of pattern classification.

【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2017
【分類號】：TP391.41;TP181

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