本文選題：維數(shù)約簡(jiǎn) + 譜聚類�。� 參考：《西安電子科技大學(xué)》2016年博士論文

【摘要】：近年來(lái),在很多實(shí)際問(wèn)題中,人們獲取的數(shù)據(jù)具有很高的維數(shù)。數(shù)據(jù)的高維性使得計(jì)算機(jī)對(duì)數(shù)據(jù)的處理越來(lái)越復(fù)雜,導(dǎo)致“維數(shù)災(zāi)難”的現(xiàn)象發(fā)生,另外數(shù)據(jù)的高維性也掩蓋了數(shù)據(jù)的內(nèi)在特性,使人們不便于發(fā)現(xiàn)其中的規(guī)律。如何從高維數(shù)據(jù)中挖掘出有效的數(shù)據(jù)信息并發(fā)現(xiàn)數(shù)據(jù)的低維本質(zhì)屬性已經(jīng)成為模式識(shí)別、應(yīng)用數(shù)學(xué)、計(jì)算機(jī)視覺(jué)等領(lǐng)域的研究者所關(guān)注的共同問(wèn)題。維數(shù)約簡(jiǎn)是人們處理這一問(wèn)題的有效方法。另外,譜聚類也是數(shù)據(jù)挖掘的一個(gè)重要手段。本文對(duì)譜聚類和維數(shù)約簡(jiǎn)方法進(jìn)行深入的研究,提出了一些新的有效的譜聚類和維數(shù)約簡(jiǎn)方法,并應(yīng)用于圖像分割和人臉識(shí)別中。本文的主要工作和創(chuàng)新成果如下：1.針對(duì)譜聚類算法對(duì)高斯核尺度參數(shù)敏感且該參數(shù)難以確定的缺陷,首先,利用核模糊C均值聚類算法進(jìn)行粗聚類,得到隸屬度向量構(gòu)成的劃分矩陣；其次,利用隸屬度向量的內(nèi)積,提出了一個(gè)無(wú)參數(shù)的核模糊相似度度量；最后,提出了一個(gè)基于核模糊相似度的譜聚類算法。實(shí)驗(yàn)結(jié)果表明,所提出的譜聚類算法不僅有效克服了算法對(duì)參數(shù)的敏感性,而且解決了高斯核尺度參數(shù)難以確定的問(wèn)題。2.針對(duì)傳統(tǒng)譜聚類算法中使用歐氏距離的相似性度量不適用于分布復(fù)雜數(shù)據(jù)及對(duì)參數(shù)敏感的問(wèn)題,利用測(cè)地線距離,設(shè)計(jì)了一種基于流形距離的相似度度量,有效改善了算法對(duì)參數(shù)的敏感性及對(duì)分布復(fù)雜數(shù)據(jù)的實(shí)用性。在此基礎(chǔ)上,針對(duì)譜映射空間K-均值聚類對(duì)初始聚類中心敏感、容易陷入局部最優(yōu)的問(wèn)題,提出了一個(gè)新的基于模擬退火的譜聚類方法,并將其應(yīng)用于圖像分割中。實(shí)驗(yàn)結(jié)果表明,所提出的新譜聚類算法不僅有效降低了算法對(duì)參數(shù)的敏感性,而且能有效避免算法陷入局部最優(yōu),改善了傳統(tǒng)譜聚類算法的性能。3.當(dāng)樣本規(guī)模較大時(shí),譜聚類方法復(fù)雜性過(guò)高、計(jì)算量大。針對(duì)此問(wèn)題,提出基于超像素的譜聚類方法。該算法首先通過(guò)超像素的方法預(yù)處理,用超像素代替原來(lái)單個(gè)的像素；然后利用本文已提出的基于核模糊相似度度量構(gòu)造加權(quán)無(wú)向圖；最后采用譜聚類算法進(jìn)行聚類,并將其應(yīng)用于圖像分割。所提方法大大降低了傳統(tǒng)譜聚類算法的復(fù)雜度,減少了計(jì)算量。實(shí)驗(yàn)表明,相比較傳統(tǒng)譜聚類方法,基于超像素的譜聚類方法獲得了更好的分割效果。4.針對(duì)判別稀疏鄰域保持嵌入(DSNPE)算法類間離散度構(gòu)造復(fù)雜的問(wèn)題,首先,通過(guò)保持平均臉的稀疏重構(gòu)關(guān)系,設(shè)置了新的類間離散度；然后,通過(guò)同時(shí)最大化類間離散度和最小化類內(nèi)緊湊度構(gòu)造維數(shù)約簡(jiǎn)的目標(biāo)函數(shù)；最后,提出了一種改進(jìn)的維數(shù)約簡(jiǎn)算法,并將其應(yīng)用于人臉識(shí)別。所提出算法不僅有效降低了DSNPE算法的復(fù)雜度,而且增強(qiáng)了類間判別力。人臉識(shí)別的仿真實(shí)驗(yàn)結(jié)果表明,相比較已有的其他算法,該算法具有較高的識(shí)別率。
[Abstract]:In recent years, in many practical problems, the data obtained by people have a high dimension.The high dimension of data makes the processing of data by computer more and more complex, which leads to the phenomenon of "dimensionality disaster". In addition, the high dimension of data also conceals the inherent characteristics of data, which makes it difficult for people to find the rules.How to mine effective data information from high-dimensional data and find the essential attributes of low-dimensional data has become a common concern of researchers in the fields of pattern recognition, applied mathematics, computer vision and so on.Dimension reduction is an effective method to deal with this problem.In addition, spectral clustering is also an important means of data mining.In this paper, spectral clustering and dimension reduction methods are deeply studied, and some new and effective spectral clustering and dimension reduction methods are proposed, which are applied to image segmentation and face recognition.The main work and innovative results of this paper are as follows: 1.Aiming at the limitation that spectral clustering algorithm is sensitive to Gao Si's kernel scale parameter and this parameter is difficult to determine, firstly, the kernel fuzzy C-means clustering algorithm is used for coarse clustering, and the partition matrix of membership vector is obtained.By using the inner product of membership degree vector, a nonparametric kernel fuzzy similarity measure is proposed. Finally, a spectral clustering algorithm based on kernel fuzzy similarity is proposed.The experimental results show that the proposed spectral clustering algorithm not only overcomes the sensitivity of the algorithm to the parameters, but also solves the problem of the difficult determination of Gao Si kernel scale parameters.To solve the problem that Euclidean distance is not suitable for distributed complex data and sensitive to parameters in traditional spectral clustering algorithm, a similarity measure based on manifold distance is designed by using geodesic distance.The sensitivity of the algorithm to the parameters and the practicability of the distributed complex data are improved effectively.On this basis, a new spectral clustering method based on simulated annealing is proposed to solve the problem that K-means clustering in spectral mapping space is sensitive to the center of initial clustering and is prone to fall into local optimal condition, and it is applied to image segmentation.Experimental results show that the proposed new spectral clustering algorithm not only effectively reduces the sensitivity of the algorithm to the parameters, but also effectively avoids the algorithm falling into local optimum, and improves the performance of the traditional spectral clustering algorithm.When the sample size is large, the complexity of the spectral clustering method is too high and the computation is large.To solve this problem, a spectral clustering method based on hyperpixel is proposed.The algorithm uses super-pixel preprocessing method to replace the original single pixel, and then constructs weighted undirected graph based on kernel fuzzy similarity measure proposed in this paper. Finally, spectral clustering algorithm is used to cluster.It is applied to image segmentation.The proposed method greatly reduces the complexity and computational complexity of the traditional spectral clustering algorithm.The experimental results show that compared with the traditional spectral clustering method, the spectral clustering method based on super-pixel has better segmentation effect.In order to solve the complex problem of discriminating the discrete degree between classes of sparse neighborhood preserving embedding (DSNPE) algorithm, firstly, by maintaining the sparse reconstruction relation of the average face, a new inter-class dispersion is set up.The objective function of dimension reduction is constructed by simultaneously maximizing inter-class dispersion and minimizing intra-class compactness. Finally, an improved dimension reduction algorithm is proposed and applied to face recognition.The proposed algorithm not only reduces the complexity of the DSNPE algorithm, but also enhances the discriminant power between classes.The simulation results of face recognition show that compared with other existing algorithms, this algorithm has a higher recognition rate.
【學(xué)位授予單位】：西安電子科技大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：TP311.13

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