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薩摩亞文翻譯

方式錯誤謬誤1.2：Additionally, since the criterion does not attempt to minimize the withinclass variation, the resulting classes may tend to have more overlap than other approaches. Thus翻譯社 the projection vectors chosen for optimal reconstruction may obscure the existence of the separate classes.

作法：In this method, all image samples are first projected onto the null space of SW, resulting in a new within-class scatter that is a zero matrix. Then, PCA is applied to the projected samples to obtain the optimal projection vectors.

方法描寫：This method uses the simultaneous diagonalization method [8]. First, the null space of SB is removed and, then, the projection vectors that minimize the within-class scatter in the transformed space are selected from the range space of SB.

方式3.1和3.2的錯誤謬誤：Although, the PCA+Null Space method and the variation proposed by Yang et al., use the original sample space, applying PCA and using all eigenvectors corresponding to the nonzero eigenvalues make these methods impractical for face recognition applications when the training set size is large. This is due to the fact that the computational expense of training becomes very large.

In Section 2, the Discriminative Common Vector approach is introduced. In Section 3, we describe the data sets and experimental results. Finally翻譯社 we formulate our conclusions in Section 4.

方式2：這個方式與前面的方式有關，它是為了改善方式1的瑕玷來的；基本上，若是你有兩類的方法，你要交代這兩類方法分歧的地方在那裡。
The Linear Discriminant Analysis (LDA) method is proposed in [6] and [7]. （這裡用現在式有點不太准確，我會建議用曩昔式，因為這兩篇論文的提出已曩昔了。）

這篇文章的導論一開始講利用，上面的敘述比較一般化，後面的論述將局限縮小：A more challenging class of application imagery includes real-time detection and recognition of faces in surveillance video images翻譯社 which present additional constraints in terms of speed and processing requirements [1].

起：問題描寫

However, they did not propose an efficient algorithm for applying this method in the original sample space. Instead翻譯社 a pixel grouping method is applied to extract geometric features and reduce the dimension of the sample space. Then, they applied the Null Space method in this new reduced space.

再轉：

轉：研究的必要性，既然有了一些相幹研究，那為什麼翻譯公司還要做這個研究翻譯

It is a difficult problem as there are numerous factors such as 3D pose翻譯社 facial expression, hair style翻譯社 make up, etc.翻譯社 which affect the appearance of an individual’s facial features. In addition to these varying factors翻譯社 lighting, background翻譯社 and scale changes make this task even more challenging. Additional problematic conditions include noise, occlusion, and many other possible factors.

方式2的問題：In face recognition tasks翻譯社 this method cannot be applied directly since the dimension of the sample space is typically larger than the number of samples in the training set. As a consequence, SW is singular in this case. This problem is also known as the “small sample size problem” [8].

一些觀察：In our experiments, we observed that the performance of the Null Space method depends on the dimension of the null space of SW in the sense that larger dimension provides better performance. Thus, any kind of preprocessing that reduces the original sample space should be avoided.

方式描述：In this method, at first, PCA is applied to remove the null space of ST 翻譯社 which contains the intersection of the null spaces of SB and SW. Then, the optimal projection vectors are found in the remaining lowerdimensional space by using the Null Space method. The difference between the Fisherface method and the PCA+Null Space method is that for the latter, the within-class scatter matrix in the reduced space is typically singular. This occurs because all eigenvectors corresponding to the nonzero eigenvalues of ST are used for dimension reduction.

面部辨識為什麼很艱巨，它們受到哪些身分的影響：This task is complex and can be decomposed into the smaller steps of detection of faces in a cluttered background, localization of these faces followed by extraction of features from the face regions翻譯社 and, finally翻譯社 recognition and verification [2].

承：相幹研究─
Many methods have been proposed for face recognition within the last two decades [1]翻譯社 [3]. （提出什麼方法都用現在完成式來表達）

承：相幹研究，具體的申明這個問題的領域有兩些相關的研究翻譯你可以將相幹研究分成兩或三大類（有需要的話，大類還可以，再分一級），然後每大類約略的依年代介紹相幹研究的方法和它們可能的缺點。

本研究的限制：Thus, the proposed method can be only used when the dimension of the sample space is larger than the rank of SW.

其他改良2：Chen et al. also proved that by applying this method, the modified Fisher’s Linear Discriminant criterion attains its maximum.

The remainder of the paper is organized as follows: （這一句話是科技陳腔濫調，照著寫就對了；也請注意標點符號。）

合：研究目的（Purpose)翻譯社用很明確的文字界說你的研究目的，有時也能夠再加上對自己方式價值的評議。

方式2的相幹研究論文四篇：In the last decade numerous methods have been proposed to solve this problem, Tian et al. [9] used the Pseudoinverse method by replacing ... with its pseudoinverse. The Perturbation method is used in [2] and [10]翻譯社 where a small perturbation matrix  is added to SW in order to make it nonsingular. Cheng et al. [11] proposed the Rank Decomposition method based on successive eigendecompositions of the total scatter matrix ST and the between-class scatter matrix SB.

針對上面錯誤謬誤的改善：However, in order to make SW nonsingular翻譯社 some directions corresponding to the small eigenvalues of ST are thrown away in the PCA step. Thus, applying PCA for dimensionality reduction has the potential to remove dimensions that contain discriminative information [12], [13]翻譯社 [14]翻譯社 [15], [16]. Chen et al. [17] proposed the Null Space method based on the modified Fisher’s Linear Discriminant criterion（數學式子，省略）This method has been proposed to be used when the dimension of the sample space is larger than the rank of the within-class scatter matrix SW.

方式的缺點：However, removing the null space of SB by dimensionality reduction will also remove part of the null space of SW and may result in the loss of important discriminative information [13], [15], [16]. Furthermore, SB is whitened as a part of this method. This whitening process can be shown to be redundant and, therefore, should be skipped.（講方法的弱點就是為了「轉」到自己的研究翻譯）

轉：研究的必要性

下面開始界說手藝問題：Face recognition can be defined as the identification of individuals from images of their faces by using a stored database of faces labeled with people’s identities.

相幹方法出來了：Among these methods, appearance-based approaches operate directly on images or appearances of face objects, and process the images as two-dimensional holistic patterns. In these approaches翻譯社 a two-dimensional image of size w by h pixels is represented by a vector in a wh-dimensional space. Therefore翻譯社 each facial image corresponds to a point in this space. This space is called the sample space or the image space, and its dimension typically is very high [4]. 注意：對這些方式的描寫全部用現在式，這是因為這些方式現在進行也是如許（事實）翻譯

起：問題描寫，從遠到近交代你的論文要解問題的範疇。

一篇學術論文除了摘要給人的第一個感覺很主要外，第一章的導論部門可能也是決意翻譯公司這篇論文會不會被接受的關頭，良多人一樣的要把導論留到最後寫，萬國翻譯公司的建議是一開始就要寫，寫完就交給指點傳授改，因為在導論中，問題的界說已經出來，對問題的約略走向也已約略的講清楚翻譯大部門寫科技論文的學生對方式的描寫、實驗的進行、資料的闡發等可能比力沒有問題，但要整理出一篇學術論文可能會有障礙，這部分要和指導傳授多溝通幾回。

合：研究目標

方式3.2：Yang et al. applied a variation of this method in [16]. After dimension reduction, they split the new within-class scatter matrix翻譯社 ... (where PPCA is the matrix whose columns are the orthonormal eigenvectors corresponding to the nonzero eigenvalues of ST ), into its null space .... Then, all the projection vectors that maximize the betweenclass scatter in the null space are chosen. If, according to some criterion, more projection vectors are needed, the remaining projection vectors are obtained from the range space.

方式弱點1.1：This method is an unsupervised technique since it does not consider the classes within the training set data. In choosing a criterion that maximizes the total scatter, this approach tends to model unwanted within-class variations such as those resulting from the differences in lighting, facial expression翻譯社 and other factors [6], [7].

下面我就用一篇2006年揭橥在IEEE trans. on Pattern Analysis and Machine Intelligence上面的一篇文章Discriminative Common Vectors for Face Recognition來跟大師做申明，因為這篇講「臉部辨識」的文章是長文，導論的部門有點長：

這一類方式會碰到的問題：However, since face images have similar structure翻譯社 the image vectors are correlated, and any image in the sample space can be represented in a lower-dimensional subspace without losing a significant amount of information.

再轉：對一篇完全的論文而言，導論是「起」，所以，一般的學位論文或期刊長文導論的最後一段還要再加上後面各章節的簡要描寫。

導論要怎麼寫？「起承轉合」這四個字倒可以幫你的論文導論建立一個架構：

其他改進1：It has been shown that the original Fisher’s Linear Discriminant criterion can be replaced by the modified Fisher’s Linear Discriminant criterion in the course of solving the discriminant vectors of the optimal set in [18].

回頭再「承」：

本想再剖析另外一篇論文的導論，但篇幅有點太長了，就此打住。要寫論文的人就按照上面起承轉合的四步寫法，找兩到三篇期刊論文來剖析一下，剖析一下每篇論文寫法的「同、異」，然後將之記錄下來，以後本身的寫作就會順遂的多。

方式2約略的描寫：This method overcomes the limitations of the Eigenface method by applying the Fisher’s Linear Discriminant criterion. This criterion tries to maximize the ratio（數學式子，省略）where SB is the between-class scatter matrix, and SW is the within-class scatter matrix.

方式2的特點/優點：Thus翻譯社 by applying this method, we find the projection directions that on one hand maximize the Euclidean distance between the face images of different classes and on the other minimize the distance between the face images of the same class. This ratio is maximized when the column vectors of the projection matrix W are the eigenvectors of ....

（後註：這一篇我整頓了兩個多小時喔。）

方式3.1：Another novel method, the PCA+Null Space method, was proposed by Huang et al. in [15] for dealing with the small sample size problem.

相幹研究的缺點：However, the above methods are typically computationally expensive since the scatter matrices are very large (e.g., images of size 256 by 256 yield scatter matrices of size 65翻譯社536 by 65,536). Swets and Weng [7] proposed a two stage PCA+LDA method翻譯社 also known as the Fisherface method, in which PCA is first used for dimension reduction so as to make SW nonsingular before the application of LDA.

RECENTLY, due to military翻譯社 commercial, and law enforcement applications, there has been much interest in automatically recognizing faces in still and video images. This research spans several disciplines such as image processing翻譯社 pattern recognition, computer vision, and neural networks. The data come from a wide variety of sources. One group of sources is the relatively controlled format images such as passports, credit cards翻譯社 photo IDs翻譯社 drivers’ licenses, and mug shots.

In this paper, a new method is proposed which addresses the limitations of other methods that use the null space of SW to find the optimal projection vectors.

方式4：Last, the Direct-LDA method is proposed in [12].

解決問題的方法1：The Eigenface method has been proposed for finding such a lowerdimensional subspace [5]. The key idea behind the Eigenface method翻譯社 which uses Principal Component Analysis (PCA), is to find the best set of projection directions in the sample space that will maximize the total scatter across all images such that （數學式子，省略）is maximized. Here, ST is the total scatter matrix of the training set samples, and W is the matrix whose columns are the orthonormal projection vectors. The projection directions are also called the eigenfaces. Any face image in the sample space can be approximated by a linear combination of the significant eigenfaces. The sum of the eigenvalues that correspond to the eigenfaces not used in reconstruction gives the mean square error of reconstruction.