人脸识别中基于流形学习的子空间特征提取方法研究
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摘要
特征提取是模式识别中最基本的问题之一。在人脸识别中,提取有效的鉴别特征是实现人脸准确识别的一个关键因素。由于人脸空间被认为是嵌入高维的外围空间中的低维流形,与人脸类别有关的特征信息就存在这个流形中,所以许多子空间特征提取方法采用流形学习来发现人脸模式的内蕴结构。本文对基于流形学习的子空间特征提取方法进行了研究,论文的主要工作和贡献体现在以下几个方面:
1.针对线性局部切空间排列没有利用人脸样本的类别信息,提取的特征有冗余,而且不能保持高维数据空间测度的问题,利用类别信息,同时根据谱回归理论,提出了使用岭回归技术的判别的线性局部切空间排列。在此基础上,引入正交变换,提出了正交判别的线性局部切空间排列,降低了算法复杂度,解决了测度保持问题。
2.当人脸特征维数远远大于样本数目时,一般线性子空间方法学习得到的嵌入子空间非光滑且不能获得稀疏解。针对这种情况,使用空间光滑正则化和稀疏化技术,将正单纯形的顶点作为映射目标,采用弹性网络建立映射关系,提出了稀疏光滑的临界费舍尔分析算法,解决了反映最强信息的最小特征子集的选择问题。
3.针对局部敏感判别分析只能处理向量类型的数据,不能保持图像像素间的空间信息,并且容易造成奇异性问题,提出了张量局部判别投影。提出的算法归结为迭代求解广义特征向量问题来求取张量子空间的两个变换矩阵,从而在水平和垂直方向消除图像行和列的相关性,而且压缩了特征维数,保持了图像空间信息的完整性。
4.当人脸特征呈现高度非线性分布时,线性子空间方法很难提取出有效的人脸特征。将核映射的思想和邻域保持最大间距分析相结合,提出了核邻域保持最大间距分析,然后使用核岭回归技术,提出了核岭回归的邻域保持最大间距分析,克服了非线性特征提取的困难,较好地保持了人脸流形的几何结构和判别结构信息。
在图嵌入框架下,对本文提出的算法进行了分析和比较,表明了提出的算法具有相应的图嵌入扩展方式和适用性。
Feature extraction is one of the most elementary problems in the area of pattern recognition. It is a critical factor to extract effectively discriminant features for face recognition. As face space is always believed to be a low-dimensional submanifold embedded in high-dimensional ambient space, many methods of subspace feature extraction adopt manifold learning to explore intrinsic structure of face patterns. This dissertation mainly deals with methods of subspace feature extraction based on manifold learning, and the main work and contributions are presented in the following aspects:
1. Linear local tangent space alignment does not make use of class information of face samples and the extracted features are redundant, moreover, it can not maintain the measure of high-dimensional data space. Discriminant linear local tangent space alignment using ridge regression is proposed, which takes advantage of class information and spectral regression theory. On this basis, orthogonal discriminant linear local tangent space alignment is proposed with introduction of orthogonalization, which reduces algorithm complexity and maintains the measure.
2. When the number of facial feature dimensions is much larger than the number of face samples, the subspace learned from the common linear subspace is not smooth and sparse solutions can not be obtained. To address this situation, a algorithm named sparsely and smoothly marginal fisher analysis is proposed, which adopots spatially smoothly and sparsely regularized techniques and chooses the vertices of regular simplex as the mapped targets, then uses elastic net to construct mapped relationship, at last the smallest feature subset which reflects the best information can be obtained.
3. Locality sensitive discriminant analysis can only handle vector-based data, which can not preserve spatial information of image pixels and easily leads to singular problem. Tensor local discriminant projection is proposed to resolve the case, and the actual computation of the algorithm is reduced to a generalized eigenvalue problem to gain two transformation matrices of tensor subspace. The proposed algorithm eliminates the relevance of rows and columns from horizontal and vertical directions, compresses feature dimensions and preserves the integrity of spatial information of the images.
4. When facial features are highly nonlinear distributed, linear subspace methods are difficult to extract effectively facial features. Combing the idea of kernel mapping and neighborhood preserving maximal margin analysis, kernel neighborhood preserving maximal margin analysis is proposed, then neighborhood preserving maximal margin analysis using kernel ridge regression is proposed which overcomes the difficulty of extracting nonlinear features and preserves information of geometrical and discriminant structure of face manifold.
In the framework of graph embedding, it shows that the proposed algorithms have correspondingly extensional type of graph embedding and applicability.
1.针对线性局部切空间排列没有利用人脸样本的类别信息,提取的特征有冗余,而且不能保持高维数据空间测度的问题,利用类别信息,同时根据谱回归理论,提出了使用岭回归技术的判别的线性局部切空间排列。在此基础上,引入正交变换,提出了正交判别的线性局部切空间排列,降低了算法复杂度,解决了测度保持问题。
2.当人脸特征维数远远大于样本数目时,一般线性子空间方法学习得到的嵌入子空间非光滑且不能获得稀疏解。针对这种情况,使用空间光滑正则化和稀疏化技术,将正单纯形的顶点作为映射目标,采用弹性网络建立映射关系,提出了稀疏光滑的临界费舍尔分析算法,解决了反映最强信息的最小特征子集的选择问题。
3.针对局部敏感判别分析只能处理向量类型的数据,不能保持图像像素间的空间信息,并且容易造成奇异性问题,提出了张量局部判别投影。提出的算法归结为迭代求解广义特征向量问题来求取张量子空间的两个变换矩阵,从而在水平和垂直方向消除图像行和列的相关性,而且压缩了特征维数,保持了图像空间信息的完整性。
4.当人脸特征呈现高度非线性分布时,线性子空间方法很难提取出有效的人脸特征。将核映射的思想和邻域保持最大间距分析相结合,提出了核邻域保持最大间距分析,然后使用核岭回归技术,提出了核岭回归的邻域保持最大间距分析,克服了非线性特征提取的困难,较好地保持了人脸流形的几何结构和判别结构信息。
在图嵌入框架下,对本文提出的算法进行了分析和比较,表明了提出的算法具有相应的图嵌入扩展方式和适用性。
Feature extraction is one of the most elementary problems in the area of pattern recognition. It is a critical factor to extract effectively discriminant features for face recognition. As face space is always believed to be a low-dimensional submanifold embedded in high-dimensional ambient space, many methods of subspace feature extraction adopt manifold learning to explore intrinsic structure of face patterns. This dissertation mainly deals with methods of subspace feature extraction based on manifold learning, and the main work and contributions are presented in the following aspects:
1. Linear local tangent space alignment does not make use of class information of face samples and the extracted features are redundant, moreover, it can not maintain the measure of high-dimensional data space. Discriminant linear local tangent space alignment using ridge regression is proposed, which takes advantage of class information and spectral regression theory. On this basis, orthogonal discriminant linear local tangent space alignment is proposed with introduction of orthogonalization, which reduces algorithm complexity and maintains the measure.
2. When the number of facial feature dimensions is much larger than the number of face samples, the subspace learned from the common linear subspace is not smooth and sparse solutions can not be obtained. To address this situation, a algorithm named sparsely and smoothly marginal fisher analysis is proposed, which adopots spatially smoothly and sparsely regularized techniques and chooses the vertices of regular simplex as the mapped targets, then uses elastic net to construct mapped relationship, at last the smallest feature subset which reflects the best information can be obtained.
3. Locality sensitive discriminant analysis can only handle vector-based data, which can not preserve spatial information of image pixels and easily leads to singular problem. Tensor local discriminant projection is proposed to resolve the case, and the actual computation of the algorithm is reduced to a generalized eigenvalue problem to gain two transformation matrices of tensor subspace. The proposed algorithm eliminates the relevance of rows and columns from horizontal and vertical directions, compresses feature dimensions and preserves the integrity of spatial information of the images.
4. When facial features are highly nonlinear distributed, linear subspace methods are difficult to extract effectively facial features. Combing the idea of kernel mapping and neighborhood preserving maximal margin analysis, kernel neighborhood preserving maximal margin analysis is proposed, then neighborhood preserving maximal margin analysis using kernel ridge regression is proposed which overcomes the difficulty of extracting nonlinear features and preserves information of geometrical and discriminant structure of face manifold.
In the framework of graph embedding, it shows that the proposed algorithms have correspondingly extensional type of graph embedding and applicability.
引文
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