Sparse kernel logistic regression based on L 1/2 regularization

The sparsity driven classification technologies have attracted much attention in recent years, due to their capability of providing more compressive representations and clear interpretation. Two most popular classification approaches are support vector machines (SVMs) and kernel logistic regression (KLR), each having its own advantages. The sparsification of SVM has been well studied, and many sparse versions of 2-norm SVM, such as 1-norm SVM (1-SVM), have been developed. But, the sparsification of KLR has been less studied. The existing sparsification of KLR is mainly based on L ₁ norm and L ₂ norm penalties, which leads to the sparse versions that yield solutions not so sparse as it should be. A very recent study on L _1/2 regularization theory in compressive sensing shows that L _1/2 sparse modeling can yield solutions more sparse than those of 1 norm and 2 norm, and, furthermore, the model can be efficiently solved by a simple iterative thresholding procedure. The objective function dealt with in L _1/2 regularization theory is, however, of square form, the gradient of which is linear in its variables (such an objective function is the so-called linear gradient function). In this paper, through extending the linear gradient function of L _1/2 regularization framework to the logistic function, we propose a novel sparse version of KLR, the 1/2 quasi-norm kernel logistic regression (1/2-KLR). The version integrates advantages of KLR and L _1/2 regularization, and defines an efficient implementation scheme of sparse KLR. We suggest a fast iterative thresholding algorithm for 1/2-KLR and prove its convergence. We provide a series of simulations to demonstrate that 1/2-KLR can often obtain more sparse solutions than the existing sparsity driven versions of KLR, at the same or better accuracy level. The conclusion is also true even in comparison with sparse SVMs (1-SVM and 2-SVM). We show an exclusive advantage of 1/2-KLR that the regularization parameter in the algorithm can be adaptively set whenever the sparsity (correspondingly, the number of support vectors) is given, which suggests a methodology of comparing sparsity promotion capability of different sparsity driven classifiers. As an illustration of benefits of 1/2-KLR, we give two applications of 1/2-KLR in semi-supervised learning, showing that 1/2-KLR can be successfully applied to the classification tasks in which only a few data are labeled.     

Numerical approximation of solution of nonhomogeneous backward heat conduction problem in bounded region

In this paper we consider a numerical approximation of solution of nonhomogeneous backward heat conduction problem (BHCP) in bounded region based on Tikhonov regularization method. Error estimate at t=0$t=0$ for this method is provided. According to the error estimate, a selection of regularization parameter is given. Meanwhile, a numerical implementation is described and the numerical results show that our algorithm is effective.     

Over-Parameterized Variational Optical Flow

A novel optical flow estimation process based on a spatio-temporal model with varying coefficients multiplying a set of basis functions at each pixel is introduced. Previous optical flow estimation methodologies did not use such an over parameterized representation of the flow field as the problem is ill-posed even without introducing any additional parameters: Neighborhood based methods of the Lucas–Kanade type determine the flow at each pixel by constraining the flow to be described by a few parameters in small neighborhoods. Modern variational methods represent the optic flow directly via the flow field components at each pixel. The benefit of over-parametrization becomes evident in the smoothness term, which instead of directly penalizing for changes in the optic flow, accumulates a cost of deviating from the assumed optic flow model. Our proposed method is very general and the classical variational optical flow techniques are special cases of it, when used in conjunction with constant basis functions. Experimental results with the novel flow estimation process yield significant improvements with respect to the best results published so far.     

基于遗传算法和广义交叉原理求解正则参数

本文研究了正则化方法中正则参数的求解问题,提出了一种新的正则参数求解策略,即利用遗传算法基于广义交叉检验准则求解正则参数,数值模拟验证了该方法的可行性和有效性。     

原对偶积极集法求解改进的有界约束图像恢复问题

为了提高模糊加噪声图像的恢复质量,提出了一种用于图像恢复处理的改进的带约束的正则化模型。该模型首先利用Levine等人提出的变指数、线性增长函数作为正则项,并根据图像局部特征选择合适的正则参数,这样既保留了总变差正则化方法在恢复图像边缘方面的优势,又减少了梯子现象;其次,为进一步提高恢复图像的质量,在此基础上再添加有界约束条件,如将灰度值固定在某范围内,以形成约束优化问题。由于它的求解相对复杂,为此可应用原对偶积极集法求解,其实质就是用半光滑Newton法来求解由约束优化问题转化所得到的方程组。数值实验表明,此方法是可行的和有效的。     

The anti-reflective algebra: structural and computational analysis with application to image deblurring and denoising

Anti-reflective (AR) boundary conditions (BC) have been introduced recently in connection with fast deblurring algorithms, both in the case of signals and images. Here we extend such BCs to d dimensions (d ≥ 1) and we study in detail the algebra induced by the AR-BCs, with strongly symmetric point spread functions (PSF), both from a structural and computational point of view. The use of the re-blurring idea and the computational features of the AR-algebra allow us to apply Tikhonov-like techniques within O(n ^d log(n)) arithmetic operations, where n ^d is the number of pixels of the reconstructed object. Extensive numerical experimentation concerning 2D images and strongly symmetric PSFs confirms the effectiveness of our proposal.      

图像恢复的正则化混合GMRES(m)方法

为了充分利用广义极小化残量方法在处理大规模线性问题时的优势,将其同正则化技术相结合应用于图像恢复领域,提出了一种新的图像恢复方法。该方法基于Arnoldi过程,用一系列规模远小于原不适定问题的最小二乘问题来逼近原问题,并应用截断奇异值分解正则化技术保证稳定求解这些最小二乘问题。其中,根据图像恢复问题的具体特点,在确定截断奇异值分解的截断次数时,对传统的L-曲线准则进行了少许修改。数值试验结果表明,试验数据与肉眼观察恢复图像的清晰程度相吻合,说明新方法是有效的。     

基于人脸关键特征提取的表情识别

自然场景下人脸表情由于受遮挡、光照等因素影响,以及表情局部变化细微,导致现有人脸表情识别方法准确率较低。提出一种人脸表情识别的新方法,以ResNet18为主干网络,利用残差连接模块加深网络结构,以提取更多深层次的表情特征。通过引入裁剪掩码模块,在训练集图像上的某个区域进行掩码,向训练模型中增加遮挡等非线性因素,提升模型在遮挡情形下的鲁棒性。分别从特征图的通道和空间两个维度提取表情的关键特征,并分配更多的权重给表情变化明显的特征图,同时抑制非表情特征。在特征图输出前加入Dropout正则化策略,通过在训练中随机失活部分神经元,达到集成多个网络模型的训练效果,提升模型泛化能力。实验结果表明,与L2-SVMs、IcRL、DLP-CNN等方法相比,该方法有效提高了表情识别准确率,在2个公开表情数据集Fer2013和RAF-DB上的识别准确率分别为74.366%和86.115%。     

稀疏约束的时空正则相关滤波无人机视觉跟踪

目的 基于相关滤波的跟踪算法在无人机(unmanned aerial vehicle,UAV)视觉跟踪领域表现出卓越的性能。现有的相关滤波类跟踪算法从样本区域的所有特征中学习滤波器,然而某些来自遮挡或形变的特征可能会污染滤波器,降低模型判别能力。针对此问题,提出一种稀疏约束的时空正则相关滤波跟踪算法。方法 在相关滤波目标函数上施加空间弹性网络约束以自适应地抑制跟踪过程中的干扰特征,同时集成空间—时间正则相关滤波算法(spatial-temporal regularized correlation filter,STRCF)中的时间正则项以增强滤波器抑制畸变的能力。采用交替方向乘子法(alternating direction method of multipliers,ADMM)将带有约束项的目标函数转化为两个具有闭式解的子问题迭代求局部最优解。此外,提出一种相关滤波框架通用的加速策略,根据当前帧的目标位移量,对检测定位阶段的特征矩阵进行等距离的循环移位,将其作为在线学习阶段的特征矩阵,每帧可节省一次训练样本的特征提取操作,提高跟踪速度。结果 在3个UAV数据集上与14种主流跟踪算法进...     

基于Hessian图正则稀疏NMF的高光谱解混

基于非负矩阵分解(Nonnegative Matrix Factorization, NMF)的高光谱解混(Hyperspectral Unmixing,HU)方法引起了大家的关注,因为可以将一个非负高光谱图像(Hyperspectral Imagery, HSI)数据矩阵分解为两个非负矩阵的乘积,分别对应于端元矩阵和丰度系数矩阵。目前,图约束的NMF算法已经被证明对高光谱解混是有效的,因为它们可以捕获HSI的几何特性。为了挖掘数据在混合过程中的几何结构和稀疏性,提出了一种稀疏的Hessian图正则化NMF(SHGNMF)算法。SHGNMF算法是将丰度矩阵的L1/2正则化器和Hessian图正则化项都添加到每个NMF模型中,同时采用乘法更新规则。最后用模拟数据和真实数据进行实验,验证了所提出的SHGNMF算法相对于其他NMF算法的优越性。