Semi‐supervised classification of facial expression using a mixture of multivariate t distributions

Abstract: This paper addresses the semi‐supervised classification of facial expression images using a mixture of multivariate t distributions. The facial expression features are first extracted into labelled graph vectors using the Gabor wavelet transformation. We then learn a mixture of multivariate t distributions by using the labelled graph vectors, and set correspondence between the component distributions and the basic facial emotions. According to this correspondence, the classification of a given testing image is implemented in a probabilistic way according to its fitted posterior probabilities of component memberships. Specifically, we perform hard classification of the testing image by assigning it into an emotional class that the corresponding mixture component has the highest posterior probability, or softly use the posterior probabilities as the estimates of the semantic ratings of expressions. The experimental results on the Japanese female facial expression database, Ekman's Pictures of Facial Affect database and the AR database demonstrate the effectiveness of the proposed method.     

Combining Generative and Discriminative Models in a Framework for Articulated Pose Estimation

We develop a method for the estimation of articulated pose, such as that of the human body or the human hand, from a single (monocular) image. Pose estimation is formulated as a statistical inference problem, where the goal is to find a posterior probability distribution over poses as well as a maximum a posteriori (MAP) estimate. The method combines two modeling approaches, one discriminative and the other generative. The discriminative model consists of a set of mapping functions that are constructed automatically from a labeled training set of body poses and their respective image features. The discriminative formulation allows for modeling ambiguous, one-to-many mappings (through the use of multi-modal distributions) that may yield multiple valid articulated pose hypotheses from a single image. The generative model is defined in terms of a computer graphics rendering of poses. While the generative model offers an accurate way to relate observed (image features) and hidden (body pose) random variables, it is difficult to use it directly in pose estimation, since inference is computationally intractable. In contrast, inference with the discriminative model is tractable, but considerably less accurate for the problem of interest. A combined discriminative/generative formulation is derived that leverages the complimentary strengths of both models in a principled framework for articulated pose inference. Two efficient MAP pose estimation algorithms are derived from this formulation; the first is deterministic and the second non-deterministic. Performance of the framework is quantitatively evaluated in estimating articulated pose of both the human hand and human body. Most of this work was done while the first author was with Boston University.     

Semi-parametric nonlinear regression and transformation using functional networks

Functional networks are used to solve some nonlinear regression problems. One particular problem is how to find the optimal transformations of the response and/or the explanatory variables and obtain the best possible functional relation between the response and predictor variables. After a brief introduction to functional networks, two specific transformation models based on functional networks are proposed. Unlike in neural networks, where the selection of the network topology is arbitrary, the selection of the initial topology of a functional network is problem driven. This important feature of functional networks is illustrated for each of the two proposed models. An equivalent, but simpler network may be obtained from the initial topology using functional equations. The resultant model is then checked for uniqueness of representation. When the functions specified by the transformations are unknown in form, families of linear independent functions are used as approximations. Two different parametric criteria are used for learning these functions: the constrained least squares and the maximum canonical correlation. Model selection criteria are used to avoid the problem of overfitting. Finally, performance of the proposed method are assessed and compared to other methods using a simulation study as well as several real-life data.     

Threshold Extraction Framework for Software Metrics

Software metrics are used to measure different attributes of software. To practically measure software attributes using these metrics, metric thresholds are needed. Many researchers attempted to identify these thresholds based on personal experiences. However, the resulted experience-based thresholds cannot be generalized due to the variability in personal experiences and the subjectivity of opinions. The goal of this paper is to propose an automated clustering framework based on the expectation maximization (EM) algorithm where clusters are generated using a simplified 3-metric set (LOC, LCOM, and CBO). Given these clusters, different threshold levels for software metrics are systematically determined such that each threshold reflects a specific level of software quality. The proposed framework comprises two major steps:the clustering step where the software quality historical dataset is decomposed into a fixed set of clusters using the EM algorithm, and the threshold extraction step where thresholds, specific to each software metric in the resulting clusters, are estimated using statistical measures such as the mean (μ) and the standard deviation (σ) of each software metric in each cluster. The paper's findings highlight the capability of EM-based clustering, using a minimum metric set, to group software quality datasets according to different quality levels.     

基于压缩感知的期望最大化贝努利非对称高斯近似信息传递算法

期望最大化贝努利高斯(BG)近似信息传递(EM-BG-AMP)算法中的BG模型因为具有对称性,在逼近实际信号先验分布时会受到限制;而期望最大化高斯混合近似信息传递(EM-GM-AMP)算法中的GM模型是BG模型的高阶形式,复杂度较高。为了解决以上问题,提出贝努利不对称高斯模型(BAG),进而推导得到期望最大化贝努利不对称高斯近似信息传递(EM-BAG-AMP)算法。该算法的主要思路是假设输入信号服从BAG模型,然后使用广义近似信息传递(GAMP)重构信号并在算法迭代中同时更新模型参数。实验证明,在处理不同图像数据时,EM-BAG-AMP和EM-BG-AMP相比,时间增加了1.2%,峰值信噪比(PSNR)值提升了0.1~0.5 dB,尤其在处理纹理较少以及色差变化明显的图像时峰值信噪比(PSNR)值提升了0.4~0.5 dB。EM-BAG-AMP是对EM-BG-AMP算法的扩展和延伸,更适合实际信号的处理。     

基于EM的直方图逼近及其应用

由于直方图一般是图像灰度或者其他分量的统计信息,因此分析图像的直方图是图像处理中的一个实用方法。直方图逼近是直方图分析方法之一,一般利用若干高斯分布函数来对直方图进行逼近。如何得到各个高斯分布函数的参数是问题的难点,解决此问题的一条途径把直方图逼近问题转化为统计学中的混合模型参数估计问题。文章首先采用EM(数学期望最大化)方法解决了这个问题,然后介绍了基于EM的直方图逼近方法在最优阈值化、直方图成份分析方面的应用。     

A Probabilistic Approach to Concurrent Mapping and Localization for Mobile Robots

This paper addresses the problem of building large-scale geometric maps of indoor environments with mobile robots. It poses the map building problem as a constrained, probabilistic maximum-likelihood estimation problem. It then devises a practical algorithm for generating the most likely map from data, along with the most likely path taken by the robot. Experimental results in cyclic environments of size up to 80 by 25 meter illustrate the appropriateness of the approach.     

热含量不变量的SAR图像点特征变化检测

针对区域变化检测受分类器精度影响大、无法探测出内部细微变化这一问题,本文提出了基于热含量不变量的合成孔径雷达（Synthetic aperture radar,SAR）图像点特征变化检测.该方法利用热核特征,具有计算简便、矩阵扰动性小的特点,且有效地降低了噪声的干扰.由热核不变量的统计特性,采用期望极大化（Expectation maximization,EM）算法解决了SAR图像的自动变化检测.同时通过对权的讨论,给出了适用于SAR图像的权函数定义.对单波段单极化SAR与多极化SAR图像,本文算法相比于基于像素和似然比的方法,能够更快速更精确地检测到变化区域.     

本原?-LFSR序列距离向量性质研究

根据不同类距离向量的分量大小关系,对本原?-LFSR的距离向量进行分类,每一个距离向量有n!个等价类。通过研究距离向量的基本性质,得到一类Z本原?-LFSR的距离向量的期望为(0, T/2, T/2,…, T/2),在此基础上给出2种Z本原?-LFSR的构造方法。对距离向量和线性复杂度之间的关系进行讨论,得出距离向量到线性复杂度是一个满射的结论。     

基于敏感属性值泄露个数期望的匿名模型

当前K-匿名成为解决隐私保护的重要模型,但其不能解决同质攻击造成的属性泄露。对K-匿名模型进行了扩展,提出一种新的基于敏感属性值泄露个数期望的匿名模型,该模型能很好地解决属性泄露问题,同时通过实验证明了该模型的可行性。