子空间学习若干问题研究及其应用

发布时间：2019-03-15 19:34

【摘要】：子空间学习是机器学习领域的一个热门课题,被广泛应用于计算机视觉、分析化学、生物信息学等领域。对维度高、训练样本少的数据,常用的回归、分类模型经常出现过拟合、参数估计误差大等问题。然而,数据虽然是高维的,但是可能分布在一个低维的子空间上,在此低维子空间上对数据的回归或分类就能避免出现过拟合、参数估计误差大等问题。子空间学习是解决这个问题的一个重要途径。针对具体的回归、分类等任务,学习最优的子空间是子空间学习的核心问题。针对回归、分类等问题,研究者基于各种准则通过设计对应的目标函数以及对回归系数、投影向量的正则化方法提出了多种子空间学习模型,然而,由于具体问题的复杂性,如何根据具体的回归、分类任务设计目标函数以及回归系数、投影向量的正则化方法以得到最高的回归、分类准确度,仍然是子空间学习中的一个困难问题。本文的工作围绕子空间学习理论中设计最优的目标函数以及回归系数、投影向量的正则化方法的几个问题展开研究,集中研究了以最小化错误分类率、最小化均方误差为目标学习最优投影向量、数据之间具有相关性的子空间建模这三个问题。本文的研究内容及取得的成果包括以下几个方面:1.研究了线性分类问题中的最优投影向量的问题,提出了一种近似最优的线性判别模型。针对现有的线性判别分析模型没有考虑投影向量是否最优的、依赖于从样本中估计分布的均值和协方差矩阵等问题,在数据服从Laplacian分布的情况下,分析了最小错分率意义下求最优投影向量的准则,并给出了鲁棒的线性判别分析模型及线性规划求解方法。该模型依赖于中值和平均绝对偏差的估计,比均值和协方差矩阵的估计要鲁棒,适合训练样本较少、有噪声或异常点的情况。在服从高斯分布、Laplacian分布、有属性缺失的高斯分布的数据上的仿真实验显示该模型都具有较好的分类效果。2.研究了线性回归问题中的最优投影向量的问题,提出了一种近似最优的偏最小二乘模型。针对特征有噪声的情况,分析了均方误差与投影向量的关系,给出了基于偏最小二乘框架提取最优投影向量的回归模型。并进一步提出了一种近似最优模型,给出了基于广义特征值分解的模型求解方法。标准库上的实验显示该模型具有更小的预测误差,且使用了更少的隐藏变量。3.研究了对不同样本之间的相关性、同一样本不同特征之间相关性的联合建模问题,提出了基于回归框架的多任务多视角学习模型以及对应的核多任务多视角学习模型,给出了显示求解算法。并将该学习模型应用到视频跟踪问题中,通过该模型实现了对视频相邻帧之间的相关性、多种特征的相关性性的联合建模,在多个标准数据库上的实验结果显示该方法在实时性、跟踪精度与现有方法比有明显提高。
[Abstract]:Subspace learning is a hot topic in the field of machine learning, which is widely used in computer vision, analytical chemistry, bioinformatics and other fields. For the data with high dimension and few training samples, the commonly used regression, the classification model is often overfitted, and the error of parameter estimation is large and so on. However, although the data is high-dimensional, it may be distributed in a low-dimensional subspace. The regression or classification of the data in this low-dimensional subspace can avoid over-fitting and large error in parameter estimation. Subspace learning is an important way to solve this problem. For specific tasks such as regression, classification and so on, learning the optimal subspace is the core problem of subspace learning. Aiming at the problems of regression, classification and so on, researchers put forward multiple sub-spatial learning models by designing corresponding objective functions and regularization methods of regression coefficients and projection vectors based on various criteria. However, due to the complexity of the specific problems, the authors put forward a multi-sub-spatial learning model. How to design objective function, regression coefficient and projection vector regularization method according to specific regression, classification task and regression coefficient, projection vector to obtain the highest regression, classification accuracy is still a difficult problem in subspace learning. In this paper, several problems of designing optimal objective function, regression coefficient and regularization method of projection vector in the subspace learning theory of work-around in this paper are studied, focusing on minimizing the error classification rate. Minimizing mean square error is the objective learning optimal projection vector, and the subspace modeling with correlation between data is three problems. The research contents and achievements of this paper include the following aspects: 1. In this paper, the problem of optimal projection vector in linear classification problem is studied, and an approximate optimal linear discriminant model is proposed. The existing linear discriminant analysis model does not consider whether the projection vector is optimal and depends on the estimation of the mean value and covariance matrix of the distribution from the sample. The data obeys the Laplacian distribution. The criterion for finding the optimal projection vector in the sense of minimum error rate is analyzed, and the robust linear discriminant analysis model and the solution method of linear programming are given. The model depends on the estimation of mean and mean absolute deviation and is more robust than the estimation of mean and covariance matrix. It is suitable for the case of fewer training samples with noise or outliers. Simulation experiments on the data of Gao Si distribution following Gao Si distribution, Laplacian distribution and Gao Si distribution with missing attributes show that the model has a good classification effect. 2. In this paper, the problem of optimal projection vector in linear regression problem is studied, and an approximate optimal partial least squares model is proposed. In this paper, the relation between mean square error and projection vector is analyzed, and the regression model based on partial least squares frame is given to extract the optimal projection vector. Furthermore, an approximate optimal model is proposed, and the solution method of the model based on generalized eigenvalue decomposition is given. Experiments on the standard library show that the model has a smaller prediction error and uses fewer hidden variables. 3. This paper studies the joint modeling of the correlation between different samples and different features of the same sample, and proposes a multi-task multi-perspective learning model based on regression framework and the corresponding kernel multi-task multi-perspective learning model. The display algorithm is given. The learning model is applied to the problem of video tracking, and the joint modeling of the correlation between adjacent frames and the correlation of multiple features is realized by this model. The experimental results on several standard databases show that the real-time performance and tracking accuracy of the proposed method are obviously improved compared with the existing methods.
【学位授予单位】：华中科技大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP391.41;TP181

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