面向缺损数据的流形学习方法研究

发布时间：2018-02-28 10:31

本文关键词： 缺损数据流形学习余弦相似度核范数正则化　出处：《华侨大学》2017年硕士论文　论文类型：学位论文

【摘要】：在很多实际应用问题中,高维数据集可能具有缺失数据值。如在视频监控中,监控目标可能被其他物体部分遮挡,此时只能获取监控目标的部分图像,这些被遮挡的图像即为缺损数据,如何挖掘缺损数据的本质特征尤其是非线性特征逐渐成为机器学习和数据挖掘的一个热点。流形学习作为一种非线性的降维技术,能够较好地挖掘高维数据的非线性特征。但是,传统的流形学习算法大多基于一种近似理想的情况下,即样本数据均匀采样于一个高维欧式空间中的低维流形。当数据缺损时,流形学习的效果会受到很大的影响。因此,本文主要围绕现有流形学习算法无法较好地挖掘缺损数据集的非线性特征问题展开,从构造缺损数据集的局部邻域和局部几何结构出发,提出可以较好地挖掘缺损数据集的流形学习算法。本文主要有以下两个方面的工作:1.针对缺失像素的图像集,我们提出了一种面向缺失像素图像集的修正拉普拉斯特征映射算法。该算法将缺失像素图像集看成向量集,首先利用图像向量之间的余弦相似度衡量缺失像素图像之间的距离,构造样本点的近邻域。然后提出一种新的权值构造函数,构造权值矩阵。最后,通过极小化价值函数计算样本点的低维嵌入坐标。在多组真实图像集上的分类实验结果表明,修正的拉普拉斯特征映射算法可以很好地挖掘缺失像素图像集的内在流形结构,减弱缺失像素带来的不良影响。2.我们提出了一种基于核范数正则化的局部切空间排列算法(Local Tangent Space Alignment via Nuclear Norm Regularization,简称LTSA-NNR)。该算法首先使用余弦相似性的度量方法构造缺损数据的局部邻域,然后提出了一种核范数正则化模型用于提取邻域的局部坐标,区别于传统的流形学习算法,LTSA-NNR算法提取的局部坐标的维度位于一个合理的范围内。最后,将这些局部坐标进行排列,构造缺损数据的全局坐标。我们在一些真实数据集上进行了多个可视化实验和分类实验,用以证明LTSA-NNR算法的有效性。
[Abstract]:In many practical applications, high-dimensional data sets may have missing data values. For example, in video surveillance, the target may be partially occluded by other objects, and only part of the image of the target can be obtained. These occluded images are called defective data. How to mine the essential features of defective data, especially nonlinear features, has gradually become a hot topic in machine learning and data mining. Manifold learning is a nonlinear dimensionality reduction technique. However, most of the traditional manifold learning algorithms are based on an approximate ideal case in which the sample data are uniformly sampled in a low-dimensional manifold in a high-dimensional Euclidean space. The effect of manifold learning will be greatly affected. Therefore, this paper focuses on the problem that the existing manifold learning algorithms can not well mine the nonlinear characteristics of the defective data sets. Based on the construction of the local neighborhood and local geometry structure of the defective dataset, a manifold learning algorithm is proposed, which can be used to mine the defective dataset. In this paper, there are two main works: 1. For the image set with missing pixels, We propose a modified Laplacian feature mapping algorithm for missing pixel image sets, which regards the missing pixel image set as a vector set. Firstly, the distance between the missing pixel images is measured by the cosine similarity between the image vectors. A new weight constructor is proposed to construct the weight matrix. Finally, the minimum value function is used to calculate the low dimensional embedded coordinates of the sample points. The modified Laplace feature mapping algorithm can well mine the intrinsic manifold structure of the missing pixel image set. 2. We propose a local Tangent Space Alignment via Nuclear Norm regularization (LTSA-NNRN) algorithm based on kernel norm regularization. The local neighborhood of the damaged data, Then a kernel norm regularization model is proposed to extract the local coordinates of the neighborhood, which is different from the dimension of the local coordinates extracted by the traditional manifold learning algorithm (LTSA-NNR). These local coordinates are arranged to construct the global coordinates of the defective data. We have carried out several visualization experiments and classification experiments on some real data sets to prove the validity of the LTSA-NNR algorithm.
【学位授予单位】：华侨大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP391.41;TP181

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