Locality-Preserved Maximum Information Projection
Locality-Preserved Maximum Information Projection
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DOI：
10.1109/tnn.2007.910733
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发表时间：
2008-04
影响因子：
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通讯作者：
Haixian Wang;Sibao Chen;Z. Hu;Wenming Zheng
中科院分区：
文献类型：
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作者：
Haixian Wang;Sibao Chen;Z. Hu;Wenming Zheng
模糊性约简通常涉及人工智能和机器学习领域。特征的线性投影对于降维特别感兴趣，因为其计算和分析简单。在本文中，我们提出了一个基本上是线性的投影技术，称为局部保持最大信息投影（LPMIP），以确定潜在的流形结构的数据集。LPMIP在流形学习过程中同时考虑了内局部性和间局部性。等价地，LPMIP的目标是保持局部结构，同时最大化样本的非局部（全局）信息。与旨在保持全局信息的主成分分析（PCA）和有利于保持数据集局部结构的局部保持投影（LPP）不同，LPMIP寻求全局和局部结构之间的折衷，其通过参数α进行调整，以便找到检测用于分类任务的内在流形结构的子空间。在计算上，通过构造邻接矩阵，LPMIP被公式化为一个特征值问题。LPMIP产生正交基函数，并完全避免了奇异性问题，因为它存在于LPP。此外，我们开发了一个有效的和稳定的LPMIP/QR算法实现LPMIP，特别是在高维数据集。理论分析表明，传统的线性投影方法，如（加权）PCA，最大间距准则（MMC），线性判别分析（LDA），和LPP可以派生的LPMIP框架，通过设置不同的图模型和约束。在人脸、数字和表情识别上的大量实验表明了该方法的有效性。
Dimensionality reduction is usually involved in the domains of artificial intelligence and machine learning. Linear projection of features is of particular interest for dimensionality reduction since it is simple to calculate and analytically analyze. In this paper, we propose an essentially linear projection technique, called locality-preserved maximum information projection (LPMIP), to identify the underlying manifold structure of a data set. LPMIP considers both the within-locality and the between-locality in the processing of manifold learning. Equivalently, the goal of LPMIP is to preserve the local structure while maximize the out-of-locality (global) information of the samples simultaneously. Different from principal component analysis (PCA) that aims to preserve the global information and locality-preserving projections (LPPs) that is in favor of preserving the local structure of the data set, LPMIP seeks a tradeoff between the global and local structures, which is adjusted by a parameter alpha, so as to find a sub- space that detects the intrinsic manifold structure for classification tasks. Computationally, by constructing the adjacency matrix, LPMIP is formulated as an eigenvalue problem. LPMIP yields orthogonal basis functions, and completely avoids the singularity problem as it exists in LPP. Further, we develop an efficient and stable LPMIP/QR algorithm for implementing LPMIP, especially, on high-dimensional data set. Theoretical analysis shows that conventional linear projection methods such as (weighted) PCA, maximum margin criterion (MMC), linear discriminant analysis (LDA), and LPP could be derived from the LPMIP framework by setting different graph models and constraints. Extensive experiments on face, digit, and facial expression recognition show the effectiveness of the proposed LPMIP method.