高维数据的维数约简算法研究
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摘要
在这个“信息爆炸”的时代,人类常常要面临分析和处理各种数据信息的要求,如海量web数据、大规模数据库文本、大量遥感图像等,这就对统计学、模式识别、人工智能、数据挖掘、机器学习等相关学科领域的发展提出了挑战。这些数据不仅呈几何级数式增长,而且现实中通常是高维的。这些高维数据常常会引发所谓的“维数灾难”,一方面,它们通常是稀疏的、冗余的,容易掩盖数据的真实结构,甚至会导致错误的分析处理结果；另一方面,它们增加了分析处理数据的负担。作为解决“维数灾难”的有效途径,维数约简发展成为一个重要的研究课题,它将数据从高维特征空间约简到低维特征空间,约简后的特征空间更能体现数据的本质结构,并且提高了数据的分析处理效率。本文对维数约简的理论方法和实际应用进行了深入的研究,主要工作概括如下：
1.提出一种动态寻优子空间方法。该方法是通过寻找平衡主成分分析(PCA)和最大边缘准则(MMC)目标函数的最佳系数来实现的,它的目的是使得PCA寻找代表原始数据结构的线性投影方向时,能够更多地考虑判别信息,同时也使得MMC在寻找实现约简特征维数和提取分类信息的线性投影方向时,能够更好地表达样本的原始数据结构。另外,不同的数据,甚至是同种数据不同条件下,会有不同的结构特点,因此应该根据数据的结构特点来选择算法,而该方法很好地满足了这个要求。使用基因微阵列数据的肿瘤分类实验证明了,这种新的特征提取方法是有效的、稳定的。
2.提出一种基于稀疏表示的无监督特征选择算法一稀疏评分(SS)。稀疏表示虽然属于全局性的方法,却含有天然的判别性和局部性,这就使得SS不仅具有较强的判别能力,还有局部结构保持能力和一定的全局结构保持能力。另外,SS所选取的特征方差比较大,即信息含量比较大。人脸图像的聚类实验结果显示,SS对特征重要性的评价效果明显优于方差评分(VS)和拉普拉斯评分(LS)这两种特征选择算法。
3.提出一种基于低秩表示的监督特征提取算法--低秩表示判别投影(LRDP)。基于低秩表示,LRDP拥有良好的数据全局结构表达能力和一定的判别结构表达能力,另外,LRDP依据SRC决策准则,使得它拥有良好的判别性能。人脸图像的分类实验结果显示,LRDP的性能要优于其它一些特征提取算法,包括主成分分析(PCA)、线性判别分析(LDA)和稀疏保持投影(SPP)。
4.以本体理论为依据,提出一种基于农业本体的农业文本特征优化方法。首先进行特征映射,即用农业本体的概念取代向量空间模型的术语,概念频率权重由术语频率权重统计得到。其次进行特征加权,即根据农业本体的概念层次结构,将概念相似度权重追加到概念权重。该方法结合特征频率权重和特征相似度权重,不仅大幅减少了特征空间的维数,而且为特征空间引入了语义信息。通过农业文本文档的聚类实验,该方法的可行性和有效性得到了验证。
In the era of "information explosion", we are often faced with the analysis and processing of various data, such as the mass of web data, large-scale database text, and a large number of remote sensing images, which present a challenge to the development of statistics, pattern recognition, artificial intelligence, data mining, machine learning and other related disciplines. These data show rapid growth with geometric progression and are usually with high dimensionality in reality. These high-dimensional data often led to the so-called "the curse of dimensionality". On the one hand, they are usually sparse and redundant, thus are easy to conceal the true structure of the data, and even can lead to erroneous results. On the other hand, they increase the burden of analyzing and processing data. As an effective way to solve "the curse of dimensionality", dimensionality reduction has become an important research topic. Dimensionality reduction can reduce the high-dimensional feature space into a low-dimensional feature space, which can better reflect the nature of the data structure and improve the efficiency of data analysis and processing. In this paper, we made a thorough research on the theoretics and applications of dimensionality reduction.
1. A novel subspace learning method of dynamic optimization for feature extraction was proposed. This method is accomplished by searching for the optimal coefficient to balance the objective function of the principal component analysis (PCA) and maximum margin criterion (MMC). The PCA can consider more of the discriminant information while representing the original data structure by linear projection direction. Moreover, the MMC can better express the original data structure of the sample while searching the linear projection direction for the reduction of feature dimensionality and the extraction of classified information simultaneously. In addition, different data, or even those with the same kind under different conditions, may have different structural characteristics. Therefore, algorithm should be developed based on the structural characteristics of the data. Actually this method can meet this requirement. Finally, tumor classification experiments on gene microarray data verified that this new feature extraction method was effective and stable.
2. An unsupervised feature selection algorithm based on sparse representation called sparse score (SS) was proposed. Although sparse representation belongs to global methods in nature, it owns some discriminating and local properties, which makes SS not only have strong discriminating ability, but also have the abilities of preserving local structure and certain global structure. In addition, SS selected features with relatively large variance, i.e., large information content. Experimental results of clustering on face images show that, in the evaluation of feature significance, SS significantly outperformed the other two kinds of feature selection algorithms, Variance Score (VS) and Laplacian Score (LS).
3. A supervised feature extraction algorithm based on low-rank discriminant projection (LRDP) was proposed. Based on low-rank representation, LRDP has good abilities for representing global structure and certain discrimination structure. In addition, LRDP based on the decision rule of SRC, which makes it have good discriminating ability. Experimental results of classification on face images reveal that, the LRDP has better performance than some other feature extraction algorithms, including PCA, LDA and sparsity preserving projections (SPP).4. Based on ontology theory, a novel method of ontology-based feature optimization for agricultural text was proposed. First, the terms of vector space model were replaced by concepts of agricultural ontology, where the concept frequency weights were computed statistically by term frequency weights. Second, the concept similarity weights were assigned to the concept weights, through the concept hierarchy structure of agricultural ontology. By combining feature frequency weights and feature similarity weights based on agricultural ontology, the dimensionality of the feature space can be reduced dramatically. Moreover, the semantic information can be incorporated into the feature space. Finally, the agricultural text clustering experiments were carried out to verify the effectiveness of this method.
1.提出一种动态寻优子空间方法。该方法是通过寻找平衡主成分分析(PCA)和最大边缘准则(MMC)目标函数的最佳系数来实现的,它的目的是使得PCA寻找代表原始数据结构的线性投影方向时,能够更多地考虑判别信息,同时也使得MMC在寻找实现约简特征维数和提取分类信息的线性投影方向时,能够更好地表达样本的原始数据结构。另外,不同的数据,甚至是同种数据不同条件下,会有不同的结构特点,因此应该根据数据的结构特点来选择算法,而该方法很好地满足了这个要求。使用基因微阵列数据的肿瘤分类实验证明了,这种新的特征提取方法是有效的、稳定的。
2.提出一种基于稀疏表示的无监督特征选择算法一稀疏评分(SS)。稀疏表示虽然属于全局性的方法,却含有天然的判别性和局部性,这就使得SS不仅具有较强的判别能力,还有局部结构保持能力和一定的全局结构保持能力。另外,SS所选取的特征方差比较大,即信息含量比较大。人脸图像的聚类实验结果显示,SS对特征重要性的评价效果明显优于方差评分(VS)和拉普拉斯评分(LS)这两种特征选择算法。
3.提出一种基于低秩表示的监督特征提取算法--低秩表示判别投影(LRDP)。基于低秩表示,LRDP拥有良好的数据全局结构表达能力和一定的判别结构表达能力,另外,LRDP依据SRC决策准则,使得它拥有良好的判别性能。人脸图像的分类实验结果显示,LRDP的性能要优于其它一些特征提取算法,包括主成分分析(PCA)、线性判别分析(LDA)和稀疏保持投影(SPP)。
4.以本体理论为依据,提出一种基于农业本体的农业文本特征优化方法。首先进行特征映射,即用农业本体的概念取代向量空间模型的术语,概念频率权重由术语频率权重统计得到。其次进行特征加权,即根据农业本体的概念层次结构,将概念相似度权重追加到概念权重。该方法结合特征频率权重和特征相似度权重,不仅大幅减少了特征空间的维数,而且为特征空间引入了语义信息。通过农业文本文档的聚类实验,该方法的可行性和有效性得到了验证。
In the era of "information explosion", we are often faced with the analysis and processing of various data, such as the mass of web data, large-scale database text, and a large number of remote sensing images, which present a challenge to the development of statistics, pattern recognition, artificial intelligence, data mining, machine learning and other related disciplines. These data show rapid growth with geometric progression and are usually with high dimensionality in reality. These high-dimensional data often led to the so-called "the curse of dimensionality". On the one hand, they are usually sparse and redundant, thus are easy to conceal the true structure of the data, and even can lead to erroneous results. On the other hand, they increase the burden of analyzing and processing data. As an effective way to solve "the curse of dimensionality", dimensionality reduction has become an important research topic. Dimensionality reduction can reduce the high-dimensional feature space into a low-dimensional feature space, which can better reflect the nature of the data structure and improve the efficiency of data analysis and processing. In this paper, we made a thorough research on the theoretics and applications of dimensionality reduction.
1. A novel subspace learning method of dynamic optimization for feature extraction was proposed. This method is accomplished by searching for the optimal coefficient to balance the objective function of the principal component analysis (PCA) and maximum margin criterion (MMC). The PCA can consider more of the discriminant information while representing the original data structure by linear projection direction. Moreover, the MMC can better express the original data structure of the sample while searching the linear projection direction for the reduction of feature dimensionality and the extraction of classified information simultaneously. In addition, different data, or even those with the same kind under different conditions, may have different structural characteristics. Therefore, algorithm should be developed based on the structural characteristics of the data. Actually this method can meet this requirement. Finally, tumor classification experiments on gene microarray data verified that this new feature extraction method was effective and stable.
2. An unsupervised feature selection algorithm based on sparse representation called sparse score (SS) was proposed. Although sparse representation belongs to global methods in nature, it owns some discriminating and local properties, which makes SS not only have strong discriminating ability, but also have the abilities of preserving local structure and certain global structure. In addition, SS selected features with relatively large variance, i.e., large information content. Experimental results of clustering on face images show that, in the evaluation of feature significance, SS significantly outperformed the other two kinds of feature selection algorithms, Variance Score (VS) and Laplacian Score (LS).
3. A supervised feature extraction algorithm based on low-rank discriminant projection (LRDP) was proposed. Based on low-rank representation, LRDP has good abilities for representing global structure and certain discrimination structure. In addition, LRDP based on the decision rule of SRC, which makes it have good discriminating ability. Experimental results of classification on face images reveal that, the LRDP has better performance than some other feature extraction algorithms, including PCA, LDA and sparsity preserving projections (SPP).4. Based on ontology theory, a novel method of ontology-based feature optimization for agricultural text was proposed. First, the terms of vector space model were replaced by concepts of agricultural ontology, where the concept frequency weights were computed statistically by term frequency weights. Second, the concept similarity weights were assigned to the concept weights, through the concept hierarchy structure of agricultural ontology. By combining feature frequency weights and feature similarity weights based on agricultural ontology, the dimensionality of the feature space can be reduced dramatically. Moreover, the semantic information can be incorporated into the feature space. Finally, the agricultural text clustering experiments were carried out to verify the effectiveness of this method.
引文
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