Random walk-based fuzzy linear discriminant analysis for dimensionality reduction

Dealing with high-dimensional data has always been a major problem with the research of pattern recognition and machine learning, and linear discriminant analysis (LDA) is one of the most popular methods for dimensionality reduction. However, it suffers from the problem of being too sensitive to outliers. Hence to solve this problem, fuzzy membership can be introduced to enhance the performance of algorithms by reducing the effects of outliers. In this paper, we analyze the existing fuzzy strategies and propose a new effective one based on Markov random walks. The new fuzzy strategy can maintain high consistency of local and global discriminative information and preserve statistical properties of dataset. In addition, based on the proposed fuzzy strategy, we then derive an efficient fuzzy LDA algorithm by incorporating the fuzzy membership into learning. Theoretical analysis and extensive simulations show the effectiveness of our algorithm. The presented results demonstrate that our proposed algorithm can achieve significantly improved results compared with other existing algorithms.     

Orthogonal margin discriminant projection for dimensionality reduction

Dimensionality reduction aims to represent high-dimensional data with much smaller number of features, which plays as a preprocessing step to remove the insignificant and irrelevant features in many machine learning applications, resulting in lower computational cost and better performance of classifiers. In most cases, the data points can be well classified with margin samples which are defined as furthest intra-class samples and nearest inter-class samples. Motivated by this observation, this paper proposes a linear supervised dimensionality reduction method called orthogonal margin discriminant projection (OMDP). After OMDP projection, intra-class data points become more compact and inter-class data points become more separated. Extensive experiments have been conducted to evaluate the proposed OMDP algorithm using several benchmark face data sets. The experimental results confirm the effectiveness of the proposed method.     

Generalized null space uncorrelated Fisher discriminant analysis for linear dimensionality reduction

We propose a generalized null space uncorrelated Fisher discriminant analysis (GNUFDA) technique integrating the uncorrelated discriminant analysis and weighted pairwise Fisher criterion. The GNUFDA can effectively deal with the small sample-size problem and perform satisfactorily when the dimensionality of the null space decreases with increase in the number of training samples per class and/or classes, C. The proposed GNUFDA can extract at most C-1 optimal uncorrelated discriminative vectors without being influenced by the null-space dimensionality.     

基于遗传算法的无监督分形属性规约技术

属性规约是应对“维数灾难”的有效技术,分形属性规约FDR（Fractal Dimensionality Reduction）是近年来出现的一种无监督属性选择技术,令人遗憾的是其需要多遍扫描数据集,因而难于应对高维数据集情况;基于遗传算法的属性规约技术对于高维数据而言优越于传统属性选择技术,但其无法应用于无监督学习领域。为此,结合遗传算法内在随机并行寻优机制及分形属性选择的无监督特点,设计并实现了基于遗传算法的无监督分形属性子集选择算法GABUFSS（Genetic Algorithm Based Unsupervised Feature Subset Selection）。基于合成与实际数据集的实验对比分析了GABUFSS算法与FDR算法的性能,结果表明GABUFSS相对优于FDR算法,并具有发现等价结果属性子集的特点。     

多标记学习自编码网络无监督维数约简

多标记学习是针对一个实例同时与一组标签相关联而提出的一种机器学习框架,是该领域研究热点之一,降维是多标记学习一个重要且具有挑战性的工作。针对有监督的多标记维数约简方法,提出一种无监督自编码网络的多标记降维方法。首先,通过构建自编码神经网络,对输入数据进行编码和解码输出;然后,引入稀疏约束计算总体成本,使用梯度下降法进行迭代求解;最后,通过深度学习训练获得自编码网络学习模型,提取数据特征实现维数约简。实验中使用多标记算法ML-kNN做分类器,在6个公开数据集上与其他4种方法对比。实验结果表明,该方法能够在不使用标记的情况下有效提取特征,降低多标记数据维度,稳定提高多标记学习性能。     

Extracting the optimal dimensionality for local tensor discriminant analysis

Supervised dimensionality reduction with tensor representation has attracted great interest in recent years. It has been successfully applied to problems with tensor data, such as image and video recognition tasks. However, in the tensor-based methods, how to select the suitable dimensions is a very important problem. Since the number of possible dimension combinations exponentially increases with respect to the order of tensor, manually selecting the suitable dimensions becomes an impossible task in the case of high-order tensor. In this paper, we aim at solving this important problem and propose an algorithm to extract the optimal dimensionality for local tensor discriminant analysis. Experimental results on a toy example and real-world data validate the effectiveness of the proposed method.     

基于半监督典型相关分析的多视图维数约简

为了有效地在半监督多视图情景下进行维数约简,提出了使用非负低秩图进行标签传播的半监督典型相关分析方法。非负低秩图捕获的全局线性近邻可以利用直接邻居和间接可达邻居的信息维持全局簇结构,同时,低秩的性质可以保持图的压缩表示。当无标签样本通过标签传播算法获得估计的标签信息后,在每个视图上构建软标签矩阵和概率类内散度矩阵。然后,通过最大化不同视图同类样本间相关性的同时最小化每个视图低维特征空间类内变化来提升特征鉴别能力。实验表明所提方法比已有相关方法能够取得更好的识别性能且更鲁棒。     

Discover latent discriminant information for dimensionality reduction: Non-negative Sparseness Preserving Embedding

How to define sparse affinity weight matrices is still an open problem in existing manifold learning algorithms. In this paper, we propose a novel unsupervised learning method called Non-negative Sparseness Preserving Embedding (NSPE) for linear dimensionality reduction. Differing from the manifold learning-based subspace learning methods such as Locality Preserving Projections (LPP), Neighbor Preserving Embedding (NPE) and the recently proposed sparse representation based Sparsity Preserving Projections (SPP); NSPE preserves the non-negative sparse reconstruction relationships in low-dimensional subspace. Another novelty of NSPE is the sparseness constraint, which is directly added to control the non-negative sparse representation coefficients. This gives a more ground truth model to imitate the actions of the active neuron cells of V1 of the primate visual cortex on information processing. Although labels are not used in the training steps, the non-negative sparse representation can still discover the latent discriminant information and thus provides better measure coefficients and significant discriminant abilities for feature extraction. Moreover, NSPE is more efficient than the recently proposed sparse representation based SPP algorithm. Comprehensive comparison and extensive experiments show that NSPE has the competitive performance against the unsupervised learning algorithms such as classical PCA and the state-of-the-art techniques: LPP, NPE and SPP.     

Kernel based nonlinear dimensionality reduction for microarray gene expression data analysis

Accurate recognition of cancers based on microarray gene expressions is very important for doctors to choose a proper treatment. Genomic microarrays are powerful research tools in bioinformatics and modern medicinal research. However, a simple microarray experiment often leads to very high-dimensional data and a huge amount of information, the vast amount of data challenges researchers into extracting the important features and reducing the high dimensionality. This paper proposed the kernel method based locally linear embedding to selecting the optimal number of nearest neighbors, constructing uniform distribution manifold. In this paper, a nonlinear dimensionality reduction kernel method based locally linear embedding is proposed to select the optimal number of nearest neighbors, constructing uniform distribution manifold. In addition, support vector machine which has given rise to the development of a new class of theoretically elegant learning machines will be used to classify and recognise genomic microarray. We demonstrate the application of the techniques to two published DNA microarray data sets. The experimental results and comparisons demonstrate that the proposed method is effective approach.     

Unsupervised feature selection based on kernel fisher discriminant analysis and regression learning

In this paper, we propose a new feature selection method called kernel fisher discriminant analysis and regression learning based algorithm for unsupervised feature selection. The existing feature selection methods are based on either manifold learning or discriminative techniques, each of which has some shortcomings. Although some studies show the advantages of two-steps method benefiting from both manifold learning and discriminative techniques, a joint formulation has been shown to be more efficient. To do so, we construct a global discriminant objective term of a clustering framework based on the kernel method. We add another term of regression learning into the objective function, which can impose the optimization to select a low-dimensional representation of the original dataset. We use L_2,1-norm of the features to impose a sparse structure upon features, which can result in more discriminative features. We propose an algorithm to solve the optimization problem introduced in this paper. We further discuss convergence, parameter sensitivity, computational complexity, as well as the clustering and classification accuracy of the proposed algorithm. In order to demonstrate the effectiveness of the proposed algorithm, we perform a set of experiments with different available datasets. The results obtained by the proposed algorithm are compared against the state-of-the-art algorithms. These results show that our method outperforms the existing state-of-the-art methods in many cases on different datasets, but the improved performance comes with the cost of increased time complexity.

     

Stable and orthogonal local discriminant embedding using trace ratio criterion for dimensionality reduction

Stable orthogonal local discriminant embedding (SOLDE) is a recently proposed dimensionality reduction method, in which the similarity, diversity and interclass separability of the data samples are well utilized to obtain a set of orthogonal projection vectors. By combining multiple features of data, it outperforms many prevalent dimensionality reduction methods. However, the orthogonal projection vectors are obtained by a step-by-step procedure, which makes it computationally expensive. By generalizing the objective function of the SOLDE to a trace ratio problem, we propose a stable and orthogonal local discriminant embedding using trace ratio criterion (SOLDE-TR) for dimensionality reduction. An iterative procedure is provided to solve the trace ratio problem, due to which the SOLDE-TR method is always faster than the SOLDE. The projection vectors of the SOLDE-TR will always converge to a global solution, and the performances are always better than that of the SOLDE. Experimental results on two public image databases demonstrate the effectiveness and advantages of the proposed method.     

Principal components selection for dimensionality reduction using discriminant information applied to fault diagnosis

The Principal Component Analysis is one of most applied dimensionality reduction techniques for process monitoring and fault diagnosis in industrial process. This work proposes a procedure based on the discriminant information contained in the principal components to determine the most significant ones in fault separability. The Tennessee Eastman Process industrial benchmark is used to illustrate the effectiveness of the proposal. The use of statistical hypothesis tests as a separability measure between multiple failures is proposed for the selection of the principal components. The classifier profile concept has been introduced for comparison purposes. Results show an improvement in the classification process when compared with traditional techniques and the StepWise selection. This has resulted in a better classification for a fixed number of components, or a smaller number of required components to obtain a prefixed error rate. In addition, the computational advantage is demonstrated.     

基于边界鉴别分析的递归维数约简算法

提出一种基于边界鉴别分析的递归维数约简算法.该算法把已求取边界鉴别向量正交于待求超平面法向量作为支持向量机(SVM)优化问题新的约束条件;然后对改进SVM进行递归求解,得到正交边界鉴别向量基;最后将数据样本在正交边界鉴别向量上投影实现维数约简.该算法不仅克服了现有维数约简算法难以支持小样本数据集、受数据样本分布影响等问题,而且抽取的特征向量具有更优的分类性能.仿真实验说明了算法的有效性.     

Local binary pattern-based discriminant graph construction for dimensionality reduction with application to face recognition

Multimedia Tools and Applications - Graph construction has attracted increasing interest in recent years due to its key role in many dimensionality reduction (DR) algorithms. On the other hand, our...     

Relative manifold based semi-supervised dimensionality reduction

A well-designed graph plays a fundamental role in graph-based semi-supervised learning; however, the topological structure of a constructed neighborhood is unstable in most current approaches, since they are very sensitive to the high dimensional, sparse and noisy data. This generally leads to dramatic performance degradation. To deal with this issue, we developed a relative manifold based semisupervised dimensionality reduction （RMSSDR） approach by utilizing the relative manifold to construct a better neighborhood graph with fewer short-circuit edges. Based on the relative cognitive law and manifold distance, a relative transformation is used to construct the relative space and the relative manifold. A relative transformation can improve the ability to distinguish between data points and reduce the impact of noise such that it may be more intuitive, and the relative manifold can more truly reflect the manifold structure since data sets commonly exist in a nonlinear structure. Specifically, RMSSDR makes full use of pairwise constraints that can define the edge weights of the neighborhood graph by minimizing the local reconstruction error and can preserve the global and local geometric structures of the data set. The experimental results on face data sets demonstrate that RMSSDR is better than the current state of the art comparing methods in both performance of classification and robustness.     

Relative manifold based semi-supervised dimensionality reduction

Figure 8 of this article shows YaleB and CMU PIE with incorrect legend titles:YaleB(Tr=1900,Te=514,NOC=100)should be YaleB(Tr=1900,Te=514,d=100)(Fig.8(a));TIE(Tr=1200,Te=2880,d=100)should be PIE(Tr=1200,Te=2880,d=100)(Fig.8(b)).In Fig.9,the legend keys and the legend texts are mismatched.The correct figure is ilustrated as follows.     

基于Fisher鉴别分析的支持向量机训练样本缩减策略

提出一种用于支持向量机训练样本集的缩减策略。该策略运用Fisher鉴别分析方法快速地提取潜在的支持向量,并构成用于SVM的新的训练样本集。仿真实验表明,该算法能在保证不降低分类精度的前提下,对较大规模的样本进行有效的缩减,提高运算效率。     

Mixture graph based semi-supervised dimensionality reduction

Graph structure is crucial to graph based dimensionality reduction. A mixture graph based semi-supervised dimensionality reduction (MGSSDR) method with pairwise constraints is proposed. MGSSDR first constructs multiple diverse graphs on different random subspaces of dataset, then it combines these graphs into a mixture graph and does dimensionality reduction on this mixture graph. MGSSDR can preserve the pairwise constraints and local structure of samples in the reduced subspace. Meanwhile, it is robust to noise and neighborhood size. Experimental results on facial images feature extraction demonstrate its effectiveness.     

Adaptive sparse graph learning based dimensionality reduction for classification

To preserve the sparsity structure in dimensionality reduction, sparsity preserving projection (SPP) is widely used in many fields of classification, which has the advantages of noise robustness and data adaptivity compared with other graph based method. However, the sparsity parameter of SPP is fixed for all samples without any adjustment. In this paper, an improved SPP method is proposed, which has an adaptive parameter adjustment strategy during sparse graph construction. With this adjustment strategy, the sparsity parameter of each sample is adjusted adaptively according to the relationship of those samples with nonzero sparse representation coefficients, by which the discriminant information of graph is enhanced. With the same expectation, similarity information both in original space and projection space is applied for sparse representation as guidance information. Besides, a new measurement is introduced to control the influence of each sample’s local structure on projection learning, by which more correct discriminant information should be preserved in the projection space. With the contributions of above strategies, the low-dimensional space with high discriminant ability is found, which is more beneficial for classification. Experimental results on three datasets demonstrate that the proposed approach can achieve better classification performance over some available state-of-the-art approaches.