Multi-view Dimensionality Reduction Research Articles

Partial Tubal Nuclear Norm-Regularized Multiview Subspace Learning.

In this article, a unified multiview subspace learning model, called partial tubal nuclear norm-regularized multiview subspace learning (PTN 2 MSL), was proposed for unsupervised multiview subspace clustering (MVSC), semisupervised MVSC, and multiview dimension reduction. Unlike most of the existing methods which treat the above three related tasks independently, PTN 2 MSL integrates the projection learning and the low-rank tensor representation to promote each other and mine their underlying correlations. Moreover, instead of minimizing the tensor nuclear norm which treats all singular values equally and neglects their differences, PTN 2 MSL develops the partial tubal nuclear norm (PTNN) as a better alternative solution by minimizing the partial sum of tubal singular values. The PTN 2 MSL method was applied to the above three multiview subspace learning tasks. It demonstrated that these tasks organically benefited from each other and PTN 2 MSL has achieved better performance in comparison to state-of-the-art methods.

Robust image hashing based on multi-view dimension reduction

In the field of multimedia security, image hashing is an effective technology for solving image content identification. Image hashing algorithm aims to map the high dimensional input features onto perceptual hashing values in terms of their perceptual content, in which visually identical images are mapped to similar digital representations. In this paper, we focus on multi-view dimensionality reduction based hashing generation, and propose a novel method, called Multi-view Dimensionality Reduction based Robust Image Hashing (MDRIH). Our MDRIH scheme maps the multi-view features into a compact binary space by considering the complementarity and similarity between image features across these different views. For preprocessing, bilinear interpolation is applied on the host image to adjust to a standard size, and ensure the different images with same hash size. Specifically, in order to improve the robustness of the algorithm against content-preserving operations, multi-view features, including structural features, edge features, and color features are extracted. After that, multi-view dimension reduction is adopted to obtain meaningful low-dimensional information from multi-feature fusion. Finally, the data in low-dimensional subspace is encoded into a compact binary sequence. The experimental results indicate that the proposed hashing method not only preserves the correlation between multiple views and the similarity among different data points within each view, but also achieves a better balance between robustness and discriminability compared to existing hashing methods.

Multi-View Learning to Unravel the Different Levels Underlying Hepatitis B Vaccine Response.

The immune system acts as an intricate apparatus that is dedicated to mounting a defense and ensures host survival from microbial threats. To engage this faceted immune response and provide protection against infectious diseases, vaccinations are a critical tool to be developed. However, vaccine responses are governed by levels that, when interrogated, separately only explain a fraction of the immune reaction. To address this knowledge gap, we conducted a feasibility study to determine if multi-view modeling could aid in gaining actionable insights on response markers shared across populations, capture the immune system's diversity, and disentangle confounders. We thus sought to assess this multi-view modeling capacity on the responsiveness to the Hepatitis B virus (HBV) vaccination. Seroconversion to vaccine-induced antibodies against the HBV surface antigen (anti-HBs) in early converters (n = 21; <2 months) and late converters (n = 9; <6 months) and was defined based on the anti-HBs titers (>10IU/L). The multi-view data encompassed bulk RNA-seq, CD4+ T-cell parameters (including T-cell receptor data), flow cytometry data, and clinical metadata (including age and gender). The modeling included testing single-view and multi-view joint dimensionality reductions. Multi-view joint dimensionality reduction outperformed single-view methods in terms of the area under the curve and balanced accuracy, confirming the increase in predictive power to be gained. The interpretation of these findings showed that age, gender, inflammation-related gene sets, and pre-existing vaccine-specific T-cells could be associated with vaccination responsiveness. This multi-view dimensionality reduction approach complements clinical seroconversion and all single modalities. Importantly, this modeling could identify what features could predict HBV vaccine response. This methodology could be extended to other vaccination trials to identify the key features regulating responsiveness.

Multi-View Projection Learning via Adaptive Graph Embedding for Dimensionality Reduction

In order to explore complex structures and relationships hidden in data, plenty of graph-based dimensionality reduction methods have been widely investigated and extended to the multi-view learning field. For multi-view dimensionality reduction, the key point is extracting the complementary and compatible multi-view information to analyze the complex underlying structure of the samples, which is still a challenging task. We propose a novel multi-view dimensionality reduction algorithm that integrates underlying structure learning and dimensionality reduction for each view into one framework. Because the prespecified graph derived from original noisy high-dimensional data is usually low-quality, the subspace constructed based on such a graph is also low-quality. To obtain the optimal graph for dimensionality reduction, we propose a framework that learns the affinity based on the low-dimensional representation of all views and performs the dimensionality reduction based on it jointly. Although original data is noisy, the local structure information of them is also valuable. Therefore, in the graph learning process, we also introduce the information of predefined graphs based on each view feature into the optimal graph. Moreover, assigning the weight to each view based on its importance is essential in multi-view learning, the proposed GoMPL automatically allocates an appropriate weight to each view in the graph learning process. The obtained optimal graph is then adopted to learn the projection matrix for each individual view by graph embedding. We provide an effective alternate update method for learning the optimal graph and optimal subspace jointly for each view. We conduct many experiments on various benchmark datasets to evaluate the effectiveness of the proposed method.

Two-directional two-dimensional fractional-order embedding canonical correlation analysis for multi-view dimensionality reduction and set-based video recognition

Set-based video recognition is an important application in practice, and many specialized approaches have been proposed. However, most of these methods either only use one kind of visual features for classification, or are sensitive to the noises and the number of training images when using several kinds of features, resulting in limited discrimination. To explore a possible solution to these issues, in this paper, a novel efficiently and effectively dimensionality reduction method, named two-directional two-dimensional fractional-order embedding canonical correlation analysis ((2D)2FECCA), is proposed. (2D)2FECCA borrows the idea of fractional-order embedding to correct the estimation of sample covariance matrices, which can significantly reduce the influence of noise disturbance and effectively utilizing the discriminative information from different view features. In addition, several set-based video recognition schemes are introduced to determine the labels of the test videos. Extensive experimental results on four familiar single image based databases and two video based benchmark databases demonstrate the effectiveness of the proposed method. These quantitative assessments reinforce the significance as well as the importance of embedding the proposed method in other intelligent systems application areas.

Multi-view dimensionality reduction learning with hierarchical sparse feature selection

Multi-view dimensionality reduction learning with hierarchical sparse feature selection

Double information preserving canonical correlation analysis

The methods based on canonical correlation analysis (CCA-based methods) are typical and effective methods for unsupervised dimensionality reduction of multi-view data. However, the traditional CCA-based methods ignore the dissimilarity information while considering the similarity information of samples, which will make the heterogeneous samples in the subspace cannot be well separated. In this paper, we propose a novel unsupervised multi-view dimensionality reduction method: Double Information Preserving Canonical Correlation Analysis (DIPCCA). DIPCCA aims at finding two projection matrices by integrating two cross double weight graphs with CCA to explore the similarity and dissimilarity information of data in cross views. Furthermore, on the basis of consistency and complementarity, DIPCCA uses the similarity information to maintain the local structure, and the dissimilarity information to disperse embedded samples of distinct clusters, so as to extract more discriminative features. Moreover, CCA and a new locality-preserving CCA are two special cases of DIPCCA when parameters take special values. In order to better extract the features of nonlinear data and more than two views, DIPCCA is extended to Double Information Preserving Kernel Canonical Correlation Analysis and Double Information Preserving Multiple Canonical Correlation Analysis, respectively. Experiments on an artificial dataset and three real multi-view datasets show our proposed methods have better performance than the traditional CCA-based methods.

Autoweighted multi-view smooth representation preserve projection for dimensionality reduction

Over the past few decades, we have witnessed a large family of algorithms that has been designed to provide different solutions to the problem of dimensionality reduction (DR). DR is an essential tool to excavate important information from the high-dimensional data by mapping the data to a low-dimensional subspace. Even though most DR algorithms can achieve satisfactory performance for many practical applications, they fail to fully consider the information from multiple views. Therefore, how to learn the subspace for high-dimensional features by utilizing the consistency and complementary properties of multi-view features is important and challenging in the present. To tackle this problem, we propose an effective multi-view DR algorithm named multi-view smooth representation preserve projection (MvSMRP2). MvSMRP2 seeks to find a set of linear transformations to project each view features into one common low-dimensional subspace where the multi-view smooth reconstructive weights are preserved as much as possible. A pair-wise-consistent scheme is designed by fully exploiting the Hilbert–Schmidt independence criterion to maximize the dependence among different views, which can obtain one common subspace and force multiple views to learn from each other jointly. Moreover, MvSMRP2 can allocate ideal weight for each view automatically according to view importance without explicit weight definition. Finally, an iterative alternating strategy is proposed to obtain the optimal solution of MvSMRP2. Plenty of experiments on various datasets show the excellent performances of the proposed method.

Flexible Multi-View Unsupervised Graph Embedding

Faced with the increasing data diversity and dimensionality, multi-view dimensionality reduction has been an important technique in computer vision, data mining and multi-media applications. Since collecting labeled data is difficult and costly, unsupervised learning is of great significance. Generally, it is crucial to explore the complementarity or independence of different feature spaces in multi-view learning. How to find a low-dimensional subspace to preserve the intrinsic structure of original unlabeled high-dimensional multi-view data is still challenging. In addition, noises and outliers always appear in real data. In this study, we propose a novel model called flexible multi-view unsupervised graph embedding (FMUGE). A flexible regression residual term is introduced so that the strict linear mapping is relaxed, new-coming data and noises are better handled, and the raw data negotiate with the learned low-dimensional representation in the procedure. To ensure the consistency among multiple views, FMUGE adaptively weights different features and fuses them to get an optimal multi-view consensus similarity graph, which assists high-quality graph embedding. We propose an efficient alternating iterative algorithm to optimize the proposed model. Finally, experimental results on synthetic and benchmark datasets show the significant improvement of FMUGE over the state-of-the-art methods.

Multiview Diffusion Map Improves Prediction of Fluid Intelligence With Two Paradigms of fMRI Analysis.

To understand the association between brain networks and behaviors of an individual, most studies build predictive models based on functional connectivity (FC) from a single dataset with linear analysis techniques. Such approaches may fail to capture the nonlinear structure of brain networks and neglect the complementary information contained in FC networks (FCNs) from multiple datasets. To address this challenging issue, we use multiview dimensionality reduction to extract a coherent low-dimensional representation of the FCNs from resting-state and emotion identification task-based functional magnetic resonance imaging (fMRI) datasets. We propose a scheme based on multiview diffusion map to extract intrinsic features while preserving the underlying geometric structure of high dimensional datasets. This method is robust to noise and small variations in the data. After validation on the Philadelphia Neurodevelopmental Cohort data, the predictive model built from both resting-state and emotion identification task-based fMRI datasets outperforms the one using each individual fMRI dataset. In addition, the proposed model achieves better prediction performance than principal component analysis (PCA) and three other competing data fusion methods. Our framework for combing multiple FCNs in one predictive model exhibits improved prediction performance. To our knowledge, we demonstrate a first application of multiview diffusion map to successfully fuse different types of fMRI data for predicting fluid intelligence (gF).

Generalized Multi-manifold Graph Ensemble Embedding for Multi-View Dimensionality Reduction

In this paper, we propose a new dimension reduction (DR) algorithm called ensemble graph-based locality preserving projections (EGLPP); to overcome the neighborhood size k sensitivity in locally preserving projections (LPP). EGLPP constructs a homogeneous ensemble of adjacency graphs by varying neighborhood size k and finally uses the integrated embedded graph to optimize the low-dimensional projections. Furthermore, to appropriately handle the intrinsic geometrical structure of the multi-view data and overcome the dimensionality curse, we propose a generalized multi-manifold graph ensemble embedding framework (MLGEE). MLGEE aims to utilize multi-manifold graphs for the adjacency estimation with automatically weight each manifold to derive the integrated heterogeneous graph. Experimental results on various computer vision databases verify the effectiveness of proposed EGLPP and MLGEE over existing comparative DR methods.

Consistent Discriminant Correlation Analysis

Multi-view dimensionality reduction is an importan subject in multi-view learning. Canonical correlation analysis and its various improved forms can effectively solve this problem. But most of these algorithms do not fully consider the discriminant information and view consistency information contained in the data itself simultaneously. To solve this problem, a new multi-view dimensionality reduction algorithm, consistent discriminant correlation analysis, is proposed in this paper. The algorithm integrates the class information and the consistency information between views into the dimension reduction process. By maximizing the within-class correlations and the consistency between views, and minimizing the between-class correlations simultaneously, it extracts the low-dimensional features that are more efficient to classification. Furthermore, a kernel consistent discriminant correlation analysis is proposed. The experimental results on several data sets demonstrate the effectiveness of the proposed methods.

Efficient Unsupervised Dimension Reduction for Streaming Multiview Data.

Multiview learning has received substantial attention over the past decade due to its powerful capacity in integrating various types of information. Conventional unsupervised multiview dimension reduction (UMDR) methods are usually conducted in an offline manner and may fail in many real-world applications, where data arrive sequentially and the data distribution changes periodically. Moreover, satisfying the requirements of high memory consumption and expensive retraining of the time cost in large-scale scenarios are difficult. To remedy these drawbacks, we propose an online UMDR (OUMDR) framework. OUMDR aims to seek a low-dimensional and informative consensus representation for streaming multiview data. View-specific weights are also learned in this article to reflect the contributions of different views to the final consensus presentation. A specific model called OUMDR-E is developed by introducing the exclusive group LASSO (EG-LASSO) to explore the intraview and interview correlations. Then, we develop an efficient iterative algorithm with limited memory and time cost requirements for optimization, where the convergence of each update is theoretically guaranteed. We evaluate the proposed approach in video-based expression recognition applications. The experimental results demonstrate the superiority of our approach in terms of both effectiveness and efficiency.

Tensor mutual information and its applications

SummaryCorrelation analysis has long been a question of great interest in measuring the relationship among different variables and has been applied in many fields, such as dimension reduction, classification, and so on. However, current methods of correlation analysis take into account the linear relationship between multiple variables and only few works on nonlinear interaction of two variables have been considered. In this article, we first present a nonlinear analysis method of multiple (two or more) variables based on mutual information for tensor analysis (MITA). In addition, we extend the mutual‐information matrix analysis directly to MITA and show the multivariable mutual information formula based on Venn diagram. Experiments on multiview dimension reduction, including attacking internet traffic prediction, advertisement classification, and biometric structure prediction illustrate the effectiveness of the proposed method, especially in the case of low‐dimensional subspace.

Multiset Canonical Correlations Analysis With Global Structure Preservation

This paper considers unsupervised dimensionality reduction of multi-view data, where locality preserving canonical correlation analysis and a new locality-preserving canonical correlation analysis are two typical effective methods. However, they ignore the global structure while considering the local structure of data, and are sensitive to noises because of the relationship of neighbors based on the Euclidean distance. In this paper, we propose a novel multi-view dimensionality reduction method: multiset canonical correlations analysis based on low-rank representation. Our model introduces the cross-view similarity matrix to consider the correlation of all different points in cross views, which makes it not only preserve the local structure but also the global structure of data. And the cross-view similarity matrix is constructed by using low-rank representation, which can make the model more robust. In addition, a parameter $\beta $ is introduced to adjust the importance of the correlation of different sample points, enhancing the generalization ability for different datasets. Experiments on four multi-view datasets show our proposed method has better performance than the related methods.

Low-rank graph optimization for multi-view dimensionality reduction.

Graph-based dimensionality reduction methods have attracted substantial attention due to their successful applications in many tasks, including classification and clustering. However, most classical graph-based dimensionality reduction approaches are only applied to data from one view. Hence, combining information from different data views has attracted considerable attention in the literature. Although various multi-view graph-based dimensionality reduction algorithms have been proposed, the graph construction strategies utilized in them do not adequately take noise and different importance of multiple views into account, which may degrade their performance. In this paper, we propose a novel algorithm, namely, Low-Rank Graph Optimization for Multi-View Dimensionality Reduction (LRGO-MVDR), that overcomes these limitations. First, we construct a low-rank shared matrix and a sparse error matrix from the graph that corresponds to each view for capturing potential noise. Second, an adaptive nonnegative weight vector is learned to explore complementarity among views. Moreover, an effective optimization procedure based on the Alternating Direction Method of Multipliers scheme is utilized. Extensive experiments are carried out to evaluate the effectiveness of the proposed algorithm. The experimental results demonstrate that the proposed LRGO-MVDR algorithm outperforms related methods.

Analysis of nonstandardized stress echocardiography sequences using multiview dimensionality reduction.

Alternative stress echocardiography protocols such as handgrip exercise are potentially more favorable towards large-scale screening scenarios than those currently adopted in clinical practice. However, these are still underexplored because the maximal exercise levels are not easily quantified and regulated, requiring the analysis of the complete data sequences (thousands of images), which represents a challenging task for the clinician. We propose a framework for the analysis of these complex datasets, and illustrate it on a handgrip exercise dataset including complete acquisitions of 10 healthy controls and 5 ANT1 mutation patients (1377 cardiac cycles). The framework is based on an unsupervised formulation of multiple kernel learning, which is used to integrate information coming from myocardial velocity traces and heart rate to obtain a lower-dimensional representation of the data. Such simplified representation is then explored to discriminate groups of response and understand the underlying pathophysiological mechanisms. The analysis pipeline involves the reconstruction of population-specific signatures using multiscale kernel regression, and the clustering of subjects based on the trajectories defined by their projected sequences. The results confirm that the proposed framework is able to detect distinctive clusters of response and to provide insight regarding the underlying pathophysiology.

Multi-view Locality Low-rank Embedding for Dimension Reduction

During the last decades, we have witnessed a surge of interest in learning a low-dimensional space with discriminative information from one single view. Even though most of them can achieve satisfactory performance in certain situations, they fail to fully consider the information from multiple views which are highly relevant but sometimes look different from each other. Besides, correlations between features from multiple views always vary greatly, which challenges the capability of multi-view subspace learning methods. Therefore, how to learn an appropriate subspace which could maintain valuable information from multi-view features is of vital importance but challenging. To tackle this problem, this paper proposes a novel multi-view dimension reduction method named Multi-view Locality Low-rank Embedding for Dimension Reduction (MvL2E). MvL2E mainly focuses on capturing a common low-dimensional embedding among multiple different views, which makes full use of correlations between multi-view features by adopting low-rank representations. Meanwhile, it aims to maintain the correlations and construct a suitable manifold structure to capture the low-dimensional embedding for multi-view features. A centroid based scheme is designed to get one common low-dimensional manifold space and force multiple views to learn from each other. And an iterative alternating strategy is developed to obtain the optimal solution of MvL2E. The proposed method is evaluated on 5 benchmark datasets. Comprehensive experiments show that our proposed MvL2E can achieve comparable performance with previous approaches proposed in recent works of literature.

Multiview Uncorrelated Locality Preserving Projection.

Canonical Correlation Analysis (CCA) is a popular multiview dimension reduction method, which aims to maximize the correlation between two views to find the common subspace shared by these two views. However, it can only deal with two-view data, while the number of views frequently exceeds two in many real applications. To handle data with more than two views, in the previous studies, either the pairwise correlation or the high-order correlation was employed. These two types of correlation define the relation of multiview data from different viewpoints, and both have special effects for view consistency. To obtain flexible view consistency, in this article, we propose multiview uncorrelated locality preserving projection (MULPP), which considers two types of correlation simultaneously. The MULPP also considers the complementary property of different views by preserving the local structures of all the views. To obtain multiple projections and minimize the redundancy of low-dimensional features, for each view, the MULPP makes the features extracted by different projections uncorrelated. The MULPP is solved by an iteration algorithm, and the convergence of the algorithm is proven. The experiments on Multiple Feature, Coil-100, 3Sources, and NUS-WIDE data sets demonstrate the effectiveness of MULPP.

Multi-view reconstructive preserving embedding for dimension reduction

With the development of feature extraction technique, one sample always can be represented by multiple features which locate in high-dimensional space. Multiple features can re ect various perspectives of one same sample, so there must be compatible and complementary information among the multiple views. Therefore, it's natural to integrate multiple features together to obtain better performance. However, most multi-view dimension reduction methods cannot handle multiple features from nonlinear space with high dimensions. To address this problem, we propose a novel multi-view dimension reduction method named Multi-view Reconstructive Preserving Embedding (MRPE) in this paper. MRPE reconstructs each sample by utilizing its k nearest neighbors. The similarities between each sample and its neighbors are primely mapped into lower-dimensional space in order to preserve the underlying neighborhood structure of the original manifold. MRPE fully exploits correlations between each sample and its neighbors from multiple views by linear reconstruction. Furthermore, MRPE constructs an optimization problem and derives an iterative procedure to obtain the low-dimensional embedding. Various evaluations based on the applications of document classification, face recognition and image retrieval demonstrate the effectiveness of our proposed approach on multi-view dimension reduction.