Multi-view Dimensionality Reduction Research Articles

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.

Multi-view diffusion maps

In this paper, we address the challenging task of achieving multi-view dimensionality reduction. The goal is to effectively use the availability of multiple views for extracting a coherent low-dimensional representation of the data. The proposed method exploits the intrinsic relation within each view, as well as the mutual relations between views. The multi-view dimensionality reduction is achieved by defining a cross-view model in which an implied random walk process is restrained to hop between objects in the different views. The method is robust to scaling and insensitive to small structural changes in the data. We define new diffusion distances and analyze the spectra of the proposed kernel. We show that the proposed framework is useful for various machine learning applications such as clustering, classification, and manifold learning. Finally, by fusing multi-sensor seismic data we present a method for automatic identification of seismic events.

Adaptive graph weighting for multi-view dimensionality reduction

Multi-view learning has become a flourishing topic in recent years since it can discover various informative structures with respect to disparate statistical properties. However, multi-view data fusion remains challenging when exploring a proper way to find shared while complementary information. In this paper, we present an adaptive graph weighting scheme to conduct semi-supervised multi-view dimensional reduction. Particularly, we construct a Laplacian graph for each view, and thus the final graph is approximately regarded as a centroid of these single view graphs with different weights. Based on the learned graph, a simple yet effective linear regression function is employed to project data into a low-dimensional space. In addition, our proposed scheme can be well extended to an unsupervised version within a unified framework. Extensive experiments on varying benchmark datasets illustrate that our proposed scheme is superior to several state-of-the-art semi-supervised/unsupervised multi-view dimensionality reduction methods. Last but not least, we demonstrate that our proposed scheme provides a unified view to explain and understand a family of traditional schemes.

Auto-weighted Mutli-view Sparse Reconstructive Embedding

With the development of multimedia era, multi-view data is generated in various fields. Contrast with those single-view data, multi-view data brings more useful information and should be carefully excavated. Therefore, it is essential to fully exploit the complementary information embedded in multiple views to enhance the performances of many tasks. Especially for those high-dimensional data, how to develop a multi-view dimension reduction algorithm to obtain the low-dimensional representations is of vital importance but chanllenging. In this paper, we propose a novel multi-view dimensional reduction algorithm named Auto-weighted Mutli-view Sparse Reconstructive Embedding (AMSRE) to deal with this problem. AMSRE fully exploits the sparse reconstructive correlations between features from multiple views. Furthermore, it is equipped with an auto-weighted technique to treat multiple views discriminatively according to their contributions. Various experiments have verified the excellent performances of the proposed AMSRE.

Co-regularized multi-view sparse reconstruction embedding for dimension reduction

With the development of information technology, we have witnessed an age of data explosion which produces a large variety of data filled with redundant information. Because dimension reduction is an essential tool which embeds high-dimensional data into a lower-dimensional subspace to avoid redundant information, it has attracted interests from researchers all over the world. However, facing with features from multiple views, it’s difficult for most dimension reduction methods to fully comprehended multi-view features and integrate compatible and complementary information from these features to construct low-dimensional subspace directly. Furthermore, most multi-view dimension reduction methods cannot handle features from nonlinear spaces with high dimensions. Therefore, how to construct a multi-view dimension reduction methods which can deal with multi-view features from high-dimensional nonlinear space is of vital importance but challenging. In order to address this problem, we proposed a novel method named Co-regularized Multi-view Sparse Reconstruction Embedding (CMSRE) in this paper. By exploiting correlations of sparse reconstruction from multiple views, CMSRE is able to learn local sparse structures of nonlinear manifolds from multiple views and constructs significative low-dimensional representations for them. Due to the proposed co-regularized scheme, correlations of sparse reconstructions from multiple views are preserved by CMSRE as much as possible. Furthermore, sparse representation produces more meaningful correlations between features from each single view, which helps CMSRE to gain better performances. Various evaluations based on the applications of document classification, face recognition and image retrieval can demonstrate the effectiveness of the proposed approach on multi-view dimension reduction.

Multiview: a software package for multiview pattern recognition methods.

Multiview datasets are the norm in bioinformatics, often under the label multi-omics. Multiview data are gathered from several experiments, measurements or feature sets available for the same subjects. Recent studies in pattern recognition have shown the advantage of using multiview methods of clustering and dimensionality reduction; however, none of these methods are readily available to the extent of our knowledge. Multiview extensions of four well-known pattern recognition methods are proposed here. Three multiview dimensionality reduction methods: multiview t-distributed stochastic neighbour embedding, multiview multidimensional scaling and multiview minimum curvilinearity embedding, as well as a multiview spectral clustering method. Often they produce better results than their single-view counterparts, tested here on four multiview datasets. R package at the B2SLab site: http://b2slab.upc.edu/software-and-tutorials/ and Python package: https://pypi.python.org/pypi/multiview. Supplementary data are available at Bioinformatics online.

A novel multi-view dimensionality reduction and recognition framework with applications to face recognition

Multi-view data with each view corresponding to a type of feature generally provides more comprehensive information. Learning from multi-view data is a challenging research topic in pattern recognition. For recognition task, most multi-view learning methods separately learn multi-view dimensionality reduction (MvDR) and classification models. Thus, the connection between the two models has not been well studied. In this paper, we propose a novel multi-view dimensionality reduction and recognition framework, which can establish the connection between MvDR and classification. Specifically, a multi-view dimensionality reduction method, termed as sparse representation regularized multiset canonical correlation analysis (SR2MCC) is first proposed. SR2MCC considers both correlation and sparse discrimination among multiple views. In accord with SR2MCC, a classifier, called multi-view sparse representation based classifier (MvSRC) is further developed. MvSRC performs classification by comparing the reconstruction residuals of different classes among all views. An efficient iterative algorithm is proposed to solve the proposed model. Extensive experiments on the AR, CMU PIE, FERET, and FRGC datasets demonstrate that the proposed framework can achieve superior recognition performance than several state-of-the-art methods.

Bilevel Multiview Latent Space Learning

Different kinds of features describe different aspects of image data, and each feature can be treated as a view when we take it as a particular understanding of images. Leveraging multiple views provides a richer and comprehensive description than using only a single view. However, multiview data are often represented by high-dimensional heterogeneous features, so it is meaningful to find a low-dimensional consensus representation from multiple views. In this paper, we propose an unsupervised multiview dimensionality reduction method for images based on bilevel latent space learning. As different views have different physical meanings and statistical properties, they are not directly comparable. Therefore, we learn the comparable representation for each view in the first level. The shared and the private nature of multiview data are exploited to accurately preserve the information of each view. Then, we fuse different views into a low-dimensional representation by conducting joint matrix factorization in the second level. To guarantee the low-dimensional representation to be compact and discriminative, the intrinsic geometric structure of data is utilized. Besides, our method considers resisting the outliers and noise contained in multiview data, which may influence the learned representation and deteriorate its semantic consistency. We design appropriate optimization objectives to learn the latent spaces in different levels. Compared with the existing methods, our method could provide a more flexible multiview learning strategy that not only accurately captures the information of each view but also is robust to outliers and noise, which can obtain a more discriminative and compact low-dimensional representation. Experiments on two real-world image data sets demonstrate the advantages of our method over the existing multiview dimensionality reduction methods.

Multi-view dimensionality reduction based on Universum learning

Abstract Canonical correlation analysis (CCA) is a useful dimensionality reduction method and has been widely used in projecting multi-view data. However, CCA learns from training data consisting of only target classes, ignoring Universum data that belongs to none of the target classes but comes from the same domain as the target classes. Recently, incorporating Universum data in learning has been used to gain more prior knowledge about the application domain and has been shown to achieve favorable improvements. In this paper, we extend CCA with Universum learning for multi-view data and the proposed method is termed as Universum CCA (UCCA). Due to the fact that Universum data in each view does not belong to any target class, correlation between Universum data and target data should be minimized. Consequently, UCCA aims to find basis vectors in multiple views to ensure that correlations between projections of target data are mutually maximized but correlations between projections of Universum data and target data mutually minimized. UCCA can be expressed as a generalized eigenvalue problem and the extracted features express patterns more distinctly. The experimental results on several real-world datasets demonstrate its marked improvements over conventional methods.

Multiview dimension reduction via Hessian multiset canonical correlations

Canonical correlation analysis (CCA) is a main technique of linear subspace approach for two-view dimension reduction by finding basis vectors with maximum correlation between the pair of variables. The shortcoming of the traditional CCA lies that it only handles data represented by two-view features and cannot reveal the nonlinear correlation relationship. In recent years, many variant algorithms have been developed to extend the capability of CCA such as discriminative CCA, sparse CCA, kernel CCA, locality preserving CCA and multiset canonical correlation analysis (MCCA). One representative work is Laplacian multiset canonical correlations (LapMCC) that employs graph Laplacian to exploit the nonlinear correlation information for multiview high-dimensional data. However, it possibly leads to poor extrapolating power because Laplacian regularization biases the solution towards a constant function. In this paper, we present Hessian multiset canonical correlations (HesMCC) for multiview dimension reduction. Hessian can properly exploit the intrinsic local geometry of the data manifold in contrast to Laplacian. HesMCC takes the advantage of Hessian and provides superior extrapolating capability and finally leverage the performance. Extensive experiments on several popular datasets for handwritten digits classification, face classification and object classification validate the effectiveness of the proposed HesMCC algorithm by comparing it with baseline algorithms including TCCA, KMUDA, MCCA and LapMCC.

Joint Structured Sparsity Regularized Multiview Dimension Reduction for Video-Based Facial Expression Recognition

Video-based facial expression recognition (FER) has recently received increased attention as a result of its widespread application. Using only one type of feature to describe facial expression in video sequences is often inadequate, because the information available is very complex. With the emergence of different features to represent different properties of facial expressions in videos, an appropriate combination of these features becomes an important, yet challenging, problem. Considering that the dimensionality of these features is usually high, we thus introduce multiview dimension reduction (MVDR) into video-based FER. In MVDR, it is critical to explore the relationships between and within different feature views. To achieve this goal, we propose a novel framework of MVDR by enforcing joint structured sparsity at both inter- and intraview levels. In this way, correlations on and between the feature spaces of different views tend to be well-exploited. In addition, a transformation matrix is learned for each view to discover the patterns contained in the original features, so that the different views are comparable in finding a common representation. The model can be not only performed in an unsupervised manner, but also easily extended to a semisupervised setting by incorporating some domain knowledge. An alternating algorithm is developed for problem optimization, and each subproblem can be efficiently solved. Experiments on two challenging video-based FER datasets demonstrate the effectiveness of the proposed framework.

Multi-view dimensionality reduction via subspace structure agreement

Many state-of-the-art biometric systems make use of high-dimensional features to represent data samples, which often contain substantial amount of intra-class variation. In this paper, we propose an unsupervised multi-view dimensionality reduction approach to extract discriminative low-dimensional features and apply it to multi-modal biometric retrieval problems. The proposed approach is based on a novel concept referred to as multi-view subspace structure agreement, which aims to learn a subspace projection for each view, such that the k-nearest-neighbour similarity graphs built in subspaces of different views are maximumly compatible. The proposed method is unsupervised in nature, but exhibits high discriminative power and is thus well suited to applications where class labels are generally unavailable such as retrieval and clustering. We evaluate the performance of the proposed algorithm under an audio-visual speaker retrieval experiment, as well as a multi-feature face retrieval experiment. Experimental results show that the retrieval performance of the proposed approach out-performs other competing methods with a significant margin.

Cost Sensitive Semi-Supervised Canonical Correlation Analysis for Multi-view Dimensionality Reduction

To deal with the cost sensitive and semi-supervised learning problems in Multi-view Dimensionality Reduction (MDR), we propose a Cost Sensitive Semi-Supervised Canonical Correlation Analysis $$(\hbox {CS}^{3}\hbox {CCA}). \hbox {CS}^{3}\hbox {CCA}$$(CS3CCA).CS3CCA first uses the $$L_2$$L2 norm approach to obtain the soft label for each unlabeled data, and then embed the misclassification cost into the framework of Canonical Correlation Analysis (CCA). Compared with existing CCA based methods, $$\hbox {CS}^{3}\hbox {CCA}$$CS3CCA has the following advantages: (1) It uses the $$L_2$$L2 norm approach to infer the soft label for unlabeled data, which is computationally efficient and effective, especially for cost sensitive face recognition. (2) The objective function of $$\hbox {CS}^{3}\hbox {CCA}$$CS3CCA not only maximizes the soft cost sensitive within-class correlations and minimizes the soft cost sensitive between-class correlations in the inter-view, but also considers the class imbalance problem simultaneously. With the discriminant projections learned by $$\hbox {CS}^{3}\hbox {CCA}$$CS3CCA, we employ it for cost sensitive face recognition. The experimental results on four well-known face data sets, including AR, Extended Yale B, PIE and ORL, demonstrate the effectiveness of $$\hbox {CS}^{3}\hbox {CCA}$$CS3CCA.

Fractional-Order Embedding Supervised Canonical Correlations Analysis with Applications to Feature Extraction and Recognition

Due to the noise disturbance and limited number of training samples, within-set and between-set sample covariance matrices in canonical correlations analysis (CCA) based methods usually deviate from the true ones. In this paper, we re-estimate the covariance matrices by embedding fractional order and incorporate the class label information. First, we illustrate the effectiveness of the fractional-order embedding model through theory analysis and experiments. Then, we quote fractional-order within-set and between-set scatter matrices, which can significantly reduce the deviation of sample covariance matrices. Finally, we incorporate the supervised information, novel generalized CCA and discriminative CCA are presented for multi-view dimensionality reduction and recognition, called fractional-order embedding generalized canonical correlations analysis and fractional-order embedding discriminative canonical correlations analysis. Extensive experimental results on various handwritten numeral, face and object recognition problems show that the proposed methods are very effective and obviously outperform the existing methods in terms of classification accuracy.

Multi-view dimensionality reduction via canonical random correlation analysis

Canonical correlation analysis (CCA) is one of the most well-known methods to extract features from multi-view data and has attracted much attention in recent years. However, classical CCA is unsupervised and does not take discriminant information into account. In this paper, we add discriminant information into CCA by using random cross-view correlations between within-class samples and propose a new method for multi-view dimensionality reduction called canonical random correlation analysis (RCA). In RCA, two approaches for randomly generating cross-view correlation samples are developed on the basis of bootstrap technique. Furthermore, kernel RCA (KRCA) is proposed to extract nonlinear correlations between different views. Experiments on several multi-view data sets show the effectiveness of the proposed methods.

Laplacian multiset canonical correlations for multiview feature extraction and image recognition

Multiset canonical correlation analysis (MCCA) aims at revealing the linear correlations among multiple sets of high-dimensional data. Therefore, it is only a linear multiview dimensionality reduction technique and such a linear model is insufficient to discover the nonlinear correlation information hidden in multiview data. In this paper, we incorporate the local structure information into MCCA and propose a novel algorithm for multiview dimensionality reduction, called Laplacian multiset canonical correlations (LapMCCs), which simultaneously considers local within-view and local between-view correlations by using nearest neighbor graphs. This makes LapMCC capable of discovering the nonlinear correlation information among multiview data by combining many locally linear problems together. Moreover, we also develop an orthogonal version of LapMCC to preserve the metric structure. The proposed LapMCC method is applied to face and object image recognition. The experimental results on AR, Yale-B, AT&T, and ETH-80 databases demonstrate the superior performance of LapMCC compared to existing multiview dimensionality reduction methods.

Tensor Canonical Correlation Analysis for Multi-View Dimension Reduction

Canonical correlation analysis (CCA) has proven an effective tool for two-view dimension reduction due to its profound theoretical foundation and success in practical applications. In respect of multi-view learning, however, it is limited by its capability of only handling data represented by two-view features, while in many real-world applications, the number of views is frequently many more. Although the ad hoc way of simultaneously exploring all possible pairs of features can numerically deal with multi-view data, it ignores the high order statistics (correlation information) which can only be discovered by simultaneously exploring all features. Therefore, in this work, we develop tensor CCA (TCCA) which straightforwardly yet naturally generalizes CCA to handle the data of an arbitrary number of views by analyzing the covariance tensor of the different views. TCCA aims to directly maximize the canonical correlation of multiple (more than two) views. Crucially, we prove that the multi-view canonical correlation maximization problem is equivalent to finding the best rank-1 approximation of the data covariance tensor, which can be solved efficiently using the well-known alternating least squares (ALS) algorithm. As a consequence, the high order correlation information contained in the different views is explored and thus a more reliable common subspace shared by all features can be obtained. In addition, a non-linear extension of TCCA is presented. Experiments on various challenge tasks, including large scale biometric structure prediction, internet advertisement classification and web image annotation, demonstrate the effectiveness of the proposed method.

A novel semi-supervised canonical correlation analysis and extensions for multi-view dimensionality reduction

Canonical correlation analysis (CCA) is an efficient method for dimensionality reduction on two-view data. However, as an unsupervised learning method, CCA cannot utilize partly given label information in multi-view semi-supervised scenarios. In this paper, we propose a novel two-view semi-supervised learning method, called semi-supervised canonical correlation analysis based on label propagation (LPbSCCA). LPbSCCA incorporates a new sparse representation based label propagation algorithm to infer label information for unlabeled data. Specifically, it firstly constructs dictionaries consisting of all labeled samples; and then obtains reconstruction coefficients of unlabeled samples using sparse representation technique; at last, by combining given labels of labeled samples, estimates label information for unlabeled ones. After that, it constructs soft label matrices of all samples and probabilistic within-class scatter matrices in each view. Finally, in order to enhance discriminative power of features, it is formulated to maximize the correlations between samples of the same class from cross views, while minimizing within-class variations in the low-dimensional feature space of each view simultaneously. Furthermore, we also extend a general model called LPbSMCCA to handle data from multiple (more than two) views. Extensive experimental results from several well-known datasets demonstrate that the proposed methods can achieve better recognition performances and robustness than existing related methods.

Spectral embedding based facial expression recognition with multiple features

Many approaches to facial expression recognition utilize only one type of features at a time. It can be difficult for a single type of features to characterize in a best possible way the variations and complexity of realistic facial expressions. In this paper, we propose a spectral embedding based multi-view dimension reduction method to fuse multiple features for facial expression recognition. Facial expression features extracted from one type of expressions can be assumed to form a manifold embedded in a high dimensional feature space. We construct a neighborhood graph that encodes the structure of the manifold locally. A graph Laplacian matrix is constructed whose spectral decompositions reveal the low dimensional structure of the manifold. In order to obtain discriminative features for classification, we propose to build a neighborhood graph in a supervised manner by utilizing the label information of training data. As a result, multiple features are able to be transformed into a unified low dimensional feature space by combining the Laplacian matrix of each view with the multiview spectral embedding algorithm. A linearization method is utilized to map unseen data to the learned unified subspace. Experiments are conducted on a set of established real-world and benchmark datasets. The experimental results provide a strong support to the effectiveness of the proposed feature fusion framework on realistic facial expressions.

Fractional-order embedding canonical correlation analysis and its applications to multi-view dimensionality reduction and recognition

Due to the noise disturbance and limited number of training samples, within-set and between-set sample covariance matrices in canonical correlation analysis (CCA) usually deviate from the true ones. In this paper, we re-estimate within-set and between-set covariance matrices to reduce the negative effect of this deviation. Specifically, we use the idea of fractional order to respectively correct the eigenvalues and singular values in the corresponding sample covariance matrices, and then construct fractional-order within-set and between-set scatter matrices which can obviously alleviate the problem of the deviation. On this basis, a new approach is proposed to reduce the dimensionality of multi-view data for classification tasks, called fractional-order embedding canonical correlation analysis (FECCA). The proposed method is evaluated on various handwritten numeral, face and object recognition problems. Extensive experimental results on the CENPARMI, UCI, AT&T, AR, and COIL-20 databases show that FECCA is very effective and obviously outperforms the existing joint dimensionality reduction or feature extraction methods in terms of classification accuracy. Moreover, its improvements for recognition rates are statistically significant on most cases below the significance level 0.05.