Multiview Privileged Support Vector Machines

Enhancing multiview synergy: Robust learning by exploiting the wave loss function with consensus and complementarity principles

Multiview learning (MvL) is an advancing domain in machine learning, leveraging multiple data perspectives to enhance model performance through view-consistency and view-discrepancy. Despite numerous successful multiview-based support vector machine (SVM) models, existing frameworks predominantly focus on the consensus principle, often overlooking the complementarity principle. Furthermore, they exhibit limited robustness against noisy, error-prone, and view-inconsistent samples, prevalent in multiview datasets. To tackle the aforementioned limitations, this paper introduces Wave-MvSVM, a novel multiview support vector machine framework leveraging the wave loss (W-loss) function, specifically designed to harness both consensus and complementarity principles. Unlike traditional approaches that often overlook the complementary information among different views, the proposed Wave-MvSVM ensures a more comprehensive and resilient learning process by integrating both principles effectively. The W-loss function, characterized by its smoothness, asymmetry, and bounded nature, is particularly effective in mitigating the adverse effects of noisy and outlier data, thereby enhancing model stability. Theoretically, the W-loss function also exhibits a crucial classification-calibrated property, further boosting its effectiveness. The proposed Wave-MvSVM employs a between-view co-regularization term to enforce view consistency and utilizes an adaptive combination weight strategy to maximize the discriminative power of each view, thus fully exploiting both consensus and complementarity principles. The optimization problem is efficiently solved using a combination of gradient descent (GD) and the alternating direction method of multipliers (ADMM), ensuring reliable convergence to optimal solutions. The generalization abilities of the proposed Wave-MvSVM model is theoretically supported through analyses based on Rademacher complexity. Extensive empirical evaluations across diverse datasets demonstrate the superior performance of Wave-MvSVM in comparison to existing benchmark models, highlighting its potential as a robust and efficient solution for MvL challenges. Furthermore, we implemented the proposed Wave-MvSVM model on Schizophrenia dataset, showcasing the model's efficacy in real-world applications. The source code of the proposed Wave-MvSVM model is available at https://github.com/mtanveer1/Wave-MvSVM.

Multiview Large Margin Distribution Machine

Margin distribution has been proven to play a crucial role in improving generalization ability. In recent studies, many methods are designed using large margin distribution machine (LDM), which combines margin distribution with support vector machine (SVM), such that a better performance can be achieved. However, these methods are usually proposed based on single-view data and ignore the connection between different views. In this article, we propose a new multiview margin distribution model, called MVLDM, which constructs both multiview margin mean and variance. Besides, a framework is proposed to achieve multiview learning (MVL). MVLDM provides a new way to explore the utilization of complementary information in MVL from the perspective of margin distribution and satisfies both the consistency principle and the complementarity principle. In the theoretical analysis, we used Rademacher complexity theory to analyze the consistency error bound and generalization error bound of the MVLDM. In the experiments, we constructed a new performance metric, the view consistency rate (VCR), for the characteristics of multiview data. The effectiveness of MVLDM was evaluated using both VCR and other traditional performance metrics. The experimental results show that MVLDM is superior to other benchmark methods.

Self-adaptive label discovery and multi-view fusion for complementary label learning

Unlike traditional supervised classification, complementary label learning (CLL) operates under a weak supervision framework, where each sample is annotated by excluding several incorrect labels, known as complementary labels (CLs). Despite reducing the labeling burden, CLL always suffers a decline in performance due to the weakened supervised information. To overcome such limitations, in this study, a multi-view fusion and self-adaptive label discovery based CLL method (MVSLDCLL) is proposed. The self-adaptive label discovery strategy leverages graph-based semi-supervised learning to capture the label distribution of each training sample as a convex combination of all its potential labels. The multi-view fusion module is designed to adapt to various views of feature representations. In specific, it minimizes the discrepancies of label projections between pairwise views, aligning with the consensus principle. Additionally, a straightforward mechanism inspired by a teamwork analogy is proposed to incorporate view-discrepancy for each sample. Experimental results demonstrate that MVSLDCLL learns more discriminative label distribution and achieves significantly higher accuracies compared to state-of-the-art CLL methods. Ablation study has also been performed to validate the effectiveness of both the self-adaptive label discovery strategy and the multi-view fusion module.

Multiview learning with twin parametric margin SVM

Multiview learning (MVL) seeks to leverage the benefits of diverse perspectives to complement each other, effectively extracting and utilizing the latent information within the dataset. Several twin support vector machine-based MVL (MvTSVM) models have been introduced and demonstrated outstanding performance in various learning tasks. However, MvTSVM-based models face significant challenges in the form of computational complexity due to four matrix inversions, the need to reformulate optimization problems in order to employ kernel-generated surfaces for handling non-linear cases, and the constraint of uniform noise assumption in the training data. Particularly in cases where the data possesses a heteroscedastic error structure, these challenges become even more pronounced. In view of the aforementioned challenges, we propose multiview twin parametric margin support vector machine (MvTPMSVM). MvTPMSVM constructs parametric margin hyperplanes corresponding to both classes, aiming to regulate and manage the impact of the heteroscedastic noise structure existing within the data. The proposed MvTPMSVM model avoids the explicit computation of matrix inversions in the dual formulation, leading to enhanced computational efficiency. We perform an extensive assessment of the MvTPMSVM model using benchmark datasets such as UCI, KEEL, synthetic, and Animals with Attributes (AwA). Our experimental results, coupled with rigorous statistical analyses, confirm the superior generalization capabilities of the proposed MvTPMSVM model compared to the baseline models. The source code of the proposed MvTPMSVM model is available at https://github.com/mtanveer1/MvTPMSVM.

Maximal Margin Support Vector Machine for Feature Representation and Classification

High-dimensional small sample size data, which may lead to singularity in computation, are becoming increasingly common in the field of pattern recognition. Moreover, it is still an open problem how to extract the most suitable low-dimensional features for the support vector machine (SVM) and simultaneously avoid singularity so as to enhance the SVM's performance. To address these problems, this article designs a novel framework that integrates the discriminative feature extraction and sparse feature selection into the support vector framework to make full use of the classifiers' characteristics to find the optimal/maximal classification margin. As such, the extracted low-dimensional features from high-dimensional data are more suitable for SVM to obtain good performance. Thus, a novel algorithm, called the maximal margin SVM (MSVM), is proposed to achieve this goal. An alternatively iterative learning strategy is adopted in MSVM to learn the optimal discriminative sparse subspace and the corresponding support vectors. The mechanism and the essence of the designed MSVM are revealed. The computational complexity and convergence are also analyzed and validated. Experimental results on some well-known databases (including breastmnist, pneumoniamnist, colon-cancer, etc.) show the great potential of MSVM against classical discriminant analysis methods and SVM-related methods, and the codes can be available on https://www.scholat.com/laizhihui.

Attention and Prediction-Guided Motion Detection for Low-Contrast Small Moving Targets

Small target motion detection within complex natural environments is an extremely challenging task for autonomous robots. Surprisingly, the visual systems of insects have evolved to be highly efficient in detecting mates and tracking prey, even though targets occupy as small as a few degrees of their visual fields. The excellent sensitivity to small target motion relies on a class of specialized neurons, called small target motion detectors (STMDs). However, existing STMD-based models are heavily dependent on visual contrast and perform poorly in complex natural environments, where small targets generally exhibit extremely low contrast against neighboring backgrounds. In this article, we develop an attention-and-prediction-guided visual system to overcome this limitation. The developed visual system comprises three main subsystems, namely: 1) an attention module; 2) an STMD-based neural network; and 3) a prediction module. The attention module searches for potential small targets in the predicted areas of the input image and enhances their contrast against a complex background. The STMD-based neural network receives the contrast-enhanced image and discriminates small moving targets from background false positives. The prediction module foresees future positions of the detected targets and generates a prediction map for the attention module. The three subsystems are connected in a recurrent architecture, allowing information to be processed sequentially to activate specific areas for small target detection. Extensive experiments on synthetic and real-world datasets demonstrate the effectiveness and superiority of the proposed visual system for detecting small, low-contrast moving targets against complex natural environments.

Safe screening rules for multi-view support vector machines

Multi-view learning aims to make use of the advantages of different views to complement each other and fully mines the potential information in the data. However, the complexity of multi-view learning algorithm is much higher than that of single view learning algorithm. Based on the optimality conditions of two classical multi-view models: SVM-2K and multi-view twin support vector machine (MvTwSVM), this paper analyzes the corresponding relationship between dual variables and samples, and derives their safe screening rules for the first time, termed as SSR-SVM-2K and SSR-MvTwSVM. It can assign or delete four groups of different dual variables in advance before solving the optimization problem, so as to greatly reduce the scale of the optimization problem and improve the solution speed. More importantly, the safe screening criterion is "safe", that is, the solution of the reduced optimization problem is the same as that of the original problem before screening. In addition, we further give a sequence screening rule to speed up the parameter optimization process, and analyze its properties, including the similarities and differences of safe screening rules between multi-view SVMs and single-view SVMs, the computational complexity, and the relationship between the parameter interval and screening rate. Numerical experiments verify the effectiveness of the proposed methods.

Identification and immunological characterization of lipid metabolism-related molecular clusters in nonalcoholic fatty liver disease

BACKGROUND

Nonalcoholic fatty liver disease (NAFLD) is now the major contributor to chronic liver disease. Disorders of lipid metabolism are a major element in the emergence of NAFLD. This research intended to explore lipid metabolism-related clusters in NAFLD and establish a prediction biomarker.

METHODS

The expression mode of lipid metabolism-related genes (LMRGs) and immune characteristics in NAFLD were examined. The "ConsensusClusterPlus" package was utilized to investigate the lipid metabolism-related subgroup. The WGCNA was utilized to determine hub genes and perform functional enrichment analysis. After that, a model was constructed by machine learning techniques. To validate the predictive effectiveness, receiver operating characteristic curves, nomograms, decision curve analysis (DCA), and test sets were used. Lastly, gene set variation analysis (GSVA) was utilized to investigate the biological role of biomarkers in NAFLD.

RESULTS

Dysregulated LMRGs and immunological responses were identified between NAFLD and normal samples. Two LMRG-related clusters were identified in NAFLD. Immune infiltration analysis revealed that C2 had much more immune infiltration. GSVA also showed that these two subtypes have distinctly different biological features. Thirty cluster-specific genes were identified by two WGCNAs. Functional enrichment analysis indicated that cluster-specific genes are primarily engaged in adipogenesis, signalling by interleukins, and the JAK-STAT signalling pathway. Comparing several models, the random forest model exhibited good discrimination performance. Importantly, the final five-gene random forest model showed excellent predictive power in two test sets. In addition, the nomogram and DCA confirmed the precision of the model for NAFLD prediction. GSVA revealed that model genes were down-regulated in several immune and inflammatory-related routes. This suggests that these genes may inhibit the progression of NAFLD by inhibiting these pathways.

CONCLUSIONS

This research thoroughly emphasized the complex relationship between LMRGs and NAFLD and established a five-gene biomarker to evaluate the risk of the lipid metabolism phenotype and the pathologic results of NAFLD.

Rapid quantitative analysis of rare earth elements Lu and Y in rare earth ores by laser induced breakdown spectroscopy combined with iPLS-VIP and partial least squares

Rare earth ores are complex in composition and diverse in mineral composition, requiring high technical requirements for the selection of rare earth ores. It is of great significance to explore the on-site rapid detection and analysis methods of rare earth elements in rare earth ores. Laser induced breakdown spectroscopy (LIBS) is an important tool to detect rare earth ores, which can be used for in situ analyses without complicated sample preparation. In this study, a rapid quantitative analysis method for rare earth elements Lu and Y in rare earth ores was established by LIBS combined with an iPLS-VIP hybrid variable selection strategy and partial least squares (PLS) method. First, the LIBS spectra of 25 samples were studied using laser induced breakdown spectrometry. Second, taking the spectrum processed by wavelet transform (WT) as the input variables, PLS calibration models based on interval partial least squares (iPLS), variable importance projection (VIP) and iPLS-VIP hybrid variable selection were constructed to quantitatively analyze rare earth elements Lu and Y, respectively. The results show that the WT-iPLS-VIP-PLS calibration model has better prediction performance for rare earth elements Lu and Y, and the optimal coefficient of determination (R²) of Lu and Y were 0.9897 and 0.9833, the root mean square error (RMSE) were 0.8150 μg g^-1 and 97.1047 μg g^-1, and the mean relative error (MRE) were 0.0754 and 0.0766, respectively. It shows that LIBS technology combined with the iPLS-VIP and PLS calibration model provides a new method for in situ quantitative analysis of rare earth elements in rare earth ores.

Multiview Learning With Robust Double-Sided Twin SVM

Multiview learning (MVL), which enhances the learners' performance by coordinating complementarity and consistency among different views, has attracted much attention. The multiview generalized eigenvalue proximal support vector machine (MvGSVM) is a recently proposed effective binary classification method, which introduces the concept of MVL into the classical generalized eigenvalue proximal support vector machine (GEPSVM). However, this approach cannot guarantee good classification performance and robustness yet. In this article, we develop multiview robust double-sided twin SVM (MvRDTSVM) with SVM-type problems, which introduces a set of double-sided constraints into the proposed model to promote classification performance. To improve the robustness of MvRDTSVM against outliers, we take L1-norm as the distance metric. Also, a fast version of MvRDTSVM (called MvFRDTSVM) is further presented. The reformulated problems are complex, and solving them are very challenging. As one of the main contributions of this article, we design two effective iterative algorithms to optimize the proposed nonconvex problems and then conduct theoretical analysis on the algorithms. The experimental results verify the effectiveness of our proposed methods.

Elastic Net Nonparallel Hyperplane Support Vector Machine and Its Geometrical Rationality

Twin support vector machine (TWSVM), which constructs two nonparallel classifying hyperplanes, is widely applied to various fields. However, TWSVM solves two quadratic programming problems (QPPs) separately such that the final classifiers lack consistency and enough prediction accuracy. Moreover, by reason of only considering the 1-norm penalty for slack variables, TWSVM is not well defined in the geometrical view. In this article, we propose a novel elastic net nonparallel hyperplane support vector machine (ENNHSVM), which adopts elastic net penalty for slack variables and constructs two nonparallel separating hyperplanes simultaneously. We further discuss the properties of ENNHSVM theoretically and derive the violation tolerance upper bound to better demonstrate the relative violations of training samples in the same class. In particular, we design a safe screening rule for ENNHSVM to speed up the calculations. We finally compare the performance of ENNHSVM on both synthetic datasets and benchmark datasets with the Lagrangian SVM, the twin parametric-margin SVM, the elastic net SVM, the TWSVM, and the nonparallel hyperplane SVM.

Mathematical study of neural feedback roles in small target motion detection

Building an efficient and reliable small target motion detection visual system is challenging for artificial intelligence robotics because a small target only occupies few pixels and hardly displays visual features in images. Biological visual systems that have evolved over millions of years could be ideal templates for designing artificial visual systems. Insects benefit from a class of specialized neurons, called small target motion detectors (STMDs), which endow them with an excellent ability to detect small moving targets against a cluttered dynamic environment. Some bio-inspired models featured in feed-forward information processing architectures have been proposed to imitate the functions of the STMD neurons. However, feedback, a crucial mechanism for visual system regulation, has not been investigated deeply in the STMD-based neural circuits and its roles in small target motion detection remain unclear. In this paper, we propose a time-delay feedback STMD model for small target motion detection in complex backgrounds. The main contributions of this study are as follows. First, a feedback pathway is designed by transmitting information from output-layer neurons to lower-layer interneurons in the STMD pathway and the role of the feedback is analyzed from the view of mathematical analysis. Second, to estimate the feedback constant, the existence and uniqueness of solutions for nonlinear dynamical systems formed by feedback loop are analyzed via Schauder's fixed point theorem and contraction mapping theorem. Finally, an iterative algorithm is designed to solve the nonlinear problem and the performance of the proposed model is tested by experiments. Experimental results demonstrate that the feedback is able to weaken background false positives while maintaining a minor effect on small targets. It outperforms existing STMD-based models regarding the accuracy of fast-moving small target detection in visual clutter. The proposed feedback approach could inspire the relevant modeling of robust motion perception robotics visual systems.

Multi-Source Transfer Learning Via Multi-Kernel Support Vector Machine Plus for B-Mode Ultrasound-Based Computer-Aided Diagnosis of Liver Cancers

B-mode ultrasound (BUS) imaging is a routine tool for diagnosis of liver cancers, while contrast-enhanced ultrasound (CEUS) provides additional information to BUS on the local tissue vascularization and perfusion to promote diagnostic accuracy. In this work, we propose to improve the BUS-based computer aided diagnosis for liver cancers by transferring knowledge from the multi-view CEUS images, including the arterial phase, portal venous phase, and delayed phase, respectively. To make full use of the shared labels of paired of BUS and CEUS images to guide knowledge transfer, support vector machine plus (SVM+), a specifically designed transfer learning (TL) classifier for paired data with shared labels, is adopted for this supervised TL. A nonparallel hyperplane based SVM+ (NHSVM+) is first proposed to improve the TL performance by transferring the per-class knowledge from source domain to the corresponding target domain. Moreover, to handle the issue of multi-source TL, a multi-kernel learning based NHSVM+ (MKL-NHSVM+) algorithm is further developed to effectively transfer multi-source knowledge from multi-view CEUS images. The experimental results indicate that the proposed MKL-NHSVM+ outperforms all the compared algorithms for diagnosis of liver cancers, whose mean classification accuracy, sensitivity, and specificity are 88.18 ± 3.16 %, 86.98 ± 4.77 %, and 89.42±3.77%, respectively.

Multi-view learning based on maximum margin of twin spheres support vector machine

Multi-view learning utilizes information from multiple representations to advance the performance of categorization. Most of the multi-view learning algorithms based on support vector machines seek the separating hyperplanes in different feature spaces, which may be unreasonable in practical application. Besides, most of them are designed to balanced data, which may lead to poor performance. In this work, a novel multi-view learning algorithm based on maximum margin of twin spheres support vector machine (MvMMTSSVM) is introduced. The proposed method follows both maximum margin principle and consensus principle. By following the maximum margin principle, it constructs two homocentric spheres and tries to maximize the margin between the two spheres for each view separately. To realize the consensus principle, the consistency constraints of two views are introduced in the constraint conditions. Therefore, it not only deals with multi-view class-imbalanced data effectively, but also has fast calculation efficiency. To verify the validity and rationlity of our MvMMTSSVM, we do the experiments on 24 binary datasets. Furthermore, we use Friedman test to verify the effectiveness of MvMMTSSVM.

Robust cost-sensitive kernel method with Blinex loss and its applications in credit risk evaluation

Credit risk evaluation is a crucial yet challenging problem in financial analysis. It can not only help institutions reduce risk and ensure profitability, but also improve consumers' fair practices. The data-driven algorithms such as artificial intelligence techniques regard the evaluation as a classification problem and aim to classify transactions as default or non-default. Since non-default samples greatly outnumber default samples, it is a typical imbalanced learning problem and each class or each sample needs special treatment. Numerous data-level, algorithm-level and hybrid methods are presented, and cost-sensitive support vector machines (CSSVMs) are representative algorithm-level methods. Based on the minimization of symmetric and unbounded loss functions, CSSVMs impose higher penalties on the misclassification costs of minority instances using domain specific parameters. However, such loss functions as error measurement cannot have an obvious cost-sensitive generalization. In this paper, we propose a robust cost-sensitive kernel method with Blinex loss (CSKB), which can be applied in credit risk evaluation. By inheriting the elegant merits of Blinex loss function, i.e., asymmetry and boundedness, CSKB not only flexibly controls distinct costs for both classes, but also enjoys noise robustness. As a data-driven decision-making paradigm of credit risk evaluation, CSKB can achieve the "win-win" situation for both the financial institutions and consumers. We solve linear and nonlinear CSKB by Nesterov accelerated gradient algorithm and Pegasos algorithm respectively. Moreover, the generalization capability of CSKB is theoretically analyzed. Comprehensive experiments on synthetic, UCI and credit risk evaluation datasets demonstrate that CSKB compares more favorably than other benchmark methods in terms of various measures.

Multiview Concept Learning Via Deep Matrix Factorization

Multiview representation learning (MVRL) leverages information from multiple views to obtain a common representation summarizing the consistency and complementarity in multiview data. Most previous matrix factorization-based MVRL methods are shallow models that neglect the complex hierarchical information. The recently proposed deep multiview factorization models cannot explicitly capture consistency and complementarity in multiview data. We present the deep multiview concept learning (DMCL) method, which hierarchically factorizes the multiview data, and tries to explicitly model consistent and complementary information and capture semantic structures at the highest abstraction level. We explore two variants of the DMCL framework, DMCL-L and DMCL-N, with respectively linear/nonlinear transformations between adjacent layers. We propose two block coordinate descent-based optimization methods for DMCL-L and DMCL-N. We verify the effectiveness of DMCL on three real-world data sets for both clustering and classification tasks.

MVStream: Multiview Data Stream Clustering

This article studies a new problem of data stream clustering, namely, multiview data stream (MVStream) clustering. Although many data stream clustering algorithms have been developed, they are restricted to the single-view streaming data, and clustering MVStreams still remains largely unsolved. In addition to the many issues encountered by the conventional single-view data stream clustering, such as capturing cluster evolution and discovering clusters of arbitrary shapes under the limited computational resources, the main challenge of MVStream clustering lies in integrating information from multiple views in a streaming manner and abstracting summary statistics from the integrated features simultaneously. In this article, we propose a novel MVStream clustering algorithm for the first time. The main idea is to design a multiview support vector domain description (MVSVDD) model, by which the information from multiple insufficient views can be integrated, and the outputting support vectors (SVs) are utilized to abstract the summary statistics of the historical multiview data objects. Based on the MVSVDD model, a new multiview cluster labeling method is designed, whereby clusters of arbitrary shapes can be discovered for each view. By tracking the cluster labels of SVs in each view, the cluster evolution associated with concept drift can be captured. Since the SVs occupy only a small portion of data objects, the proposed MVStream algorithm is quite efficient with the limited computational resources. Extensive experiments are conducted to demonstrate the effectiveness and efficiency of the proposed method.

Iterative Privileged Learning

While in the learning using privileged information paradigm, privileged information may not be as informative as example features in the context of making accurate label predictions, it may be able to provide some effective comments (e.g., the values of the auxiliary function) like a human teacher on the efficacy of the learned model. In a departure from conventional static manipulations of privileged information within the support vector machine framework, this paper investigates iterative privileged learning within the context of gradient boosted decision trees (GBDTs). As the learned model evolves, the comments learned from privileged information to assess the model should also be actively upgraded instead of remaining static and passive. During the learning phase of the GBDT method, new DTs are discovered to enhance the performance of the model, and iteratively update the comments generated from the privileged information to accurately assess and coach the up-to-date model. The resulting objective function can be efficiently solved within the gradient boosting framework. Experimental results on real-world data sets demonstrate the benefits of studying privileged information in an iterative manner, as well as the effectiveness of the proposed algorithm.

A unified robust framework for multi-view feature extraction with L2,1-norm constraint

Multi-view feature extraction methods mainly focus on exploiting the consistency and complementary information between multi-view samples, and most of the current methods apply the F-norm or L2-norm as the metric, which are sensitive to the outliers or noises. In this paper, based on L2,1-norm, we propose a unified robust feature extraction framework, which includes four special multi-view feature extraction methods, and extends the state-of-art methods to a more generalized form. The proposed methods are less sensitive to outliers or noises. An efficient iterative algorithm is designed to solve L2,1-norm based methods. Comprehensive analyses, such as convergence analysis, rotational invariance analysis and relationship between our methods and previous F-norm based methods illustrate the effectiveness of our proposed methods. Experiments on two artificial datasets and six real datasets demonstrate that the proposed L2,1-norm based methods have better performance than the related methods.

Multiview Semantic Representation for Visual Recognition

Due to interclass and intraclass variations, the images of different classes are often cluttered which makes it hard for efficient classifications. The use of discriminative classification algorithms helps to alleviate this problem. However, it is still an open problem to accurately model the relationships between visual representations and human perception. To alleviate these problems, in this paper, we propose a novel multiview semantic representation (MVSR) algorithm for efficient visual recognition. First, we leverage visually based methods to get initial image representations. We then use both visual and semantic similarities to divide images into groups which are then used for semantic representations. We treat different image representation strategies, partition methods, and numbers as different views. A graph is then used to combine the discriminative power of different views. The similarities between images can be obtained by measuring the similarities of graphs. Finally, we train classifiers to predict the categories of images. We evaluate the discriminative power of the proposed MVSR method for visual recognition on several public image datasets. Experimental results show the effectiveness of the proposed method.

Improved multi-view GEPSVM via Inter-View Difference Maximization and Intra-view Agreement Minimization

Multiview Generalized Eigenvalue Proximal Support Vector Machine (MvGEPSVM) is an effective method for multiview data classification proposed recently. However, it ignores discriminations between different views and the agreement of the same view. Moreover, there is no robustness guarantee. In this paper, we propose an improved multiview GEPSVM (IMvGEPSVM) method, which adds a multi-view regularization that can connect different views of the same class and simultaneously considers the maximization of the samples from different classes in heterogeneous views for promoting discriminations. This makes the classification more effective. In addition, L1-norm rather than squared L2-norm is employed to calculate the distances from each of the sample points to the hyperplane so as to reduce the effect of outliers in the proposed model. To solve the resulting objective, an efficient iterative algorithm is presented. Theoretically, we conduct the proof of the algorithm's convergence. Experimental results show the effectiveness of the proposed method.

Discriminative Multi-view Privileged Information Learning for Image Re-ranking

Conventional multi-view re-ranking methods usually perform asymmetrical matching between the region of interest (ROI) in the query image and the whole target image for similarity computation. Due to the inconsistency in the visual appearance, this practice tends to degrade the retrieval accuracy particularly when the image ROI, which is usually interpreted as the image objectness, accounts for a smaller region in the image. Since Privileged Information (PI), which can be viewed as the image prior, is able to characterize well the image objectness, we are aiming at leveraging PI for further improving the performance of multi-view re-ranking in this paper. Towards this end, we propose a discriminative multi-view re-ranking approach in which both the original global image visual contents and the local auxiliary PI features are simultaneously integrated into a unified training framework for generating the latent subspaces with sufficient discriminating power. For the on-the-fly re-ranking, since the multi-view PI features are unavailable, we only project the original multi-view image representations onto the latent subspace, and thus the re-ranking can be achieved by computing and sorting the distances from the multi-view embeddings to the separating hyperplane. Extensive experimental evaluations on the two public benchmarks, Oxford5k and Paris6k, reveal that our approach provides further performance boost for accurate image re-ranking, whilst the comparative study demonstrates the advantage of our method against other multi-view re-ranking methods.

Multi-View Image Classification With Visual, Semantic And View Consistency

Multi-view visual classification methods have been widely applied to use discriminative information of different views. This strategy has been proven very effective by many researchers. On the one hand, images are often treated independently without fully considering their visual and semantic correlations. On the other hand, view consistency is often ignored. To solve these problems, in this paper, we propose a novel multi-view image classification method with visual, semantic and view consistency (VSVC). For each image, we linearly combine multi-view information for image classification. The combination parameters are determined by considering both the classification loss and the visual, semantic and view consistency. Visual consistency is imposed by ensuring that visually similar images of the same view are predicted to have similar values. For semantic consistency, we impose the locality constraint that nearby images should be predicted to have the same class by multiview combination. View consistency is also used to ensure that similar images have consistent multi-view combination parameters. An alternative optimization strategy is used to learn the combination parameters. To evaluate the effectiveness of VSVC, we perform image classification experiments on several public datasets. The experimental results on these datasets show the effectiveness of the proposed VSVC method.

Eigenfunction-Based Multitask Learning in a Reproducing Kernel Hilbert Space

Multitask learning aims to improve the performance on related tasks by exploring the interdependence among them. Existing multitask learning methods explore the relatedness among tasks on the basis of the input features and the model parameters. In this paper, we focus on nonparametric multitask learning and propose to measure task relatedness from a novel perspective in a reproducing kernel Hilbert space (RKHS). Past works have shown that the objective function for a given task can be approximated using the top eigenvalues and corresponding eigenfunctions of a predefined integral operator on an RKHS. In our method, we formulate our objective for multitask learning as a linear combination of two sets of eigenfunctions, common eigenfunctions shared by different tasks and unique eigenfunctions in individual tasks, such that the eigenfunctions for one task can provide additional information on another and help to improve its performance. We present both theoretical and empirical validations of our proposed approach. The theoretical analysis demonstrates that our learning algorithm is uniformly argument stable and that the convergence rate of the generalization upper bound can be improved by learning multiple tasks. Experiments on several benchmark multitask learning data sets show that our method yields promising results.