Absent Multiview Semisupervised Classification.

With the advent of vast data collection ways, data are often with multiple modalities or coming from multiple sources. Traditional multiview learning often assumes that each example of data appears in all views. However, this assumption is too strict in some real applications such as multisensor surveillance system, where every view suffers from some data absent. In this article, we focus on how to classify such incomplete multiview data in semisupervised scenario and a method called absent multiview semisupervised classification (AMSC) has been proposed. Specifically, partial graph matrices are constructed independently by anchor strategy to measure the relationships among between each pair of present samples on each view. And to obtain unambiguous classification results for all unlabeled data points, AMSC learns view-specific label matrices and a common label matrix simultaneously. AMSC measures the similarity between pair of view-specific label vectors on each view by partial graph matrices, and consider the similarity between view-specific label vectors and class indicator vectors based on the common label matrix. To characterize the contributions of different views, the p th root integration strategy is adopted to incorporate the losses of different views. By further analyzing the relation between the p th root integration strategy and exponential decay integration strategy, we develop an efficient algorithm with proved convergence to solve the proposed nonconvex problem. To validate the effectiveness of AMSC, comparisons are made with some benchmark methods on real-world datasets and in the document classification scenario as well. The experimental results demonstrate the advantages of our proposed approach.

Joint Embedding Learning and Low-Rank Approximation: A Framework for Incomplete Multiview Learning.

In real-world applications, not all instances in the multiview data are fully represented. To deal with incomplete data, incomplete multiview learning (IML) rises. In this article, we propose the joint embedding learning and low-rank approximation (JELLA) framework for IML. The JELLA framework approximates the incomplete data by a set of low-rank matrices and learns a full and common embedding by linear transformation. Several existing IML methods can be unified as special cases of the framework. More interestingly, some linear transformation-based complete multiview methods can be adapted to IML directly with the guidance of the framework. Thus, the JELLA framework improves the efficiency of processing incomplete multiview data, and bridges the gap between complete multiview learning and IML. Moreover, the JELLA framework can provide guidance for developing new algorithms. For illustration, within the framework, we propose the IML with the block-diagonal representation (IML-BDR) method. Assuming that the sampled examples have an approximate linear subspace structure, IML-BDR uses the block-diagonal structure prior to learning the full embedding, which would lead to more correct clustering. A convergent alternating iterative algorithm with the successive over-relaxation optimization technique is devised for optimization. The experimental results on various datasets demonstrate the effectiveness of IML-BDR.

Identifying highly influential nodes in multilayer networks based on global propagation.

Based on percolation theory and the independent cascade model, this paper considers the selection of the optimal propagation source when the propagation probability is greater than the percolation threshold. First, based on the percolation characteristics of real networks, this paper presents an iterative algorithm of linear complexity to solve the probability of the propagation source transmitting information to the network's giant component, that is, the global propagation probability. Compared with the previous multiple local simulation algorithm, this algorithm eliminates random errors and significantly reduces the operation time. A sufficient and necessary condition is provided, and it is proved that the final propagation range of the propagation source obeys the bimodal distribution. Based on this sufficient and necessary condition, we extend the efficient iterative algorithm proposed in this article to multi-layer networks and find that for two-layer networks, the final propagation range of the propagation source follows a four-peak distribution. Through iterations and calculations, the probability of each peak and the number of nodes included can be directly obtained, and the propagation expectations of the nodes in the multi-layer network can then be calculated, which can result in a better ranking of the propagation influence of the nodes. In addition, to maximize the influence of multi-propagation sources, this paper also presents a de-overlapping method, which has evident advantages over traditional methods.

Multiview Classification With Cohesion and Diversity.

Different views of multiview data share certain common information (consensus) and also contain some complementary information (complementarity). Both consensus and complementarity are of significant importance to the success of multiview learning. In this paper, we explicitly formulate both of them for multiview classification. On the one hand, a cohesion-increasing loss term with a learnable label-adjusting matrix is designed to facilitate consensus among views in the training stage. With this kind of loss, the learned classifiers of all views are more likely to obtain the correct classification, thereby maximizing the agreement among views. On the other hand, an independence measurement is adopted as the diversity-promoting regularization to encourage classifiers to be diverse such that more complementary information can be captured by these "diversified" classifiers. Overall, the resultant model is capable of achieving more comprehensive and accurate classification by exploring and exploiting the common and complementary information across multiple views more thoroughly. An iterative optimization algorithm with proved convergence is proposed for training the model. Extensive experimental results on various datasets have demonstrated the efficacy of the proposed method.

Community discovering in temporal network with spectral fusion.

With the deep understanding of the time-varying characteristics of real systems, research studies focusing on the temporal network spring up like mushrooms. Community detection is an accompanying and meaningful problem in the temporal network, but the analysis of this problem is still in its developing stage. In this paper, we proposed a temporal spectral clustering method to detect the invariable communities in the temporal network. Through integrating Fiedler's eigenvectors of normalized Laplacian matrices within a limited time window, our method can avoid the inaccurate partition caused by the mutation of the temporal network. Experiments demonstrated that our model is effective in solving this problem and performs obviously better than the compared methods. The results illustrated that taking the historical information of the network structure into consideration is beneficial in clustering the temporal network.

Robustness of partially interdependent networks under combined attack.

We thoroughly study the robustness of partially interdependent networks when suffering attack combinations of random, targeted, and localized attacks. We compare analytically and numerically the robustness of partially interdependent networks with a broad range of parameters including coupling strength, attack strength, and network type. We observe the first and second order phase transition and accurately characterize the critical points for each combined attack. Generally, combined attacks show more efficient damage to interdependent networks. Besides, we find that, when robustness is measured by the critical removing ratio and the critical coupling strength, the conclusion drawn for a combined attack is not always consistent.

Full Representation Data Embedding via Nonoverlapping Historical Features.

Data recycling, which reuses the historical data to assist the present data to achieve better performance, is an emerging and important research topic. A common case is that historical examples only have features from one source while presently have more data collection ways and extract different types of features simultaneously for new examples. Previous studies assume that either historical data appear in all sources, or at least there is one type of representations for all data. In this paper, we study the challenging problem in the above common case and propose a novel semisupervised approach by leveraging nonoverlapping historical features (NHFs). It learns full representations of both historical features and present features in a latent subspace. We utilize the intrinsic geometrical structure of all data and add the label information of historical data as a hard constraint to discover a latent subspace. Then, the classification will be performed with these new representations. Moreover, we provide an efficient algorithm to solve the formulated optimization problem with proved convergence behavior, together with some insightful discussions about parameter determination. Experimental results on real-world data sets are provided to examine the effectiveness of our algorithm. Furthermore, we have also evaluated our method in face recognition. They all demonstrate the effectiveness of our proposed approach on recycling NHFs.

Dimension Reduction for Non-Gaussian Data by Adaptive Discriminative Analysis.

High-dimensional non-Gaussian data are ubiquitous in many real applications. Face recognition is a typical example of such scenarios. The sampled face images of each person in the original data space are more closely located to each other than to those of the same individuals due to the changes of various conditions like illumination, pose variation, and facial expression. They are often non-Gaussian and differentiating the importance of each data point has been recognized as an effective approach to process the high-dimensional non-Gaussian data. In this paper, to embed non-Gaussian data well, we propose a novel unified framework named adaptive discriminative analysis (ADA), which combines the sample's importance measurement and subspace learning in a unified framework. Therefore, our ADA can preserve the within-class local structure and learn the discriminative transformation functions simultaneously by minimizing the distances of the projected samples within the same classes while maximizing the between-class separability. Meanwhile, an efficient method is developed to solve our formulated problem. Comprehensive analyses, including convergence behavior and parameter determination, together with the relationship to other related approaches, are as well presented. Systematical experiments are conducted to understand the work of our proposed ADA. Promising experimental results on various types of real-world benchmark data sets are provided to examine the effectiveness of our algorithm. Furthermore, we have also evaluated our method in face recognition. They all validate the effectiveness of our method on processing the high-dimensional non-Gaussian data.

Scalable Multi-View Semi-Supervised Classification via Adaptive Regression.

With the advent of multi-view data, multi-view learning has become an important research direction in machine learning and image processing. Considering the difficulty of obtaining labeled data in many machine learning applications, we focus on the multi-view semi-supervised classification problem. In this paper, we propose an algorithm named multi-view semi-supervised classification via adaptive regression (MVAR) to address this problem. Specifically, regression-based loss functions with l2,1 matrix norm are adopted for each view and the final objective function is formulated as the linear weighted combination of all the loss functions. An efficient algorithm with proved convergence is developed to solve the non-smooth l2,1 -norm minimization problem. Regressing to class labels directly makes the proposed algorithm efficient in calculation and can be applied to large-scale data sets. The adaptively optimized weight coefficients balance the contributions of different views automatically, which makes the performance robust against the existence of low-quality views. With the learned projection matrices and bias vectors, predictions for out-of-sample data can be easily made. To validate the effectiveness of MVAR, comparisons are made with some benchmark methods on real-world data sets and in the scene classification scenario as well. The experimental results demonstrate the effectiveness of our proposed algorithm.

Robust auto-weighted multi-view subspace clustering with common subspace representation matrix.

In many computer vision and machine learning applications, the data sets distribute on certain low-dimensional subspaces. Subspace clustering is a powerful technology to find the underlying subspaces and cluster data points correctly. However, traditional subspace clustering methods can only be applied on data from one source, and how to extend these methods and enable the extensions to combine information from various data sources has become a hot area of research. Previous multi-view subspace methods aim to learn multiple subspace representation matrices simultaneously and these learning task for different views are treated equally. After obtaining representation matrices, they stack up the learned representation matrices as the common underlying subspace structure. However, for many problems, the importance of sources and the importance of features in one source both can be varied, which makes the previous approaches ineffective. In this paper, we propose a novel method called Robust Auto-weighted Multi-view Subspace Clustering (RAMSC). In our method, the weight for both the sources and features can be learned automatically via utilizing a novel trick and introducing a sparse norm. More importantly, the objective of our method is a common representation matrix which directly reflects the common underlying subspace structure. A new efficient algorithm is derived to solve the formulated objective with rigorous theoretical proof on its convergency. Extensive experimental results on five benchmark multi-view datasets well demonstrate that the proposed method consistently outperforms the state-of-the-art methods.

Maximizing the Spread of Influence via Generalized Degree Discount.

It is a crucial and fundamental issue to identify a small subset of influential spreaders that can control the spreading process in networks. In previous studies, a degree-based heuristic called DegreeDiscount has been shown to effectively identify multiple influential spreaders and has severed as a benchmark method. However, the basic assumption of DegreeDiscount is not adequate, because it treats all the nodes equally without any differences. To consider a general situation in real world networks, a novel heuristic method named GeneralizedDegreeDiscount is proposed in this paper as an effective extension of original method. In our method, the status of a node is defined as a probability of not being influenced by any of its neighbors, and an index generalized discounted degree of one node is presented to measure the expected number of nodes it can influence. Then the spreaders are selected sequentially upon its generalized discounted degree in current network. Empirical experiments are conducted on four real networks, and the results show that the spreaders identified by our approach are more influential than several benchmark methods. Finally, we analyze the relationship between our method and three common degree-based methods.

Low-Frequency Error Extraction and Compensation for Attitude Measurements from STECE Star Tracker.

The low frequency errors (LFE) of star trackers are the most penalizing errors for high-accuracy satellite attitude determination. Two test star trackers- have been mounted on the Space Technology Experiment and Climate Exploration (STECE) satellite, a small satellite mission developed by China. To extract and compensate the LFE of the attitude measurements for the two test star trackers, a new approach, called Fourier analysis, combined with the Vondrak filter method (FAVF) is proposed in this paper. Firstly, the LFE of the two test star trackers' attitude measurements are analyzed and extracted by the FAVF method. The remarkable orbital reproducibility features are found in both of the two test star trackers' attitude measurements. Then, by using the reproducibility feature of the LFE, the two star trackers' LFE patterns are estimated effectively. Finally, based on the actual LFE pattern results, this paper presents a new LFE compensation strategy. The validity and effectiveness of the proposed LFE compensation algorithm is demonstrated by the significant improvement in the consistency between the two test star trackers. The root mean square (RMS) of the relative Euler angle residuals are reduced from [27.95'', 25.14'', 82.43''], 3σ to [16.12'', 15.89'', 53.27''], 3σ.

Effective Discriminative Feature Selection With Nontrivial Solution.

Feature selection and feature transformation, the two main ways to reduce dimensionality, are often presented separately. In this paper, a feature selection method is proposed by combining the popular transformation-based dimensionality reduction method linear discriminant analysis (LDA) and sparsity regularization. We impose row sparsity on the transformation matrix of LDA through l2,1-norm regularization to achieve feature selection, and the resultant formulation optimizes for selecting the most discriminative features and removing the redundant ones simultaneously. The formulation is extended to the l2,p-norm regularized case, which is more likely to offer better sparsity when 0 < p < 1. Thus, the formulation is a better approximation to the feature selection problem. An efficient algorithm is developed to solve the l2,p-norm-based optimization problem and it is proved that the algorithm converges when 0 < p ≤ 2. Systematical experiments are conducted to understand the work of the proposed method. Promising experimental results on various types of real-world data sets demonstrate the effectiveness of our algorithm.

Modeling the citation network by network cosmology.

Citation between papers can be treated as a causal relationship. In addition, some citation networks have a number of similarities to the causal networks in network cosmology, e.g., the similar in-and out-degree distributions. Hence, it is possible to model the citation network using network cosmology. The casual network models built on homogenous spacetimes have some restrictions when describing some phenomena in citation networks, e.g., the hot papers receive more citations than other simultaneously published papers. We propose an inhomogenous causal network model to model the citation network, the connection mechanism of which well expresses some features of citation. The node growth trend and degree distributions of the generated networks also fit those of some citation networks well.

Discriminative embedded clustering: a framework for grouping high-dimensional data.

In many real applications of machine learning and data mining, we are often confronted with high-dimensional data. How to cluster high-dimensional data is still a challenging problem due to the curse of dimensionality. In this paper, we try to address this problem using joint dimensionality reduction and clustering. Different from traditional approaches that conduct dimensionality reduction and clustering in sequence, we propose a novel framework referred to as discriminative embedded clustering which alternates them iteratively. Within this framework, we are able not only to view several traditional approaches and reveal their intrinsic relationships, but also to be stimulated to develop a new method. We also propose an effective approach for solving the formulated nonconvex optimization problem. Comprehensive analyses, including convergence behavior, parameter determination, and computational complexity, together with the relationship to other related approaches, are also presented. Plenty of experimental results on benchmark data sets illustrate that the proposed method outperforms related state-of-the-art clustering approaches and existing joint dimensionality reduction and clustering methods.

Joint embedding learning and sparse regression: a framework for unsupervised feature selection.

Feature selection has aroused considerable research interests during the last few decades. Traditional learning-based feature selection methods separate embedding learning and feature ranking. In this paper, we propose a novel unsupervised feature selection framework, termed as the joint embedding learning and sparse regression (JELSR), in which the embedding learning and sparse regression are jointly performed. Specifically, the proposed JELSR joins embedding learning with sparse regression to perform feature selection. To show the effectiveness of the proposed framework, we also provide a method using the weight via local linear approximation and adding the l2,1 -norm regularization, and design an effective algorithm to solve the corresponding optimization problem. Furthermore, we also conduct some insightful discussion on the proposed feature selection approach, including the convergence analysis, computational complexity, and parameter determination. In all, the proposed framework not only provides a new perspective to view traditional methods but also evokes some other deep researches for feature selection. Compared with traditional unsupervised feature selection methods, our approach could integrate the merits of embedding learning and sparse regression. Promising experimental results on different kinds of data sets, including image, voice data and biological data, have validated the effectiveness of our proposed algorithm.

Efficient image classification via multiple rank regression.

The problem of image classification has aroused considerable research interest in the field of image processing. Traditional methods often convert an image to a vector and then use a vector-based classifier. In this paper, a novel multiple rank regression model (MRR) for matrix data classification is proposed. Unlike traditional vector-based methods, we employ multiple-rank left projecting vectors and right projecting vectors to regress each matrix data set to its label for each category. The convergence behavior, initialization, computational complexity, and parameter determination are also analyzed. Compared with vector-based regression methods, MRR achieves higher accuracy and has lower computational complexity. Compared with traditional supervised tensor-based methods, MRR performs better for matrix data classification. Promising experimental results on face, object, and hand-written digit image classification tasks are provided to show the effectiveness of our method.

Listen to genes: dealing with microarray data in the frequency domain.

BACKGROUND: We present a novel and systematic approach to analyze temporal microarray data. The approach includes normalization, clustering and network analysis of genes. METHODOLOGY: Genes are normalized using an error model based uniform normalization method aimed at identifying and estimating the sources of variations. The model minimizes the correlation among error terms across replicates. The normalized gene expressions are then clustered in terms of their power spectrum density. The method of complex Granger causality is introduced to reveal interactions between sets of genes. Complex Granger causality along with partial Granger causality is applied in both time and frequency domains to selected as well as all the genes to reveal the interesting networks of interactions. The approach is successfully applied to Arabidopsis leaf microarray data generated from 31,000 genes observed over 22 time points over 22 days. Three circuits: a circadian gene circuit, an ethylene circuit and a new global circuit showing a hierarchical structure to determine the initiators of leaf senescence are analyzed in detail. CONCLUSIONS: We use a totally data-driven approach to form biological hypothesis. Clustering using the power-spectrum analysis helps us identify genes of potential interest. Their dynamics can be captured accurately in the time and frequency domain using the methods of complex and partial Granger causality. With the rise in availability of temporal microarray data, such methods can be useful tools in uncovering the hidden biological interactions. We show our method in a step by step manner with help of toy models as well as a real biological dataset. We also analyse three distinct gene circuits of potential interest to Arabidopsis researchers.