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.

Partial multi-view clustering has attracted various attentions from diverse fields. Most existing methods adopt separate steps to obtain unified representations and extract clustering indicators. This separate manner prevents two learning processes to negotiate to achieve optimal performance. In this paper, we propose the Joint Representation Learning and Clustering (JRLC) framework to address this issue. The JRLC framework employs representation matrices to extract view-specific clustering information directly from the presence of partial similarity matrices, and rotates them to learn a common probability label matrix simultaneously, which connects representation learning and clustering seamlessly to achieve better clustering performance. Under the guidance of JRLC framework, several new incomplete multi-view clustering methods can be developed by extending existing single-view graph-based representation learning methods. For illustration, within the framework, we propose two specific methods, JRLC with spectral embedding (JRLC-SE) and JRLC via integrating nonnegative embedding and spectral embedding (JRLC-NS). Two iterative algorithms with guaranteed convergence are designed to solve the resultant optimization problems of JRLC-SE and JRLC-NS. Experimental results on various datasets and news topic clustering application demonstrate the effectiveness of the proposed algorithms.

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.

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.

Multi-view subspace clustering has been applied to applications such as image processing and video surveillance, and has attracted increasing attention. Most existing methods learn view-specific self-representation matrices, and construct a combined affinity matrix from multiple views. The affinity construction process is time-consuming, and the combined affinity matrix is not guaranteed to reflect the whole true subspace structure. To overcome these issues, the Latent Complete Row Space Recovery (LCRSR) method is proposed. Concretely, LCRSR is based on the assumption that the multi-view observations are generated from an underlying latent representation, which is further assumed to collect the authentic samples drawn exactly from multiple subspaces. LCRSR is able to recover the row space of the latent representation, which not only carries complete information from multiple views but also determines the subspace membership under certain conditions. LCRSR does not involve the graph construction procedure and is solved with an efficient and convergent algorithm, thereby being more scalable to large-scale datasets. The effectiveness and efficiency of LCRSR are validated by clustering various kinds of multi-view data and illustrated in the background subtraction task.

Incomplete multi-view clustering has attracted various attentions from diverse fields. Most existing methods factorize data to learn a unified representation linearly. Their performance may degrade when the relations between the unified representation and data of different views are nonlinear. Moreover, they need post-processing on the unified representations to extract the clustering indicators, which separates the consensus learning and subsequent clustering. To address these issues, in this paper, we propose a Simultaneous Representation Learning and Clustering (SRLC) method. Concretely, SRLC constructs similarity matrices to measure the relations between pair of instances, and learns low-dimensional representations of present instances on each view and a common probability label matrix simultaneously. Thus, the nonlinear information can be reflected by these representations and the clustering results can obtained from label matrix directly. An efficient iterative algorithm with guaranteed convergence is presented for optimization. Experiments on several datasets demonstrate the advantages of the proposed approach.

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.

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.

With the advent of multi-view data, multi-view learning (MVL) has become an important research direction in machine learning. It is usually expected that multi-view algorithms can obtain better performance than that of merely using a single view. However, previous researches have pointed out that sometimes the utilization of multiple views may even deteriorate the performance. This will be a stumbling block for the practical use of MVL in real applications, especially for tasks requiring high dependability. Thus, it is eager to design reliable multi-view approaches, such that their performance is never degenerated by exploiting multiple views.This issue is vital but rarely studied. In this paper, we focus on clustering and propose the Reliable Multi-View Clustering (RMVC) method. Based on several candidate multi-view clusterings, RMVC maximizes the worst-case performance gain against the best single view clustering, which is equivalently expressed as no label information available. Specifically, employing the squared χ2 distance for clustering comparison makes the formulation of RMVC easy to solve, and an efficient strategy is proposed for optimization. Theoretically, it can be proved that the performance of RMVC will never be significantly decreased under some assumption. Experimental results on a number of data sets demonstrate that the proposed method can effectively improve the reliability of multi-view clustering.

Multi-label classification has attracted significant interests in various domains. In many applications, only partial labels are available and the others are missing or not provided. How to design an accurate multi-label classifier with such partial labeled data is a challenging problem. In this paper, we propose a Low Rank multi-label classification with Missing Label method (LRML), which joints label matrix recovery and multi-label classifier learning to address the classification problem. The proposed algorithm recover the missing labels via laplacian manifold regularization derived from the feature space. By utilizing the low-rank mapping, the proposed algorithm can efficiently exploit the label correlations and analyze the high-dimensional data in the discriminant subspace simultaneously. Besides, the proposed algorithm is formulated as a convex but not smooth optimization problem. An effective algorithm which divides the problem into multiple convex and smooth sub-problems is developed, together with some theoretical analyses. Experimental results validate that our method leads to a significant improvement in performance and robustness to missing labels over other well-established algorithms.

In a range of scientific coauthorship networks, transitions emerge in degree distribution, in the correlation between degree and local clustering coefficient, etc. The existence of those transitions could be regarded because of the diversity in collaboration behaviors of scientific fields. A growing geometric hypergraph built on a cluster of concentric circles is proposed to model two specific collaboration behaviors, namely the behaviors of research team leaders and those of the other team members. The model successfully predicts the transitions, as well as many common features of coauthorship networks. Particularly, it realizes a process of deriving the complex “scale‐free” property from the simple “yes/no” decisions. Moreover, it provides a reasonable explanation for the emergence of transitions with the difference of collaboration behaviors between leaders and other members. The difference emerges in the evolution of research teams, which synthetically addresses several specific factors of generating collaborations, namely the communications between research teams, academic impacts and homophily of authors.

Feature selection plays a significant role in dealing with high-dimensional data to avoid the curse of dimensionality. In many real applications, like video semantic recognition, handling few labeled and large unlabeled data samples from the same population is a recently addressed challenge in feature selection. To solve this problem, we propose a novel semi-supervised feature selection method via insensitive sparse regression (ISR). Specifically, we compute the soft label matrix by the special label propagation, which can predict the labels of the unlabeled data. To guarantee the robustness of ISR to the false labeled instances or outliers, we propose Insensitive Regression Model (IRM) by capped$l_2$-$l_p$-norm loss. The soft label is imposed as the weights of IRM to fully utilize the label information. Meanwhile, to perform feature selection, we incorporate$l_{2,q}$-norm regularizer with IRM as the structural sparsity constraint when$0 < q\leq 1$. Moreover, we put forward an effective approach for solving the formulated non-convex optimization problem. We analyze the performance of convergence rigorously and discuss the parameter determination problem. Extensive experimental results on several public data sets verify the effectiveness of our proposed algorithm in comparison with the state-of-art feature selection methods. Finally, we apply our method to video semantic recognition successfully.

Multi-view clustering, which aims to improve the clustering performance by exploring the data’s multiple representations, has become an important research direction. Graph based methods have been widely studied and achieve promising performance for multi-view clustering. However, most existing multi-view graph based methods perform clustering on the fixed input graphs, and the results are dependent on the quality of input graphs. In this paper, instead of fixing the input graphs, we propose Multi-view clustering with Adaptively Learned Graph (MALG), learning a new common similarity matrix. In our model, we not only consider the importance of multiple graphs from view level, but also focus on the performance of similarities within a view from sample-pair level. Sample-pair-specific weights are introduced to exploit the connection across views in more depth. In addition, the obtained optimal graph can be partitioned into specific clusters directly, according to its connected components. Experimental results on toy and real-world datasets demonstrate the efficacy of the proposed algorithm.

Functional annotation of human genes is fundamentally important for understanding the molecular basis of various genetic diseases. A major challenge in determining the functions of human genes lies in the functional diversity of proteins, that is, a gene can perform different functions as it may consist of multiple protein coding isoforms (PCIs). Therefore, differentiating functions of PCIs can significantly deepen our understanding of the functions of genes. However, due to the lack of isoform-level gold-standards (ground-truth annotation), many existing functional annotation approaches are developed at gene-level. In this paper, we propose a novel approach to differentiate the functions of PCIs by integrating sparse simplex projection---that is, a nonconvex sparsity-inducing regularizer---with the framework of multi-instance learning (MIL). Specifically, we label the genes that are annotated to the function under consideration as positive bags and the genes without the function as negative bags. Then, by sparse projections onto simplex, we learn a mapping that embeds the original bag space to a discriminative feature space. Our framework is flexible to incorporate various smooth and non-smooth loss functions such as logistic loss and hinge loss. To solve the resulting highly nontrivial non-convex and non-smooth optimization problem, we further develop an efficient block coordinate descent algorithm. Extensive experiments on human genome data demonstrate that the proposed approaches significantly outperform the state-of-the-art methods in terms of functional annotation accuracy of human PCIs and efficiency.

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 ℓ2,1matrix 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 realworld data sets and in the scene classification scenario as well. The experimental results demonstrate the effectiveness of our proposed algorithm.

With the advent of multi-view data, multi-view learning has become an important research direction in both machine learning and data mining. Considering the difficulty of obtaining labeled data in many real applications, we focus on the multi-view unsupervised feature selection problem. Traditional approaches all characterize the similarity by fixed and pre-defined graph Laplacian in each view separately and ignore the underlying common structures across different views. In this paper, we propose an algorithm named Multi-view Unsupervised Feature Selection with Adaptive Similarity and View Weight (ASVW) to overcome the above mentioned problems. Specifically, by leveraging the learning mechanism to characterize the common structures adaptively, we formulate the objective function by a common graph Laplacian across different views, together with the sparse ℓ2,p-norm constraint designed for feature selection. We develop an efficient algorithm to address the non-smooth minimization problem and prove that the algorithm will converge. To validate the effectiveness of ASVW, comparisons are made with some benchmark methods on real-world datasets. We also evaluate our method in the real sports action recognition task. The experimental results demonstrate the effectiveness of our proposed algorithm.

Many feature extraction methods reduce the dimensionality of data based on the input graph matrix. The graph construction which reflects relationships among raw data points is crucial to the quality of resulting low-dimensional representations. To improve the quality of graph and make it more suitable for feature extraction tasks, we incorporate a new graph learning mechanism into feature extraction and add an interaction between the learned graph and the low-dimensional representations. Based on this learning mechanism, we propose a novel framework, termed as unsupervised single view feature extraction with structured graph (FESG), which learns both a transformation matrix and an ideal structured graph containing the clustering information. Moreover, we propose a novel way to extend FESG framework for multi-view learning tasks. The extension is named as unsupervised multiple views feature extraction with structured graph (MFESG), which learns an optimal weight for each view automatically without requiring an additional parameter. To show the effectiveness of the framework, we design two concrete formulations within FESG and MFESG, together with two efficient solving algorithms. Promising experimental results on plenty of real-world datasets have validated the effectiveness of our proposed algorithms.

Multi-label data with high dimensionality arise frequently in data mining and machine learning. It is not only time consuming but also computationally unreliable when we use high-dimensional data directly. Supervised dimensionality reduction approaches are based on the assumption that there are large amounts of labeled data. It is infeasible to label a large number of training samples in practice especially in multi-label learning. To address these challenges, we propose a novel algorithm, namely Semi-Supervised Multi-Label Dimensionality Reduction (SSMLDR), which can utilize the information from both labeled data and unlabeled data in an effective way. First, the proposed algorithm enlarges the multi-label information from the labeled data to the unlabeled data through a special designed label propagation method. It then learns a transformation matrix to perform dimensionality reduction by incorporating the enlarged multi-label information. Extensive experiments on a broad range of datasets validate the effectiveness of our approach against other well-established algorithms.

Feature extraction, one kind of dimensionality reduction methodology, has aroused considerable research interests during the last few decades. Traditional graph embedding methods construct a fixed graph with original data to fulfill the aim of feature extraction. The lack of the graph learning mechanism leaves room for the improvement of their performances. In this paper, we propose a novel framework, termed as unsupervised feature extraction using a learned graph with clustering structure (LGCS), in which a graph learning mechanism has been presented. To be specific, the proposed LGCS learns both a transformation matrix and an ideal structured graph which incorporates clustering information. To show the effectiveness of the framework, we present a concrete method within our framework, and an iteration algorithm has been designed to solve the corresponding optimizing problem. Promising experimental results on real-world datasets have validated the effectiveness of our proposed algorithm.

In order to obtain high accuracy DEM products, distributed InSAR satellite system has a high requirement for the accuracy of inter-satellite baseline measurement. Baseline determination mainly consists of two procedures: GNSS baseline estimation and baseline calibration. In this paper, characters, mechanisms and accuracies of errors induced by baseline determination are analyzed. Simulation results of GNSS baseline estimation show that the random part of errors has a less impact which is only about 1 mm, while the systematic part plays a more important role in the impact of all errors. But it should be noticed that the systematic part, mainly comes from the error of antenna reference point, can be calibrated and compensated as a constant, while the random one cannot. Simulation results of baseline calibration show that: compared with interferometric phase noise and height references error, slant range distance error is the main error. The impact of slant range distance error on baseline calibration is nearly 2 mm, which can't be ignored.

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.

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.

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.

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.

The fast algorithm for satellite visibility is very important in many applications, particularly in the real-time simulation environments. In this paper, a novel algorithm, true anomaly iteration compensation (TAIC) algorithm, is proposed to predict the visibility of the elliptical orbits' satellites. A main property of our algorithm is that it could avoid solving the transcendental equation: Kepler Equation, therefore the computation of the algorithm is very small. Furthermore, a compensation method is used to yield more accurate results. The excellent performance of the algorithm is illustrated by the numerical results. For TAIC algorithm, the error of visibility- time is about 0.21% and the error of the entry-access time instant and the exit-access time instant is about 0.79 seconds.

The inter-satellite baseline plays a vital role in the formation flying satellites missions. Based on the relation between the spatial states and the inter-satellite baseline, this paper erects a model to associate these two kinds of parameters. The error propagation relations are deduced in detail, which are described by the precision influence factors and error propagation matrices. Simulations are also carried out to show the baseline determination precision in some certain scenarios.