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.

Multi-instance Learning (MIL) is a popular learning paradigm arising from many real applications. It assigns a label to a set of instances, which is called a bag, and the bag’s label is determined by the instances within it. A bag is positive if and only if it has at least one positive instance. Since labeling bags is more complicated than labeling each instance, we will often face the mislabeling problem in MIL. Furthermore, it is more common that a negative bag has been mislabeled to a positive one, since one mislabeled instance will lead to the change of the whole bag label. This is an important problem that originated from real applications, e.g., web mining and image classification, but little research has concentrated on it as far as we know. In this article, we focus on this MIL problem with one side label noise that the negative bags are mislabeled as positive ones. To address this challenging problem, we propose, to the best our our knowledge, a novel multi-instance learning method with one side label noise. We design a new double weighting approach under traditional framework to characterize the “faithfulness” of each instance and each bag in learning the classifier. Briefly, on the instance level, we employ a sparse weighting method to select the key instances, and the MIL problem with one size label noise is converted to a mislabeled supervised learning scenario. On the bag level, the weights of bags, together with the selected key instances, will be utilized to identify the real positive bags. In addition, we have solved our proposed model by an alternative iteration method with proved convergence behavior. Empirical studies on various datasets have validated the effectiveness of our method.

The scarcity of labels is common and great challenge in traditional supervised learning. Semi-supervised learning (SSL) leverages unlabeled samples to alleviate the absence of label information. Similar with annotation, label proportion is another type of prior information and plays a significant role in classification tasks. Compared with the acquisition of labels, label proportion can be obtained more easily. For example, only a small number of patients have been diagnosed with or not with cancers in hospital database, while the proportion with cancer can be generally estimated by historical records. How to incorporate such prior information of label proportion is crucial but rarely studied in literature. Traditional SSL methods often ignore this prior information and will lead to performance degradation inevitably. To solve this problem, we propose a novel SSL with Label Proportion (SSLLP). Our approach encourages to preserve label consistency and label proportion by imposing the cardinality bound constraints. Our formulated problem equals to a mixed-integer constrained submodular minimization and it is difficult to be solved directly. Therefore, we transformed the original problem into a convex one by Lov$\acute{\text{a}}$sz extension and designed an efficient solving algorithm. Extensive experimental results present the improved performance of our method over several state-of-the-art methods.

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.

Multi-instance learning (MIL) has been extensively applied to various real tasks involving objects with bags of instances, such as in drugs and images. Previous studies on MIL assume that data are entirely complete. However, in many real tasks, the instance is fragmentary. In this article, we present probably the first study on multi-instance classification with fragmentary data. In our proposed framework, called fragmentary multi-instance classification (FIC), the fragmentary data are completed and the multi-instance classifier is learned jointly. To facilitate the integration between the completion and classifier learning, FIC establishes the weighting mechanism to measure the importance levels of different instances. To validate the compatibility of our framework, four typical MIL methods, including multi-instance support vector machine (MI-SVM), expectation maximization diverse density (EM-DD), citation- K nearest neighbors (Citation-KNNs), and MIL with discriminative bag mapping (MILDM), are embedded into the framework to obtain the corresponding FIC versions. As an illustration, an efficient solving algorithm is developed to address the problem for MI-SVM, together with the proof of convergence behavior. The experimental results on various types of real-world datasets demonstrate the effectiveness.

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.

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.

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.

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.