This article presents FLGC, a simple yet effective fully linear graph convolutional network for semi-supervised and unsupervised learning. Instead of using gradient descent, we train FLGC based on computing a global optimal closed-form solution with a decoupled procedure, resulting in a generalized linear framework and making it easier to implement, train, and apply. We show that (1) FLGC is powerful to deal with both graph-structured data and regular data, (2) training graph convolutional models with closed-form solutions improve computational efficiency without degrading performance, and (3) FLGC acts as a natural generalization of classic linear models in the non-Euclidean domain (e.g., ridge regression and subspace clustering). Furthermore, we implement a semi-supervised FLGC and an unsupervised FLGC by introducing an initial residual strategy, enabling FLGC to aggregate long-range neighborhoods and alleviate over-smoothing. We compare our semi-supervised and unsupervised FLGCs against many state-of-the-art methods on a variety of classification and clustering benchmarks, demonstrating that the proposed FLGC models consistently outperform previous methods in terms of accuracy, robustness, and learning efficiency. The core code of our FLGC is released at https://github.com/AngryCai/FLGC .

Unlabeled, multi-view data presents a considerable challenge in many real-world data analysis tasks. These data are worth exploring because they often contain complementary information that improves the quality of the analysis results. Clustering with multi-view data is a particularly challenging problem as revealing the complex data structures between many feature spaces demands discriminative features that are specific to the task and, when too few of these features are present, performance suffers. Extreme learning machines (ELMs) are an emerging form of learning model that have shown an outstanding representation ability and superior performance in a range of different learning tasks. Motivated by the promise of this advancement, we have developed a novel multi-view fusion clustering framework based on an ELM, called MVEC. MVEC learns the embeddings from each view of the data via the ELM network, then constructs a single unified embedding according to the correlations and dependencies between each embedding and automatically weighting the contribution of each. This process exposes the underlying clustering structures embedded within multi-view data with a high degree of accuracy. A simple yet efficient solution is also provided to solve the optimization problem within MVEC. Experiments and comparisons on eight different benchmarks from different domains confirm MVEC’s clustering accuracy.

In traditional multi-instance learning (MIL), instances are typically represented by using a single feature view. As MIL becoming popular in domain specific learning tasks, aggregating multiple feature views to represent multi-instance bags has recently shown promising results, mainly because multiple views provide extra information for MIL tasks. Nevertheless, multiple views also increase the risk of involving redundant views and irrelevant features for learning. In this paper, we formulate a new cross-view feature selection problem that aims to identify the most representative features across all feature views for MIL. To achieve the goal, we design a new optimization problem by integrating both multi-view representation and multi-instance bag constraints. The solution to the objective function will ensure that the identified top-m features are the most informative ones across all feature views. Experiments on two real-world applications demonstrate the performance of the cross-view feature selection for content-based image retrieval and social media content recommendation.

Graph classification has traditionally focused on graphs generated from a single feature view. In many applications, it is common to have useful information from different channels/views to describe objects, which naturally results in a new representation with multiple graphs generated from different feature views being used to describe one object. In this paper, we formulate a new Multi-Graph-View learning task for graph classification, where each object to be classified contains graphs from multiple graph-views. This problem setting is essentially different from traditional single-graph-view graph classification, where graphs are from one single feature view. To solve the problem, we propose a Cross Graph-View Sub graph Feature based Learning (gCGVFL) algorithm that explores an optimal set of sub graphs, across multiple graph-views, as features to represent graphs. Specifically, we derive an evaluation criterion to estimate the discriminative power and the redundancy of sub graph features across all views, and assign proper weight values to each view to indicate its importance for graph classification. The iterative cross graph-view sub graph scoring and graph-view weight updating form a closed loop to find optimal sub graphs to represent graphs for multi-graph-view learning. Experiments and comparisons on real-world tasks demonstrate the algorithm's performance.

In this paper, we formulate a new multi-graph learning task with only positive and unlabeled bags, where labels are only available for bags but not for individual graphs inside the bag. This problem setting raises significant challenges because bag-of-graph setting does not have features to directly represent graph data, and no negative bags exits for deriving discriminative classification models. To solve the challenge, we propose a puMGL learning framework which relies on two iteratively combined processes for multigraph learning: (1) deriving features to represent graphs for learning; and (2) deriving discriminative models with only positive and unlabeled graph bags. For the former, we derive a subgraph scoring criterion to select a set of informative subgraphs to convert each graph into a feature space. To handle unlabeled bags, we assign a weight value to each bag and use the adjusted weight values to select most promising unlabeled bags as negative bags. A margin graph pool (MGP), which contains some representative graphs from positive bags and identified negative bags, is used for selecting subgraphs and training graph classifiers. The iterative subgraph scoring, bag weight updating, and MGP based graph classification forms a closed loop to find optimal subgraphs and most suitable unlabeled bags for multi-graph learning. Experiments and comparisons on real-world multigraph data demonstrate the algorithm performance.

Multi-instance learning concerns about building learning models from a number of labeled instance bags, where each bag consists of instances with unknown labels. A bag is labeled positive if one or more multiple instances inside the bag is positive, and negative otherwise. For all existing multi-instance learning algorithms, they are only applicable to the setting where instances in each bag are represented by a set of well defined feature values. In this paper, we advance the problem to a multi-instance multi-graph setting, where a bag contains a number of instances and graphs in pairs, and the learning objective is to derive classification models from labeled bags, containing both instances and graphs, to predict previously unseen bags with maximum accuracy. To achieve the goal, the main challenge is to properly represent graphs inside each bag and further take advantage of complementary information between instance and graph pairs for learning. In the paper, we propose a Dual Embedding Multi-Instance Multi-Graph Learning (DE-MIMG) algorithm, which employs a dual embedding learning approach to (1) embed instance distributions into the informative sub graphs discovery process, and (2) embed discovered sub graphs into the instance feature selection process. The dual embedding process results in an optimal representation for each bag to provide combined instance and graph information for learning. Experiments and comparisons on real-world multi-instance multi-graph learning tasks demonstrate the algorithm performance.

Because learning an optimal Bayesian network classifier is an NP-hard problem, learning-improved naive Bayes has attracted much attention from researchers. In this paper, we summarize the existing improved algorithms and propose a novel Bayes model: hidden naive Bayes (HNB). In HNB, a hidden parent is created for each attribute which combines the influences from all other attributes. We experimentally test HNB in terms of classification accuracy, using the 36 UCI data sets selected by Weka, and compare it to naive Bayes (NB), selective Bayesian classifiers (SBC), naive Bayes tree (NBTree), tree-augmented naive Bayes (TAN), and averaged one-dependence estimators (AODE). The experimental results show that HNB significantly outperforms NB, SBC, NBTree, TAN, and AODE. In many data mining applications, an accurate class probability estimation and ranking are also desirable. We study the class probability estimation and ranking performance, measured by conditional log likelihood (CLL) and the area under the ROC curve (AUC), respectively, of naive Bayes and its improved models, such as SBC, NBTree, TAN, and AODE, and then compare HNB to them in terms of CLL and AUC. Our experiments show that HNB also significantly outperforms all of them.