A support vector machine (SVM) is a popular algorithm for classification learning. The classical SVM effectively manages classification tasks defined by means of numerical attributes. However, both numerical and nominal attributes are used in practical tasks and the classical SVM does not fully consider the difference between them. Nominal attributes are usually regarded as numerical after coding. This may deteriorate the performance of learning algorithms. In this study, we propose a novel SVM algorithm for learning with heterogeneous data, known as a heterogeneous SVM (HSVM). The proposed algorithm learns an mapping to embed nominal attributes into a real space by minimizing an estimated generalization error, instead of by direct coding. Extensive experiments are conducted, and some interesting results are obtained. The experiments show that HSVM improves classification performance for both nominal and heterogeneous data.

The sizes of datasets in terms of the number of samples, features, and classes have dramatically increased in recent years. In particular, there usually exists a hierarchical structure among class labels as hundreds of classes exist in a classification task. We call these tasks hierarchical classification, and hierarchical structures are helpful for dividing a very large task into a collection of relatively small subtasks. Various algorithms have been developed to select informative features for flat classification. However, these algorithms ignore the semantic hyponymy in the directory of hierarchical classes, and select a uniform subset of the features for all classes. In this paper, we propose a new feature selection framework with recursive regularization for hierarchical classification. This framework takes the hierarchical information of the class structure into account. In contrast to flat feature selection, we select different feature subsets for each node in a hierarchical tree structure with recursive regularization. The proposed framework uses parent-child, sibling, and family relationships for hierarchical regularization. By imposing ℓ2,1 -norm regularization to different parts of the hierarchical classes, we can learn a sparse matrix for the feature ranking at each node. Extensive experiments on public datasets demonstrate the effectiveness and efficiency of the proposed algorithms.

Deep learning models often use a flat softmax layer to classify samples after feature extraction in visual classification tasks. However, it is hard to make a single decision of finding the true label from massive classes. In this scenario, hierarchical classification is proved to be an effective solution and can be utilized to replace the softmax layer. A key issue of hierarchical classification is to construct a good label structure, which is very significant for classification performance. Several works have been proposed to address the issue, but they have some limitations and are almost designed heuristically. In this article, inspired by fuzzy rough set theory, we propose a deep fuzzy tree model which learns a better tree structure and classifiers for hierarchical classification with theory guarantee. Experimental results show the effectiveness and efficiency of the proposed model in various visual classification datasets.

Multiview clustering explores complementary information among distinct views to enhance clustering performance under the assumption that all samples have complete information in all available views. However, this assumption does not hold in many real applications, where the information of some samples in one or more views may be missing, leading to partial multiview clustering problems. In this case, significant performance degeneration is usually observed. A collection of partial multiview clustering algorithms has been proposed to address this issue and most treat all different views equally during clustering. In fact, because different views provide features collected from different angles/feature spaces, they might play different roles in the clustering process. With the diversity of different views considered, in this study, a novel adaptive method is proposed for partial multiview clustering by automatically adjusting the contributions of different views. The samples are divided into complete and incomplete sets, while a joint learning mechanism is established to facilitate the connection between them and thereby improve clustering performance. More specifically, the method is characterized by a joint optimization model comprising two terms. The first term mines the underlying cluster structure from both complete and incomplete samples by adaptively updating their importance in all available views. The second term is designed to group all data with the aid of the cluster structure modeled in the first term. These two terms seamlessly integrate the complementary information among multiple views and enhance the performance of partial multiview clustering. Experimental results on real-world datasets illustrate the effectiveness and efficiency of our proposed method.

Subspace clustering is an effective method that has been successfully applied to many applications. Here, we propose a novel subspace clustering model for multi-view data using a latent representation termed Latent Multi-View Subspace Clustering (LMSC). Unlike most existing single-view subspace clustering methods, which directly reconstruct data points using original features, our method explores underlying complementary information from multiple views and simultaneously seeks the underlying latent representation. Using the complementarity of multiple views, the latent representation depicts data more comprehensively than each individual view, accordingly making subspace representation more accurate and robust. We proposed two LMSC formulations: linear LMSC (lLMSC), based on linear correlations between latent representation and each view, and generalized LMSC (gLMSC), based on neural networks to handle general relationships. The proposed method can be efficiently optimized under the Augmented Lagrangian Multiplier with Alternating Direction Minimization (ALM-ADM) framework. Extensive experiments on diverse datasets demonstrate the effectiveness of the proposed method.