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.

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.

In conventional wisdom of video modeling, the background is often treated as the primary target and foreground is derived using the technique of background subtraction. Based on the observation that foreground and background are two sides of the same coin, we propose to treat them as peer unknown variables and formulate a joint estimation problem, called Hierarchical modeling and Alternating Optimization (HMAO). The motivation behind our hierarchical extensions of background and foreground models is to better incorporate a priori knowledge about the disparity between background and foreground. For background, we decompose it into temporally low-frequency and high-frequency components for the purpose of better characterizing the class of video with dynamic background; for foreground, we construct a Markov random field prior at a spatially low resolution as the pivot to facilitate the noise-resilient refinement at higher resolutions. Built on hierarchical extensions of both models, we show how to successively refine their joint estimates under a unified framework known as alternating direction multipliers method. Experimental results have shown that our approach produces more discriminative background and demonstrates better robustness to noise than other competing methods. When compared against current state-of-the-art techniques, HMAO achieves at least comparable and often superior performance in terms of F-measure scores, especially for video containing dynamic and complex background.

Heterogeneous feature representations are widely used in machine learning and pattern recognition, especially for multimedia analysis. The multi-modal, often also high- dimensional , features may contain redundant and irrelevant information that can deteriorate the performance of modeling in classification. It is a challenging problem to select the informative features for a given task from the redundant and heterogeneous feature groups. In this paper, we propose a novel framework to address this problem. This framework is composed of two modules, namely, multi-modal deep neural networks and feature selection with sparse group LASSO. Given diverse groups of discriminative features, the proposed technique first converts the multi-modal data into a unified representation with different branches of the multi-modal deep neural networks. Then, through solving a sparse group LASSO problem, the feature selection component is used to derive a weight vector to indicate the importance of the feature groups. Finally, the feature groups with large weights are considered more relevant and hence are selected. We evaluate our framework on three image classification datasets. Experimental results show that the proposed approach is effective in selecting the relevant feature groups and achieves competitive classification performance as compared with several recent baseline methods.

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.