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With the advancement of data acquisition techniques, tensor (multidimensional data) objects are increasingly accumulated and generated, for example, multichannel electroencephalographies, multiview images, and videos. In these applications, the tensor objects are usually nonnegative, since the physical signals are recorded. As the dimensionality of tensor objects is often very high, a dimension reduction technique becomes an important research topic of tensor data. From the perspective of geometry, high-dimensional objects often reside in a low-dimensional submanifold of the ambient space. In this paper, we propose a new approach to perform the dimension reduction for nonnegative tensor objects. Our idea is to use nonnegative Tucker decomposition (NTD) to obtain a set of core tensors of smaller sizes by finding a common set of projection matrices for tensor objects. To preserve geometric information in tensor data, we employ a manifold regularization term for the core tensors constructed in the Tucker decomposition. An algorithm called manifold regularization NTD (MR-NTD) is developed to solve the common projection matrices and core tensors in an alternating least squares manner. The convergence of the proposed algorithm is shown, and the computational complexity of the proposed method scales linearly with respect to the number of tensor objects and the size of the tensor objects, respectively. These theoretical results show that the proposed algorithm can be efficient. Extensive experimental results have been provided to further demonstrate the effectiveness and efficiency of the proposed MR-NTD algorithm. [ABSTRACT FROM AUTHOR]

Multilabel learning aims to predict labels of unseen instances by learning from training samples that are associated with a set of known labels. In this paper, we propose to use a hierarchical tree model for multilabel learning, and to develop the ML-Tree algorithm for finding the tree structure. ML-Tree considers a tree as a hierarchy of data and constructs the tree using the induction of one-against-all SVM classifiers at each node to recursively partition the data into child nodes. For each node, we define a predictive label vector to represent the predictive label transmission in the tree model for multilabel prediction and automatic discovery of the label relationships. If two labels co-occur frequently as predictive labels at leaf nodes, these labels are supposed to be relevant. The amount of predictive label co-occurrence provides an estimation of the label relationships. We examine the ML-Tree method on 11 real data sets of different domains and compare it with six well-established multilabel learning algorithms. The performances of these approaches are evaluated by 16 commonly used measures. We also conduct Friedman and Nemenyi tests to assess the statistical significance of the differences in performance. Experimental results demonstrate the effectiveness of our method. [ABSTRACT FROM AUTHOR]

Kmeans-type clustering aims at partitioning a data set into clusters such that the objects in a cluster are compact and the objects in different clusters are well separated. However, most kmeans-type clustering algorithms rely on only intracluster compactness while overlooking intercluster separation. In this paper, a series of new clustering algorithms by extending the existing kmeans-type algorithms is proposed by integrating both intracluster compactness and intercluster separation. First, a set of new objective functions for clustering is developed. Based on these objective functions, the corresponding updating rules for the algorithms are then derived analytically. The properties and performances of these algorithms are investigated on several synthetic and real-life data sets. Experimental studies demonstrate that our proposed algorithms outperform the state-of-the-art kmeans-type clustering algorithms with respect to four metrics: accuracy, RandIndex, Fscore, and normal mutual information. [ABSTRACT FROM AUTHOR]