We address an ensemble clustering problem, where reliable clusters are locally embedded in given multiple partitions. We propose a new nonnegative matrix factorization (NMF)-based method, in which locally reliable clusters are explicitly considered by using instance-wise weights over clusters. Our method factorizes the input cluster assignment matrix into two matrices H and W, which are optimized by iteratively 1) updating H and W while keeping the weight matrix constant and 2) updating the weight matrix while keeping H and W constant, alternatively. The weights in the second step were updated by solving a convex problem, which makes our algorithm significantly faster than existing NMF-based ensemble clustering methods. We empirically proved that our method outperformed a lot of cutting-edge ensemble clustering methods by using a variety of datasets.

Support vector machines (SVMs) play a very dominant role in data classification due to their good generalization performance. However, they suffer from the high computational complexity in the classification phase when there are a considerable number of support vectors (SVs). Then it is desirable to design efficient algorithms in the classification phase to deal with the datasets of real-time pattern recognition systems. To this end, we propose a novel classifier called HMLSVMs (Hierarchical Mixing Linear Support Vector Machines) in this paper, which has a hierarchical structure with a mixing linear SVMs classifier at each node and predicts the label of a sample using only a few hyperplanes. We also give a generalization error bound for the class of locally linear SVMs (LLSVMs) based on the Rademacher theory, which ensures that overfitting can be effectively avoided. Experimental evaluations shows, while maintaining a comparable classification performance to kernel SVMs (KSVMs), the proposed classifier achieves the high efficiency in the classification stage.

In knowledge bases or information extraction results, differently expressed relations can be semantically similar (e.g., (X, wrote, Y) and (X,'s written work, Y)). Therefore, grouping semantically similar relations into clusters would facilitate and improve many applications, including knowledge base completion, information extraction, information retrieval, and more. This paper formulates relation clustering as a constrained tripartite graph clustering problem, presents an efficient clustering algorithm and exhibits the advantage of the constrained framework. We introduce several ways that provide side information via must-link and cannot link constraints to improve the clustering results. Different from traditional semi-supervised learning approaches, we propose to use the similarity of relation expressions and the knowledge of entity types to automatically construct the constraints for the algorithm. We show improved relation clustering results on two datasets extracted from human annotated knowledge base (i.e., Freebase) and open information extraction results (i.e., ReVerb data).

Microarray experiments are capable of measuring the expression level of thousands of genes simultaneously. Dealing with this enormous amount of information requires complex computation. Support Vector Machines (SVM) have been widely used with great efficiency to solve classification problems that have high dimension. In this sense, it is plausible to develop new feature selection strategies for microarray data that are associated with this type of classifier. Therefore, we propose, in this paper, a new method for feature selection based on an ordered search process to explore the space of possible subsets.

Kernel SVM suffers from high computational complexity when dealing with large-scale nonlinear datasets. To address this issue, locally linear classifiers have been proposed for approximating nonlinear decision boundaries with locally linear functions using a local coding scheme. The effectiveness of such coding scheme depends heavily on the quality of anchor points chosen to produce the local codes. Existing methods usually involve a phase of unsupervised anchor point learning followed by supervised classifier learning. Thus, the anchor points and classifiers are obtained separately whereas the learned anchor points may not be optimal for the discriminative task. In this paper, we present a novel fully supervised approach for anchor point learning. A single optimization problem is formulated over both anchor point and classifier variables, optimizing the initial anchor points jointly with the classifiers to minimize the classification risk. Experimental results show that our method outperforms other competitive methods which employ unsupervised anchor point learning and achieves performance on par with the kernel SVM albeit with much improved efficiency.

In this paper, we propose a stratified topic model (STM). Instead of directly modeling and inferring flat topics or hierarchically structured topics, we use the stratified relationships in topic hierarchies to regularize the flat topics. The topic structures are captured by a hierarchical clustering method and play as constraints during the learning process. We propose two theoretically sound and practical inference methods to solve the model. Experimental results with two real world data sets and various evaluation metrics demonstrate the effectiveness of the proposed model.

This paper studies an interesting problem: is it possible to predict the crowd opinion about a movie before the movie is actually released? The crowd opinion is here expressed by the distribution of ratings given by a sufficient amount of people. Consequently, the pre-release crowd opinion prediction can be regarded as a Label Distribution Learning (LDL) problem. In order to solve this problem, a Label Distribution Support Vector Regressor (LDSVR) is proposed in this paper. The basic idea of LDSVR is to fit a sigmoid function to each component of the label distribution simultaneously by a multi-output support vector machine. Experimental results show that LDSVR can accurately predict peoples's rating distribution about a movie just based on the pre-release metadata of the movie.

The k-means algorithm is one of the most often used method for data clustering. However, the standard k-means can only be applied in the original feature space. The kernel k-means, which extends k-means into the kernel space, can be used to capture the non-linear structure and identify arbitrarily shaped clusters. Since both the standard k-means and kernel k-means apply the squared error to measure the distances between data points and cluster centers, a few outliers will cause large errors and dominate the objection function. Besides, the performance of kernel method is largely determined by the choice of kernel.

Spectral dimensionality reduction methods have recently emerged as powerful tools for various applications in pattern recognition, data mining and computer vision. These methods use information contained in the eigenvectors of a data affinity (i.e, item-item similarity) matrix to reveal the low dimensional structure of the high dimensional data. One of the limitations of various spectral dimensionality reduction methods is their high computational complexity. They all need to construct a data affinity matrix and compute the top eigenvectors. This leads to O(n2) computational complexity, where n is the number of samples. Moreover, when the data are highly non-linear distributed, some linear methods have to be performed in a reproducing kernel Hilbert space (leads to the corresponding kernel methods) to learn an effective non-linear mapping. The computational complexity of these kernel methods is O(n3). In this paper, we propose a novel nonlinear dimensionality reduction algorithm, called Compressed Spectral Regression, with O(n) computational complexity. Extensive experiments on data clustering demonstrate the effectiveness and efficiency of the proposed approach.

The Nystrom method provides an efficient sampling approach for large scale clustering problems, by generating a low-rank matrix approximation. However, existing sampling methods are limited by accuracy and computing time. This paper proposes an improved Nystrom-based clustering algorithm with a new sampling procedure, Minimum Sum of Squared Similarities (MSSS). Experiments on synthetic and real data sets show that the proposed sampling performs with higher accuracy than existing algorithms, applied to Nystrom-based spectral clustering problems. Furthermore, we provide a theoretical analysis that allows us to define the upper bound of the Frobenius norm error of the MSSS.