We introduce a semi-supervised boosting approach (SSDBoost), which directly minimizes the classification errors and maximizes the margins on both labeled and unlabeled samples, without resorting to any upper bounds or approximations. A two-step algorithm based on coordinate descent/ascent is proposed to implement SSDBoost. Experiments on a number of UCI datasets and synthetic data show that SSDBoost gives competitive or superior results over the state-of-the-art supervised and semi-supervised boosting algorithms in the cases that the labeled data is limited, and it is very robust in noisy cases.

As an important machine learning topic, dimensionality reduction has been widely studied and utilized in various kinds of areas. A multitude of dimensionality reduction methods have been developed, among which unsupervised dimensionality reduction is more desirable when obtaining label information requires onerous work. However, most previous unsupervised dimensionality reduction methods call for an affinity graph constructed beforehand, with which the following dimensionality reduction steps can be then performed. Separation of graph construction and dimensionality reduction leads the dimensionality reduction process highly dependent on quality of the input graph. In this paper, we propose a novel graph embedding method for unsupervised dimensionality reduction. We simultaneously conduct dimensionality reduction along with graph construction by assigning adaptive and optimal neighbors according to the projected local distances. Our method doesn’t need an affinity graph constructed in advance, but instead learns the graph concurrently with dimensionality reduction. Thus, the learned graph is optimal for dimensionality reduction. Meanwhile, our learned graph has an explicit block diagonal structure, from which the clustering results could be directly revealed without any postprocessing steps. Extensive empirical results on dimensionality reduction as well as clustering are presented to corroborate the performance of our method.

SVM in advance, and this limits their applications to largescale problems. To address this issue, several methods for Support vector machines (SVMs) play a very dominant selecting a set of basis vectors are proposed. They include role in data classification due to their good sampling from the training set in the Nystrom method generalization performance. However, they suffer [Williams and Seeger, 2001] and variants of the Incomplete from the high computational complexity in the Cholesky factorization [Bach and Jordan, 2005], core vector classification phase when there are a considerable machine (CVM) [Tsang et al., 2005], relevance vector machine number of support vectors (SVs). Then it is desirable (RVM)[Tipping, 2001], and relevance units machine to design efficient algorithms in the classification (RUM)[Gao and Zhang, 2009]. Wu et al. [Wu et al., 2006] phase to deal with the datasets of realtime add one constraint on the number of basis vectors to the standard pattern recognition systems. To this end, we SVM optimization problem, and then solve this modified propose a novel classifier called HMLSVMs (Hierarchical nonconvex problem to build sparse kernel learning algorithms Mixing Linear Support Vector Machines) (SKLA). Joachims and Yu [Joachims and Yu, 2009] in this paper, which has a hierarchical structure explore a new sparse kernel SVMs via cutting plane training, with a mixing linear SVMs classifier at each node called cutting-plane subspace pursuit (CPSP).Although and predicts the label of a sample using only a the above methods prunes the SVs and reduces computational few hyperplanes. We also give a generalization complexity in classification phase, when a new test sample is error bound for the class of locally linear SVMs introduced, they still need to compare it with these pruned (LLSVMs) based on the Rademacher theory, which SVs via kernel calculations to predict the label of the test ensures that overfitting can be effectively avoided.

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. The algorithm, called Admissible Ordered Search (AOS), uses as evaluation function the margin values estimated for each hypothesis by a SVM classifier. An important theoretical contribution of this paper is the development of the projected margin concept. This value is computed as the margin vector projection on a lower dimensional subspace and is used as an upper bound for the current value of the hypothesis in the search process. This enables great economy in runtime and consequently efficiency in the search process as a whole. The algorithm was tested using five different microarray data sets yielding superior results when compared to three representative feature selection methods.

Generating a coherent synopsis and revealing the development threads for news stories from the increasing amounts of news content remains aformidable challenge. In this paper, we proposed a hddCRP (hybird distant-dependent ChineseRestaurant Process) based HierARChical tOpic model for news Article cLustering, abbreviated as CHARCOAL. Given a bunch of news articles, the outcome of CHARCOAL is threefold: 1) it aggregates relevant new articles into clusters (i.e., stories); 2) it disentangles the chain links (i.e., storyline) between articles in their describing story; 3) it discerns the topics that each story is assigned (e.g., Malaysia Airlines Flight 370 story belongs to the aircraft accident topic and U.S presidential election stories belong to the politics topic). CHARCOAL completes this task by utilizing a hddCRP as prior, and the entities (e.g., names of persons, organizations, or locations) that appear in news articles as clues. Moveover, the adaptation of nonparametric nature in CHARCOAL makes our model can adaptively learn the appropriate number of stories and topics from news corpus. The experimental analysis and results demonstrate both interpretability and superiority of the proposed approach.

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.

The Laplacian matrix of a graph can be used in many areas of mathematical research and has a physical interpretation in various theories. However, there are a few open issues in the Laplacian graph construction: (i) Selecting the appropriate scale of analysis, (ii) Selecting the appropriate number of neighbors, (iii) Handling multiscale data, and, (iv) Dealing with noise and outliers. In this paper, we propose that the affinity between pairs of samples could be computed using sparse representation with proper constraints. This parameter free setting automatically produces the Laplacian graph, leads to significant reduction in computation cost and robustness to the outliers and noise. We further provide an efficient algorithm to solve the difficult optimization problem based on improvement of existing algorithms. To demonstrate our motivation, we conduct spectral clustering experiments with benchmark methods. Empirical experiments on 9 data sets demonstrate the effectiveness of our method.

A common way of attacking multi-label classification problems is by splitting it into a set of binary classification problems, then solving each problem independently using traditional single-label methods. Nevertheless, by learning classifiers separately the information about the relationship between labels tends to be neglected. Built on recent advances in structure learning in Ising Markov Random Fields (I-MRF), we propose a multi-label classification algorithm that explicitly estimate and incorporate label dependence into the classifiers learning process by means of a sparse convex multi-task learning formulation.Extensive experiments considering several existing multi-label algorithms indicate that the proposed method, while conceptually simple, outperforms the contenders in several datasets and performance metrics. Besides that, the conditional dependence graph encoded in the I-MRF provides a useful information that can be used in a posterior investigation regarding the reasons behind the relationship between labels.

Recent studies have demonstrated the advantages of fusing information from multiple views for various machine learning applications. However, most existing approaches assumed the shared component common to all views and ignored the private components of individual views, which thereby restricts the learning performance. In this paper, we propose a new multi-view, low-rank, and sparse matrix decomposition scheme to seamlessly integrate diverse yet complementary information stemming from multiple views. Unlike previous approaches, our approach decomposes an input data matrix concatenated from multiple views as the sum of low-rank, sparse, and noisy parts. Then a unified optimization framework is established, where the low-rankness and group-structured sparsity constraints are imposed to simultaneously capture the shared and private components in both instance and view levels. A proven optimization algorithm is developed to solve the optimization, yielding the learned augmented representation which is used as features for classification tasks. Extensive experiments conducted on six benchmark image datasets show that our approach enjoys superior performance over the state-of-the-art approaches.

When a transition probability matrix is represented as the product of two stochastic matrices, swapping the factors of the multiplication yields another transition matrix that retains some fundamental characteristics of the original. Since the new matrix can be much smaller than its precursor, replacing the former for the latter can lead to significant savings in terms of computational effort. This strategy, dubbed the "stochastic-factorization trick," can be used to compute the stationary distribution of a Markov chain, to determine the fundamental matrix of an absorbing chain, and to compute a decision policy via dynamic programming or reinforcement learning. In this paper we show that the stochastic-factorization trick can also provide benefits in terms of the number of samples needed to estimate a transition matrix. We introduce a probabilistic interpretation of a stochastic factorization and build on the resulting model to develop an algorithm to compute the factorization directly from data. If the transition matrix can be well approximated by a low-order stochastic factorization, estimating its factors instead of the original matrix reduces significantly the number of parameters to be estimated. Thus, when compared to estimating the transition matrix directly via maximum likelihood, the proposed method is able to compute approximations of roughly the same quality using less data. We illustrate the effectiveness of the proposed algorithm by using it to help a reinforcement learning agent learn how to play the game of blackjack.