Recently, deep learning methods that employ stacked denoising autoencoders (SDAs) have been successfully applied in domain adaptation. Remarkable performance in multi-domain sentiment analysis datasets has been reported, making deep learning a promising approach to domain adaptation problems. SDAs are distinguished by learning robust data representations for recovering the original features that have been artificially corrupted with noise. The idea has been further exploited to marginalize out the random corruptions by a state-of-the-art method called mSDA. In this paper, a deep learning method for domain adaptation called l 2,1 -norm stacked robust autoencoders ( l 2,1 -SRA) is proposed to learn useful representations for domain adaptation tasks. Each layer of l 2,1 -SRA contains two steps: a robust linear reconstruction step which is based on l 2,1 robust regression and a non-linear squashing transformation step. The experimental results demonstrate that the proposed method is very effective in multiple cross domain classification datasets which include Amazon review dataset, spam dataset from ECML/PKDD discovery challenge 2006 and 20 newsgroups dataset.

We propose a probabilistic model for non-exhaustive and overlapping (NEO) bi-clustering. Our goal is to extract a few sub-matrices from the given data matrix, where entries of a sub-matrix are characterized by a specific distribution or parameters. Existing NEO biclustering methods typically require the number of sub-matrices to be extracted, which is essentially difficult to fix a priori. In this paper, we extend the plaid model, known as one of the best NEO bi-clustering algorithms, to allow infinite bi-clustering; NEO bi-clustering without specifying the number of sub-matrices. Our model can represent infinite sub-matrices formally. We develop a MCMC inference without the finite truncation, which potentially addresses all possible numbers of sub-matrices. Experiments quantitatively and qualitatively verify the usefulness of the proposed model. The results reveal that our model can offer more precise and in-depth analysis of sub-matrices.

We discuss necessary and sufficient conditions for an auto-encoder to define a conservative vector field, in which case it is associated with anenergy function akin to the unnormalized log-probability of the data.We show that the conditions for conservativeness are more general than for encoder and decoder weights to be the same ("tied weights''), and thatthey also depend on the form of the hidden unit activation functions.Moreover, we show that contractive training criteria, such as denoising, enforces these conditions locally.Based on these observations, we show how we can use auto-encoders to extract the conservative component of a vector field.

In recent years, matrix completion methods have been successfully applied to solve recommender system applications. Most of them focus on the matrix completion problem in real number domain, and produce continuous prediction values. However, these methods are not appropriate in some occasions where the entries of matrix are discrete values, such as movie ratings prediction, social network relation and interaction prediction, because their continuous outputs are not probabilities and uninterpretable. In this case, an additional step to process the continuous results with either heuristic threshold parameters or complicated mapping is necessary, while it is inefficient and may diverge from the optimal solution. There are a few matrix completion methods working on discrete number domain, however, they are not applicable to sparse and large-scale data set. In this paper, we propose a novel optimal discrete matrix completion model, which is able to learn optimal thresholds automatically and also guarantees an exact low-rank structure of the target matrix. We use stochastic gradient descent algorithm with momentum method to optimize the new objective function and speed up optimization. In the experiments, it is proved that our method can predict discrete values with high accuracy, very close to or even better than these values obtained by carefully tuned thresholds on Movielens and YouTube data sets. Meanwhile, our model is able to handle online data and easy to parallelize.

In this work, we introduce a new generalized nonlinear tensor regression framework called kernel-based multiblock tensor partial least squares (KMTPLS) for predicting a set of dependent tensor blocks from a set of independent tensor blocks through the extraction of a small number of common and discriminative latent components. By considering both common and discriminative features, KMTPLS effectively fuses the information from multiple tensorial data sources and unifies the single and multiblock tensor regression scenarios into one general model. Moreover, in contrast to multilinear model, KMTPLS successfully addresses the nonlinear dependencies between multiple response and predictor tensor blocks by combining kernel machines with joint Tucker decomposition, resulting in a significant performance gain in terms of predictability. An efficient learning algorithm for KMTPLS based on sequentially extracting common and discriminative latent vectors is also presented. Finally, to show the effectiveness and advantages of our approach, we test it on the real-life regression task in computer vision, i.e., reconstruction of human pose from multiview video sequences.

Vanishing Component Analysis (VCA) is a recently proposed prominent work in machine learning. It narrows the gap between tools and computational algebra: the vanishing ideal and its applications to classification problem. In this paper, we will analyze VCA in the kernel view, which is also another important research direction in machine learning. Under a very weak assumption, we provide a different point of view to VCA and make the kernel trick on VCA become possible. We demonstrate that the projection matrix derived by VCA is located in the same space as that of Kernel Principal Component Analysis (KPCA) with a polynomial kernel. Two groups of projections can express each other by linear transformation. Furthermore, we prove that KPCA and VCA have identical discriminative power, provided that the ratio trace criteria is employed as the measurement. We also show that the kernel formulated by the inner products of VCA's projections can be expressed by the KPCA's kernel linearly. Based on the analysis above, we proposed a novel Discriminative Vanishing Component Analysis (DVCA) approach. Experimental results are provided for demonstration.

Spatial centrality, whereby samples closer to the center of a dataset tend to be closer to all other samples, is regarded as one source of hubness. Hubness is well known to degrade k-nearest-neighbor (k-NN) classification. Spatial centrality can be removed by centering, i.e., shifting the origin to the global center of the dataset, in cases where inner product similarity is used. However, when Euclidean distance is used, centering has no effect on spatial centrality because the distance between the samples is the same before and after centering. As described in this paper, we propose a solution for the hubness problem when Euclidean distance is considered. We provide a theoretical explanation to demonstrate how the solution eliminates spatial centrality and reduces hubness. We then present some discussion of the reason the proposed solution works, from a viewpoint of density gradient, which is regarded as the origin of spatial centrality and hubness. We demonstrate that the solution corresponds to flattening the density gradient. Using real-world datasets, we demonstrate that the proposed method improves k-NN classification performance and outperforms an existing hub-reduction method.

The Graph-based Convex Clustering (GCC) method has gained increasing attention recently. The GCC method adopts a fused regularizer to learn the cluster centers and obtains a geometric clusterpath by varying the regularization parameter. One major limitation is that solving the GCC model is computationally expensive. In this paper, we develop efficient graph reduction techniques for the GCC model to eliminate edges, each of which corresponds to two data points from the same cluster, without solving the optimization problem in the GCC method, leading to improved computational efficiency. Specifically, two reduction techniques are proposed according to tree-based and cyclic-graph-based convex clustering methods separately. The proposed reduction techniques are appealing since they only need to scan the data once with negligibly additional cost and they are independent of solvers for the GCC method, making them capable of improving the efficiency of any existing solver. Experiments on both synthetic and real-world datasets show that our methods can largely improve the efficiency of the GCC model.

Multi-task learning (MTL) seeks to improve the generalization performance by sharing information among multiple tasks. Many existing MTL approaches aim to learn the low-rank structure on the weight matrix, which stores the model parameters of all tasks, to achieve task sharing, and as a consequence the trace norm regularization is widely used in the MTL literature. A major limitation of these approaches based on trace norm regularization is that all the singular values of the weight matrix are penalized simultaneously, leading to impaired estimation on recovering the larger singular values in the weight matrix. To address the issue, we propose a Reduced rAnk MUlti-Stage multi-tAsk learning (RAMUSA) method based on the recently proposed capped norms. Different from existing trace-norm-based MTL approaches which minimize the sum of all the singular values, the RAMUSA method uses a capped trace norm regularizer to minimize only the singular values smaller than some threshold. Due to the non-convexity of the capped trace norm, we develop a simple but well guaranteed multi-stage algorithm to learn the weight matrix iteratively. We theoretically prove that the estimation error at each stage in the proposed algorithm shrinks and finally achieves a lower upper-bound as the number of stages becomes large enough. Empirical studies on synthetic and real-world datasets demonstrate the effectiveness of the RAMUSA method in comparison with the state-of-the-art methods.

When there are insufficient labeled samples for training a supervised model, we can adopt active learning to select the most informative samples for human labeling, or transfer learning to transfer knowledge from related labeled data source. Combining transfer learning with active learning has attracted much research interest in recent years. Most existing works follow the setting where the class labels in source domain are the same as the ones in target domain. In this paper, we focus on a more challenging cross-class setting where the class labels are totally different in two domains but related to each other in an intermediary attribute space, which is barely investigated before. We propose a novel and effective method that utilizes the attribute representation as the seed parameters to generate the classification models for classes. And we propose a joint learning framework that takes into account the knowledge from the related classes in source domain, and the information in the target domain. Besides, it is simple to perform uncertainty sampling, a fundamental technique for active learning, based on the framework. We conduct experiments on three benchmark datasets and the results demonstrate the efficacy of the proposed method.