Tensor factorization is a fundamental framework to analyze high-order interactions in data. Despite the success of the existing methods, the valuable temporal information are severely underused. The timestamps of the interactions are either ignored or discretized into crude steps. The recent work although formulates event-tensors to keep the timestamps in factorization and can capture mutual excitation effects among the interaction events, it overlooks another important type of temporal influence, inhibition. In addition, it uses a local window to exclude all the long-term dependencies. To overcome these limitations, we propose a self-modulating nonparametric Bayesian factorization model. We use the latent factors to construct mutually governed, general random point processes, which can capture various short-term/long-term, excitation/inhibition effects, so as to encode the complex temporal dependencies into factor representations. In addition, our model couples with a latent Gaussian process to estimate and fuse nonlinear yet static relationships between the entities. For efficient inference, we derive a fully decomposed model evidence lower bound to dispense with the huge kernel matrix and costly summations inside the rate and log rate functions. We then develop an efficient stochastic optimization algorithm. We show the advantage of our method in four real-world applications.

Recurrent Neural Networks (RNNs) are powerful sequence modeling tools. However, when dealing with high dimensional inputs, the training of RNNs becomes computational expensive due to the large number of model parameters. This hinders RNNs from solving many important computer vision tasks, such as Action Recognition in Videos and Image Captioning. To overcome this problem, we propose a compact and flexible structure, namely Block-Term tensor decomposition, which greatly reduces the parameters of RNNs and improves their training efficiency. Compared with alternative low-rank approximations, such as tensortrain RNN (TT-RNN), our method, Block-Term RNN (BT-RNN), is not only more concise (when using the same rank), but also able to attain a better approximation to the original RNNs with much fewer parameters. On three challenging tasks, including Action Recognition in Videos, Image Captioning and Image Generation, BT-RNN outperforms TT-RNN and the standard RNN in terms of both prediction accuracy and convergence rate. Specifically, BT-LSTM utilizes 17,388 times fewer parameters than the standard LSTM to achieve an accuracy improvement over 15.6% in the Action Recognition task on the UCF11 dataset.

Multiway data analysis deals with multiway arrays, i.e., tensors, and the goal is twofold: predicting missing entries by modeling the interactions between array elements and discovering hidden patterns, such as clusters or communities in each mode. Despite the success of existing tensor factorization approaches, they are either unable to capture nonlinear interactions, or computationally expensive to handle massive data. In addition, most of the existing methods lack a principled way to discover latent clusters, which is important for better understanding of the data. To address these issues, we propose a scalable nonparametric tensor decomposition model. It employs Dirichlet process mixture (DPM) prior to model the latent clusters; it uses local Gaussian processes (GPs) to capture nonlinear relationships and to improve scalability. An efficient online variational Bayes Expectation-Maximization algorithm is proposed to learn the model. Experiments on both synthetic and real-world data show that the proposed model is able to discover latent clusters with higher prediction accuracy than competitive methods. Furthermore, the proposed model obtains significantly better predictive performance than the state-of-the-art large scale tensor decomposition algorithm, GigaTensor, on two large datasets with billions of entries.

Image colorization adds color to grayscale images. It not only increases the visual appeal of grayscale images, but also enriches the information conveyed by scientific images that lack color information. We develop a new image colorization method, epitomic image colorization, which automatically transfers color from the reference color image to the target grayscale image by a robust feature matching scheme using a new feature representation, namely the heterogeneous feature epitome. As a generative model, heterogeneous feature epitome is a condensed representation of image appearance which is employed for measuring the dissimilarity between reference patches and target patches in a way robust to noise in the reference image. We build a Markov Random Field (MRF) model with the learned heterogeneous feature epitome from the reference image, and inference in the MRF model achieves robust feature matching for transferring color. Our method renders better colorization results than the current state-of-the-art automatic colorization methods in our experiments.

Pair wise clustering methods, including the popular graph cut based approaches such as normalized cut, partition the data space into clusters by the pair wise affinity between data points. The success of pair wise clustering largely depends on the pair wise affinity function defined over data points coming from different clusters. Interpreting the pair wise affinity in a probabilistic framework, we build the relationship between pair wise clustering and unsupervised classification by learning the soft Nearest Neighbor (NN) classifier from unlabeled data, and search for the optimal partition of the data points by minimizing the generalization error of the learned classifier associated with the data partitions. Modeling the underlying distribution of the data by non-parametric kernel density estimation, the asymptotic generalization error of the unsupervised soft NN classification involves only the pair wise affinity between data points. Moreover, such error rate reduces to the well-known kernel form of graph cut in case of uniform data distribution, which provides another understanding of the kernel similarity used in Laplacian Eigenmaps [1] which also assumes uniform distribution. By minimizing the generalization error bound, we propose a new clustering algorithm. Our algorithm efficiently partition the data by inference in a pair wise MRF model. Experimental results demonstrate the effectiveness of our method.

Exemplar-based clustering methods have been extensively shown to be effective in many clustering problems. They adaptively determine the number of clusters and hold the appealing advantage of not requiring the estimation of latent parameters, which is otherwise difficult in case of complicated parametric model and high dimensionality of the data. However, modeling arbitrary underlying distribution of the data is still difficult for existing exemplar-based clustering methods. We present Pairwise Exemplar Clustering (PEC) to alleviate this problem by modeling the underlying cluster distributions more accurately with non-parametric kernel density estimation. Interpreting the clusters as classes from a supervised learning perspective, we search for an optimal partition of the data that balances two quantities: 1 the misclassification rate of the data partition for separating the clusters; 2 the sum of within-cluster dissimilarities for controlling the cluster size. The broadly used kernel form of cut turns out to be a special case of our formulation. Moreover, we optimize the corresponding objective function by a new efficient algorithm for message computation in a pairwise MRF. Experimental results on synthetic and real data demonstrate the effectiveness of our method.

This paper explores the possibility of acquiring inverse li ght transport directly. The current strategy of obtaining an inverse light transport ma trix involves two steps: First, acquire the forward light transport matrix (f-LTM) and then calculate the inverse of the f-LTM. Both steps of the strategy requires considerable computational power. In addition to computational cost, the measurement error incurred at the first step inevitably propagates to or potentially gets amplified in the matrix inv ersion step. In this paper, we propose a sensing strategy that acquires the inverse light transport matrix (i-LTM) directly, without reconstructing the f-LTM. Our direct strategy reduces both computational error and cost of acquiring i-LTM. For that, we propose a compressive inverse theory. Following the compressible property of i-LTM, a reconstruction condition for i-LTM is introduced. This new framework implies a trade-off between two factors: condition numbers of submatrices of f-LTM and the isometry constant of the illumination pattern. Our direct i-LTM reconstruction method is then demonstrated with a 2nd-bounce separation experiment on an M-shaped panel scene. Finally by quantitatively comparing our method with the existing two-stage approach, our method shows higher accuracy with lower complexity. The proofs of main theorem/lemma are contained in the supplementary material. The compressive inverse theory is general and potentially useful for wider application.

Due to the lack of explicit spatial consideration, existing epitome model may fail for image recognition and target detection, which directly motivates us to propose the so-called spatialized epitome in this paper. Extended from the original graphical model of epitome, the spatialized epitome provides a general framework to integrate both appearance and spatial arrangement of patches in the image to achieve a more precise likelihood representation for image(s) and eliminate ambiguities in image reconstruction and recognition. From the extended graphical model of epitome, an EM learning procedure is derived under the framework of variational approximation. The learning procedure can generate an optimized summary of the image appearance with spatial distribution of the similar patches. From the spatialized epitome, we present a principled way of inferring the probability of a new input image under the learnt model and thereby enabling image recognition and target detection. We show how the incorporation of spatial information enhances the epitome's ability for discrimination on several vision tasks, e.g., misalignment/cross-pose face recognition and vehicle detection with a few training samples.