In nonnegative matrix factorization (NMF), minimum-volume-constrained NMF is a widely used framework for identifying the solution of NMF by making basis vectors as similar as possible. This typically induces sparsity in the coefficient matrix, with each row containing zero entries. Consequently, minimum-volume-constrained NMF may fail for highly mixed data, where such sparsity does not hold. Moreover, the estimated basis vectors in minimum-volume-constrained NMF may be difficult to interpret as they may be mixtures of the ground truth basis vectors. To address these limitations, in this paper we propose a new NMF framework, called maximum-volume-constrained NMF, which makes the basis vectors as distinct as possible. We further establish an identifiability theorem for maximum-volume-constrained NMF and provide an algorithm to estimate it. Experimental results demonstrate the effectiveness of the proposed method.

Weakly-supervised Temporal Action Localization (WTAL) following a localization-by-classification paradigm has achieved significant results, yet still grapples with confounding arising from ambiguous snippets. Previous works have attempted to distinguish these ambiguous snippets from action snippets without investigating the underlying causes of their formation, thus failing to effectively eliminate the bias on both action-context and action-content. In this paper, we revisit WTAL from the perspective of structural causal model to identify the true origins of confounding, and propose an efficient dual-confounding eliminating framework to alleviate these biases. Specifically, we construct a Substituted Confounder Set (SCS) to eliminate the confounding bias on action-context by leveraging the modal disparity between RGB and FLOW. Then, a Multi-level Consistency Mining (MCM) method is designed to mitigate the confounding bias on action-content by utilizing the consistency between discriminative snippets and corresponding proposals at both the feature and label levels. Notably, SCS and MCM could be seamlessly integrated into any two-stream models without additional parameters by Expectation-Maximization (EM) algorithm. Extensive experiments on two challenging benchmarks including THUMOS14 and ActivityNet-1.2 demonstrate the superior performance of our method.

With video-level labels, weakly supervised temporal action localization (WTAL) applies a localization-by-classification paradigm to detect and classify the action in untrimmed videos. Due to the characteristic of classification, class-specific background snippets are inevitably mis-activated to improve the discriminability of the classifier in WTAL. To alleviate the disturbance of background, existing methods try to enlarge the discrepancy between action and background through modeling background snippets with pseudo-snippet-level annotations, which largely rely on artificial hypotheticals. Distinct from the previous works, we present an adversarial learning strategy to break the limitation of mining pseudo background snippets. Concretely, the background classification loss forces the whole video to be regarded as the background by a background gradient reinforcement strategy, confusing the recognition model. Reversely, the foreground(action) loss guides the model to focus on action snippets under such conditions. As a result, competition between the two classification losses drives the model to boost its ability for action modeling. Simultaneously, a novel temporal enhancement network is designed to facilitate the model to construct temporal relation of affinity snippets based on the proposed strategy, for further improving the performance of action localization. Finally, extensive experiments conducted on THUMOS14 and ActivityNet1.2 demonstrate the effectiveness of the proposed method.

Weakly supervised temporal action localization (WTAL) aims to detect action instances from untrimmed videos. It may cause two problems, namely action incompleteness and background disturbance, due to only video-level class labels given. In this paper, we propose a context driven network with Bayes to alleviate the two problems, in which an attention module is used to predict coarse probability for each snippet, and then a Bayesian refinement module is designed to refine the coarse results by capturing the relationship between context snippets. Finally, the coarse and refined probabilities are combined as the inputs of the classifier for training. Quantitative and qualitative studies on two benchmark datasets, i.e., THUMOS’14 and ActivityNet 1.2, demonstrate that the proposed approach exceeds state-of-the-art methods.

In pattern classification, polynomial classifiers are well-studied methods as they are capable of generating complex decision surfaces. Unfortunately, the use of multivariate polynomials is limited to kernels as in support-vector machines, because polynomials quickly become impractical for high-dimensional problems. In this paper, we effectively overcome the curse of dimensionality by employing the tensor train (TT) format to represent a polynomial classifier. Based on the structure of TTs, two learning algorithms are proposed, which involve solving different optimization problems of low computational complexity. Furthermore, we show how both regularization to prevent overfitting and parallelization, which enables the use of large training sets, are incorporated into these methods. The efficiency and efficacy of our tensor-based polynomial classifier are then demonstrated on the two popular data sets U.S. Postal Service and Modified NIST.

The periodic steady-state analysis of nonlinear systems has always been an important topic in electronic design automation (EDA). For autonomous systems, the mainstream approaches, like shooting Newton and harmonic balance, are difficult to employ since the period itself becomes an unknown. This paper presents an innovative state-space homotopy-based Poincaré-Lindstedt method, with a novel Padé approximation of the stretched time axis, that effectively overcomes this hurdle. Examples demonstrate the excellent efficiency and scalability of the proposed approach.

Tensors are a multi-linear generalization of matrices to their d-way counterparts, and are receiving intense interest recently due to their natural representation of high-dimensional data and the availability of fast tensor decomposition algorithms. Given the input-output data of a nonlinear system/circuit, this paper presents a non-linear model identification and simulation framework built on top of Volterra series and its seamless integration with tensor arithmetic. By exploiting partially-symmetric polyadic decompositions of sparse Toeplitz tensors, the proposed framework permits a pleasantly scalable way to incorporate high-order Volterra kernels. Such an approach largely eludes the curse of dimensionality and allows computationally fast modeling and simulation beyond weakly non-linear systems. The black-box nature of the model also hides structural information of the system/circuit and encapsulates it in terms of compact tensors. Numerical examples are given to verify the efficacy, efficiency and generality of this tensor-based modeling and simulation framework.