To tackle a challenge in high-dimensional complex features information processing, this study extends the permanent scale Wigner distribution and the single scale$k$-Wigner distribution (kWD, formerly known as$\tau $-Wigner distribution) to a novel multiscale parameterized Wigner distribution. That is the so-called$\mathbf {K}$-Wigner distribution (KWD) which is able to use different scales to extract different types of features at different dimensions. Heisenberg-type uncertainty inequalities of the KWD are established, giving rise to the tightest universal attainable lower bound for all functions on the uncertainty product in time-KWD and Fouier transform-KWD domains, and two versions of attainable lower bounds for complex-valued functions. The obtained results solve an important concern regarding the limit of the KWD’s time-frequency resolution influenced by the parameter matrix. As an application, the derived uncertainty inequalities are applied to estimate the bandwidth in KWD domains. The time-frequency resolution performance of the multiscale KWD, as compared with that of the single scale kWD, is investigated in details. The optimal parameter matrix of the KWD achieving the best performance is then generated, which solves an important concern regarding the KWD’s parameter matrix selection. Examples are also carried out to demonstrate the usefulness and effectiveness of the proposed technique.

Dictionary learning has produced state-of-the-art results in various classification tasks. However, if the training data have a different distribution than the testing data, the learned sparse representation might not be optimal. Recently, several domain-adaptive dictionary learning (DADL) methods and kernels have been proposed and have achieved impressive performance. However, the performance of these single kernel-based methods heavily depends heavily on the choice of the kernel, and the question of how to combine multiple kernel learning (MKL) with the DADL framework has not been well studied. Motivated by these concerns, in this paper, we propose a multi-kernel domain-adaptive sparse representation-based classification (MK-DASRC) and then use it as a criterion to design a multi-kernel sparse representation-based domain-adaptive discriminative projection method, in which the discriminative features of the data in the two domains are simultaneously learned with the dictionary. The purpose of this method is to maximize the between-class sparse reconstruction residuals of data from both domains, and minimize the within-class sparse reconstruction residuals of data in the low-dimensional subspace. Thus, the resulting representations can satisfactorily fit MK-DASRC and simultaneously display discriminability. Extensive experimental results on a series of benchmark databases show that our method performs better than the state-of-the-art methods.

Structural support vector machine (SSVM) is popular in the visual tracking field as it provides a consistent target representation for both learning and detection. However, the spatial distribution of feature is not considered in standard SSVM-based trackers, therefore leading to limited performance. To obtain a robust discriminative classifier, this paper proposes a novel tracking framework that spatially regularizes SSVM, which yields a new spatially regularized SSVM (SRSSVM). We utilize the spatial regularization prior to penalize the learning classifier with the same size as the target region. The location of classifier spatially located far from the center of region is assigned large weight and vice versa. Then, it is introduced into the SSVM model as a regularization factor to learn the robust discriminative model. Furthermore, an optimizing algorithm with dual coordination descent is presented to efficiently solve the SRSSVM tracking model. Our proposed SRSSVM tracking method has low computational cost like the traditional linear SSVM tracker while can significantly improve the robustness of the discriminative classifier. The experimental results on three popular tracking benchmark data sets show that the proposed SRSSVM tracking method performs favorably against the state-of-the-art trackers.

Recently, the hidden Markov model (HMM) with student’s t-mixture model (SMM), called student’s t-HMM (SHMM) for short, has received much attention in unsupervised learning of sequential data. However, the current existing SHMMs fail to take into consideration of the relevant features embedded in local subspaces, thus influencing their performances in clustering. To address the problem, a novel SHMM is proposed by combining the measure of localized feature saliency (LFS) with SMM and utilizing two student’s t-distributions as subcomponents to respectively describe the distributions of useful features and non-salient “features,” with the purpose of accurately modeling the hidden state observation emission distributions of SHMM. Moreover, we exploit the variational Bayesian learning technique to simultaneously estimate the LFS, the number of components and other parameters of the herein proposed SHMM. Experimental results on both synthetic and real data sets demonstrate the improved robustness, effectiveness, and accuracy of our model.