Shujian Yu

Multi-view non-negative matrix factorization by patch alignment framework with view consistency

Multi-view non-negative matrix factorization (NMF) has been developed to learn the latent representation from multi-view non-negative data in recent years. To make the representation more meaningful, previous works mainly exploit either the consensus information or the complementary information from different views. However, the latent local geometric structure of each view is always ignored. In this paper, we develop a novel multi-view NMF by patch alignment framework with view consistency. Different from previous works, we take the local geometric structure of each view into consideration, and penalize the disagreement of different views at the same time. More specifically, given a data in each view, we construct a local patch utilizing locally linear embedding to preserve its local geometrical structure, and obtain the global representation under the whole alignment strategy. Meanwhile, for different views, we make the representations of views to approximate the latent representation shared by different views via considering the view consistency. We adopt the correntropy-induced metric to measure the reconstruction error and employ the half-quadratic technique to solve the optimization problem. The experimental results demonstrate the proposed method can achieve satisfactory performance compared with single-view methods and other existing multi-view NMF methods.

Kernel Learning for Dynamic Texture Synthesis

Dynamic textures (DTs) that represent moving scenes such as flames, smoke, and waves, exhibit fixed dynamics within a period of time and have been successfully modeled using linear dynamic systems (LDS). In this paper, we show that the widely used LDS model can be approximated using a principal component regression (PCR) model with the main advantage of simplicity. Furthermore, to capture the nonlinearity of training frames, we extend traditional PCR to its kernelized version and introduce kernel principal component regression (KPCR) to model and synthesize DTs. To ensure algorithm stability, we remove the standard state model and directly apply the quantized kernel least mean squares algorithm from signal processing domain to approximate the performance achieved with KPCR. We term this improvement kernel adaptive dynamic texture synthesis (KADTS), which also has the benefits of computational and memory efficiency. These advantages make KADTS ideally suited for real-world applications, since the majority of electronic devices, including cell phones and laptops, suffer from limited memory and real-time constraints. We demonstrate, via both theoretical and experimental analyses, the connections between DT synthesis using KPCR and KADTS with a regularization network theory. We also show the superiority of our proposed algorithms for DT synthesis compared with other dynamic system-based benchmarks. MATLAB code is available from our project homepage http://bmal.hust.edu.cn/project/dts.html.

Kernel normalized mixed-norm algorithm for system identification

Kernel methods provide an efficient nonparametric model to produce adaptive nonlinear filtering (ANF) algorithms. However, in practical applications, standard squared error based kernel methods suffer from two main issues: (1) a constant step size is used, which degrades the algorithm performance in non-stationary environment, and (2) additive noises are assumed to follow Gaussian distribution, while in practice the noises are generally non-Gaussian and follow other statistical distributions. To address these two issues simultaneously, this paper proposes a novel kernel normalized mixed-norm (KNMN) algorithm. Compared to the standard squared error based kernel methods, the KNMN algorithm extends the linear mixed-norm adaptive filtering algorithms to Reproducing Kernel Hilbert Space (RKHS) and introduces a normalized step size as well as adaptive mixing parameter. We also conduct the mean square convergence analysis and demonstrate the desirable performance of the KNMN algorithm in solving the system identification problem.

Dynamic texture modeling and synthesis using multi-kernel Gaussian process dynamic model

Dynamic texture (DT) widely exists in various social video media. Therefore, DT modeling and synthesis plays an important role in social media analyzing and processing. In this paper, we propose a Bayesian-based nonlinear dynamic texture modeling method for dynamic texture synthesis. To capture the non-stationary distribution of DT, we utilize the Gaussian process latent variable model for dimensional reduction. Furthermore, we design a multi-kernel dynamic system for the latent dynamic behavior modeling. In our model, we do not make strong assumption on the nonlinear function. Instead, our model automatically constructs a suitable nonlinear kernel for dynamic modeling and therefore is capable of fitting various types of dynamics. We evaluate the effectiveness our methods on the DynTex database and compared with representative DT synthesis method. Experimental results show that our method can achieve synthesis results with higher visual quality. HighlightsA multi-kernel based Gaussian process dynamic model is proposed for dynamic texture modeling.We design a two-step optimization algorithm to learn the multi-kernel based Gaussian process dynamic model.We design a dynamic texture synthesis algorithm based on mean prediction for the proposed multi-kernel based Gaussian process dynamic model.

STFT-like time frequency representations of nonstationary signal with arbitrary sampling schemes

Spectrograms provide an effective way of time-frequency representation (TFR). Among these, short-time Fourier transform (STFT) based spectrograms are widely used for various applications. However, STFT spectrogram and its revised versions suffer from two main issues: (1) there is a trade-off between time resolution and frequency resolution and (2) almost all the existing TFR methods, including STFT spectrogram, are not designed to handle arbitrary nonuniformly sampled data. To address these two issues, short-time iterative adaptive approach (ST-IAA) was recently proposed as a data-dependent adaptive spectral estimation method that can provide much enhanced TFR performance. In this paper, inspired by the ST-IAA method, we present an alternative approach, namely short-time sparse learning via iterative minimization (ST-SLIM), which can provide sparser and slightly better TFR performance than its ST-IAA counterpart. Moreover, in order to extend the applicability of ST-IAA to signals in the missing data case, we also propose a short-time missing-data iterative adaptive approach (ST-MIAA) which can retrieve the missing data effectively and outperform ST-IAA and ST-SLIM in the missing data case. We will demonstrate via simulation results the superiority of our proposed algorithms in terms of resolution, sidelobe suppression and applicability to signals with arbitrary sampling patterns.

Single image rain streaks removal based on self-learning and structured sparse representation

Rain streaks removal from single image is a challenging problem for image processing. This paper proposed a novel algorithm for rain streaks removal to single image based on a self-learning framework and structured sparse representation. More precisely, our algorithm firstly segments and categorizes input image into “rain streaks” regions and “non-rain geometric” regions via texture analysis. Meanwhile, we also decompose input image into high-frequency (HF) and low-frequency (LF) parts with bilateral filtering. Followed that, we introduced our newly proposed structured dictionary learning to decompose HF part into “rain texture” details and “non-rain geometric” details, where patches for training rain and non-rain sub-dictionaries are automatically selected from “rain streaks” and “non-rain geometric” regions. Finally, we combine LF part with non-rain geometric details to get rain-streaks-removal image. Experiments demonstrate the superiority of our proposed algorithm.

Multi-view manifold learning with locality alignment

Abstract Manifold learning aims to discover the low dimensional space where the input high dimensional data are embedded by preserving the geometric structure. Unfortunately, almost all the existing manifold learning methods were proposed under single view scenario, and they cannot be straightforwardly applied to multiple feature sets. Although concatenating multiple views into a single feature provides a plausible solution, it remains a question on how to better explore the independence and interdependence of different views while conducting manifold learning. In this paper, we propose a multi-view manifold learning with locality alignment (MVML-LA) framework to learn a common yet discriminative low-dimensional latent space that contain sufficient information of original inputs. Both supervised algorithm (S-MVML-LA) and unsupervised algorithm (U-MVML-LA) are developed. Experiments on benchmark real-world datasets demonstrate the superiority of our proposed S-MVML-LA and U-MVML-LA over existing state-of-the-art methods.

Robust linear discriminant analysis with a Laplacian assumption on projection distribution

Linear discriminant analysis (LDA) is typically carried out using Fishers method, which relies heavily on the estimation of sample mean vectors and covariance matrices. However, Fisher LDA is vulnerable to outliers as it happens to other multivariate statistical methods. In this paper, we analyzed the optimal discriminant design based on the criterion of minimizing total misclassification rate, assuming that the projected samples follow Laplacian distribution. The corresponding optimization objective can be approximated as a linear programming problem. We illustrated the relations of our proposed discriminant to Fisher LDA and minimax probability machine (MPM) from the perspective of projection-pursuit. Experiments on 6 real world benchmark dataset from UCI repository validate the effectiveness of our method.

Generalized Kernel Normalized Mixed-Norm Algorithm: Analysis and Simulations

This paper is a continuation and extension of our previous research where kernel normalized mixed-norm KNMN algorithm, a combination of the kernel trick with the mixed-norm strategy, was proposed to demonstrate superior performance for system identification under non-Gaussian environment. Meanwhile, we also introduced a naive adaptive mixing parameter AMP updating mechanism to make KNMN more robust under nonstationary scenarios. The main contributions of this paper are threefold: firstly, the